Markov partition in non-hyperbolic interval dynamics

We considerC ² unimodal mapsf such that all periodic points are hyperbolic, the critical point is non-degenerated and non-recurrent, and the Julia set does not contain intervals. We construct a Markov partition for a big part of the Julia set. Then we use it to estimate the limit capacity and Hausdorff dimension of the Julia set.Partially supported by CNPq, S.C.T.-Brazil     

Biosorption of Chromium(III) by Biomass of Seaweed Sargassum sp. in a Fixed-Bed Column

This work aimed at modeling chromium biosorption using the biomass of seaweed Sargassum sp. in a fixed-bed column. The mathematical model used was obtained from the mass balance of the component in the liquid phase and in the biosorbent material. The effects of both axial dispersion in the column and the resistance to mass transfer in the solid were considered for the solution of the partial differential equations of the model, using the Galerkin method on finite elements. To represent the equilibrium data of the batch system the Langmuir isotherm were used. The chromium ion adsorption capacity of the seaweed Sargassum sp., at a temperature of 30°C and pH 3.5, was 2.61 mmol/g. The model performance was evaluated from experimental data obtained at 30°C for flow rates of 2, 6 and 8 mL/min. The parameters of the model, mass transfer and axial dispersion coefficients, were adjusted from these experimental data. The model proved adequate to describe chromium biosorption dynamics in fixed-bed columns.     

Entropy and ergodic probability for differentiable dynamical systems and their bundle extensions

We answer a problem of Liao [S.T. Liao, Standard systems of differential equations and obstruction sets—from linearity to perturbations, in: System Researches, Proceedings Dedicated to the 85th Anniversary of Qian Xue-Sen, Zhejiang Education Press, Hangzhou, China, 1996, pp. 279-290 (in Chinese)]: A C¹ vector field or a C¹ diffeomorphism on an n-dimensional manifold has equal entropy with that of its bundle extensions. We also prove that each ergodic probability with simple Lyapunov spectrum has at most n²n! covering probabilities on each bundle extension.     

Gamma-radiolysis of chiral terpenes: α-(−)pinene and α-(+)pinene

The terpenes α-(+)-pinene, and α-(−)pinene have been radiolyzed at radiation doses of 150, 300 and 600 kGy. The radiolyzed samples have been analyzed by FT-IR spectroscopy and polarimetry. Both α-(+)-, α-(−)-pinenes show a linear trend to radioracemization as a function of the radiation dose administered ≈2.5·10⁻³ [α]_D/kGy. The solvent fractionation and the liquid chromatographic analysis (HPLC) of the radiolyzed samples shows that both α-pinene enantiomers produce ocimene and dipentene together with minor quantities of other products and a resin. The kinetics of α-pinene decomposition under radiolytic conditions can be described by a pseudofirst order rate constant k∼5.3·10⁻⁷s⁻¹ while the radiation chemical yield for the same reaction has a G = 5.0 molecules/100 eV, so that about 30% of the original α-pinene is converted into other products at 600 kGy.     

The effect of gamma-irradiation of anthracite coal and oil bitumen

Anthracite coal and oil bitumen were submitted to γ-radiation at a total dose of 1 MGy and the radiation-processed samples were studied by FT-IR spectroscopy, thermogravimetric analysis (TGA) and differential thermal analysis (DTA). The coal samples were studied also by TGA coupled with FT-IR spectroscopy of the evolved gases. Thermal analysis has revealed a completely different behavior of the radiolyzed samples in comparison to the unirradiated samples. Both for coal and bitumen significantly less volatile fraction was released during the TGA and in both cases a significant increase in the amount of carbon coke produced at 800-900 °C was observed. The radiation processed bitumen increased significantly its ethyl acetate insolubles content. These results were interpreted in terms of extensive crosslinking and coalification of the samples under the action of γ-radiation. The results of this study have been applied to the carbonization process of terrestrial sedimentary organic matter which is commonly attributed to the action of heat flux from the depth of the Earth but which may be also due to the action of natural radiation. Other application of the results of the present study is to the complex organic matter present on the surfaces of comets and meteorites. This complex matter was formed by exposure of simple precursors to a field of high energy radiation for millions or billions of years and is consequently transformed into coal-like and bitumen-like matter. The same arguments apply to the carbon grains present in the interstellar and circumstellar medium. This revised version was published online in July 2006 with corrections to the Cover Date.     

Synthesis of Ultra-Fine Columbite Powder MgNb2O6 by the Polymerized Complex Method

Pure MgNb₂O₆ powders with high specific surface area and high crystallinity have been successfully synthesized by the Polymerized Complex (PC) Method. A solution of water, citric acid, ethylene glycol and niobium and magnesium ions, was polymerized at 130°C by the water elimination and was calcined at 400°C for 2 h. The precursor formed was calcined at temperatures from 700°C to 1000°C in air to obtain the columbite phase. Thermal analysis, Raman spectroscopy, x-ray diffraction, adsorption/desorption hysteresis and scanning electron microscopy were used to investigate the polymer decomposition and the columbite phase evolution. No evidence for phase separation of crystalline MgCO₃ and Nb₂O₅ in Raman spectra and x-ray diffraction pattern as distinct intermediates were found, and the MgNb₂O₆ probably is formed through a single-step decomposition of oxycarbonate intermediate, as other double oxide synthesized by the PC Method, as indicated by the thermal decomposition of the precursor.     

Effect of conformational changes on a one-electron reduction process: evidence of a one-electron P-P bond formation in a bis(phosphinine)

EPR spectra show that one-electron reduction of bis(3-phenyl-6,6-(trimethylsilyl)phosphinine-2-yl)dimethylsilane (1) on an alkali mirror leads to a radical anion that is localized on a single phosphinine ring, whereas the radical anion formed from the same reaction in the presence of cryptand or from an electron transfer with sodium naphthalenide is delocalized on the two phosphinine rings. Density functional theory (DFT) calculations show that in the last species the unpaired electron is mainly confined in a loose P-P bond (3.479 A), which results from the overlap of two phosphorus p orbitals. In contrast, as attested by X-ray spectroscopy, the P-P distance in neutral 1 is large (5.8 A). As shown by crystal structure analysis, addition of a second electron leads to the formation of a classical P-P single bond (P-P 2.389 A). Spectral modifications induced by the presence of cryptand or by a change in the reaction temperature are consistent with the formation of a tight ion pair that stabilizes the radical structure localized on a single phosphinine ring. It is suggested that the structure of this pair hinders internal rotation around the C-Si bonds and prevents 1 from adopting a conformation that shortens the intramolecular P-P distance. The ability of the phosphinine radical anion to reversibly form weak P-P bonds with neutral phosphinines in the absence of steric hindrance is confirmed by EPR spectra obtained for 2,6-bis(trimethylsilyl)-3-phenylphosphinine (2). Moreover, as shown by NMR spectroscopy, in this system, which contains only one phosphinine ring, further reduction leads to an intermolecular reaction with the formation of a classical P-P bond.     

Contribution of cyclodextrins in the development of different pharmaceutical formulations of a new matrix metalloproteinase inhibitor

Ro 28-2653 is a new synthetic inhibitor of matrix metalloproteinases. The ability of these enzymes to degrade various components of the extracellular matrix seems to play a major role in tumors progression and is potentially effective against bronchial remodeling in asthma and BPCO. Ro 28-2653 is very poorly soluble in water. This low solubility estimated at about 0.56 μg/ml in water at 25 °C gives rise to difficulties in pharmaceutical formulation of oral, injectable or nebulizable solutions. The purpose of our study is to prepare and to characterize inclusion complexes between Ro 28-2653 and cyclodextrins and to investigate the biopharmaceutical repercussion of the inclusion of the active substance. The complex formation was investigated by phase solubility studies. ¹H-NMR spectroscopy and molecular modeling studies were carried out to elucidate the structure of the inclusion complex between Ro 28-2653 and cyclodextrin. Oral, intravenous and nebulizable solutions of Ro 28-2653 were developed with cyclodextrin. The in vivo studies were performed on healthy sheep for the pharmacokinetic evaluation of the oral and intravenous formulations while the nebulization of the complex solution was studied by using an asthma model in mouse.