On the spectral norm of algebraic numbers

In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $.     

Effects of UV photon irradiation on SiOx (0 < x < 2) structural properties

Thin films of a-SiO_x (0 < x < 2) were prepared by reactive r.f. magnetron sputtering from a polycrystalline-silicon target in an Ar/O₂ gas mixture. The oxygen partial pressure in the deposition chamber was varied so as to obtain films with different values of x. The plasma was monitored, during depositions, by optical emission spectroscopy (OES) system. Energy dispersive X-ray (EDX) measurements and infra-red (IR) spectroscopy were used to study the compositional and structural properties of the deposited layers.Structural modifications of SiO_x thin films have been induced by UV photons’ bombardment (wavelength of 248 nm) using a pulsed laser. IR spectroscopy and X-ray photoemission spectroscopy (XPS) were used to investigate the structural changes as a function of x value and incident energy. SiO_x phase separation by spinodal decomposition was revealed. The IR peak position shifted towards high wavenumber values when the laser energy is increased. Values corresponding to the SiO₂ material (only Si⁴⁺) have been found for laser irradiated samples, independently on the original x value. The phase separation process has a threshold energy that is in agreement with theoretical values calculated for the dissociation energy of the investigated material.For high values of the laser energy, crystalline silicon embedded in oxygen-rich silicon oxide was revealed by Raman spectroscopy.     

Gravimetric determination of zirconium with a new azopyrazolone derivative

3-Methyl-5-oxo-1-phenyl-2-pyrazolin-4-ylazo-2'-(6',8'-naphthalenedisulfonic acid) (disodium salt) is proposed as a new reagent for the gravimetric determination of zirconium. The precipitate formed at pH 1–1.5 can be weighed directly and there are few interferences.     

The interaction between TEOS and some polyols

Hybrid organic-inorganic materials, silica – polyols (ethylene-glycol – EG; 1,2 propane diol – 1,2PG; 1,3 propane diol – 1,3PG and glycerol – GL), were prepared by a sol-gel process starting from tetraethylorthosilicate (TEOS) and polyols, in acid catalysis. The resulting materials were studied by thermal analysis (in air and nitrogen), FTIR and solid state ²⁹Si-NMR spectroscopy. These techniques evidenced the presence of polyols in the silica matrix both hydrogen bounded and chemically bounded in the silica network. The thermal analysis proves to be the most appropriate technique to evidence the organic chains linked in the matrix network and to follow the thermal evolution of the gels to the SiO₂ matrix.     

Detection of aniline at boron-doped diamond electrodes with cathodic stripping voltammetry

Boron-doped diamond (BDD) electrodes were used to investigate the possibility of detecting aniline by linear-sweep cathodic stripping voltammetry. It was found that the dimeric species (p-aminodiphenylamine and benzidine) formed by anodic oxidation of aniline during the accumulation period are involved in electrochemically reversible redox processes and, in acidic media, the shape of the stripping voltammetric response is suitable for aniline detection in the micromolar concentration range. The low background current of conductive diamond is an advantage compared to other electrode materials and allows a detection limit of 1 μM. Weak adsorption properties and the extreme electrochemical stability are additional advantages of BDD and it was found that, even after long-time measurements, the electrode surface can regain its initial activity by an anodic polarization in the potential region of water decomposition.     

Superacid cyclization of esters of some bishomoisoprenoid acids

It is shown that on the superacid cyclization of esters of bishomobicyclogeranylgeranic and E,E-bishomofarnesic acids fully cyclized hydroxyesters are formed in good yield, while on the interaction of esters of 6-hydroxy- and 6-acyloxy-15-bishomobicyclogeranylgeranic acids with a superacid no carbocyclization takes place.     

Host-guest chemistry of the chromium-wheel complex [Cr8F8(tBuCO2)16]: prediction of inclusion capabilities by using an electrostatic potential distribution determined by modeling synchrotron X-ray structure factors at 16 K

The structure and detailed electron density distribution (EDD) of the large octanuclear chromium-wheel host complex [Cr8F8(tBuCO2)16] (1) has been determined from synchrotron X-ray structure factors collected at 16(5) K. The complex has a central cavity with a minimum entry distance between carbon atoms of the pivalate methyl groups (pivalic acid = tBuCO2H) of 4.027(4) A on one side of the molecule and 7.273(4) A on the other. The screened side of the molecule can be "opened" by rotation of methyl groups to create a strained host structure, which is compensated for by improved host-guest and host-solvent interaction. The EDD of the 272-atom complex (1144 e-) was determined by multipole modeling based on the experimental structure factors. 3d orbital populations on the Cr atoms and topological analysis of the EDD show that the covalent part of the metal-ligand interactions consists mainly of sigma donation from the ligands, but that overall the interactions are predominantly electrostatic. The electrostatic potential (EP) has been calculated from the experimental EDD. Knowledge of the geometry of the naked complex 1 as well as the EP in the central cavity of this molecule allows us to deduce which characteristic properties guest molecules must have to be accepted into the void. To probe these predictions, a series of complexes of 1 with different guest inclusions were synthesized (2 = 1 + N,N'-dimethylformamide (DMF), 3 = 1 + N,N'-dimethylacetamide (DMA), 4 = 1 + DMA + DMF, 5 = 1 + 2CH3CN), and their structures were examined by using X-ray diffraction data measured at 120(1) K. Results of these studies indicate that in the crystalline state, the optimal guest molecule should be linear and possess a permanent dipole. Attempts to crystallize the host complex with cations incorporated into the cavity were fruitless, although electrospray ionization mass spectrometry showed that a [1 + potassium]+ entity pre-exists in solution and can be transferred intact into the gas phase.     

Polyelectrolyte capsules made of two biocompatible natural polymers

In this study the influence of the experimental conditions on the obtention of polyelectrolyte multilayer capsules was investigated. Two ways of the simple coacervation method was used to obtain spherical capsules involving chitosan and hyaluronan, chitosan being inside the particle covered by a hyaluronan layer to increase the biocompatibility. The ¹H-NMR spectroscopy confirmed a polyelectrolyte complex formation and the optical microscopy shows that the complexed capsules have good sphericity with average diameters ranging from 590 at 1550 μm in the experimental conditions adopted. One can observe that in the acid medium the complexed capsules are much stable than the chitosan beads. The structures described provide a starting point for the design and fabrication of complexed capsules made of two biocompatible natural polymers with potential applicability in medical or pharmaceutical applications. Few diffusion experiments demonstrated that the complexed layer controls the diffusion of dextran included in the chitosan inner domain.     

Bioaccumulation of thorium and uranyl ions on Saccharomyces cerevisiae

The efficiency of the yeast suspension ofSaccharomyces cerevisiae was studied in the decontamination of radioactive residual waste waters and in the biological behavior of the levuric mass. The effect of reaction time on the amino acid content in the supernatant and on the concentration of radioactive ions was also investigated. The reaction of yeast with the toxic agent showed that the living matter behaves differently from the chemical components of the cell. The yeast had the tendency to aggregate in the presence of radioactive ions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Multiple rate-determining steps for nonideal and fractal kinetics

We show that the kinetic model of a single rate-determining step in a reaction mechanism can be extended to systems with multiple overall reactions for which the elementary reactions obey nonideal or fractal kinetics. The following assumptions are necessary: (1) The system studied is either closed or open, but no constraints exist preventing the evolution toward equilibrium. (2) Elementary reactions occur in pairs of forward and backward steps. (3) The kinetics of the elementary steps are either nonideal or fractal and are compatible with equilibrium thermodynamics. (4) The number of reaction routes is identical with the number of rate-determining steps. If these hypotheses are valid, then the overall reaction rates can be explicitly evaluated: they have a form similar to the kinetic equations for the elementary reactions and the apparent reaction orders and fractal coefficients can be expressed analytically in terms of the kinetic parameters of the elementary reactions. We derive a set of relationships which connect the equilibrium constants of the reaction routes, the corresponding overall rate coefficients, and the stoichiometric numbers of the rate-determining steps. We also derive a set of generalized Boreskov relations among the apparent activation energies of the forward and backward overall processes, the corresponding reaction enthalpies, and the stoichiometric coefficients of the rate-determining steps. If the elementary reactions obey fractal kinetics, the same is true for the rate-determining steps. The fractal exponents of the forward and backward overall reactions are linear combinations of the fractal exponents of the fractal elementary reactions. Similar to the theory of single rate-determining steps, our approach can be used for selecting suitable reaction mechanisms from experimental data.