Integral stable manifolds in Banach spaces

We establish the existence of smooth integral stable manifoldsfor sufficiently small perturbations of nonuniform exponentialdichotomies in Banach spaces. We also consider the case of anonautonomous dynamics given by a sequence of C¹ maps. The optimalsmoothness of the manifolds is obtained at the same time astheir existence, using a convenient lemma of Henry. Furthermore,we obtain not only the exponential decay of the dynamics alongthe stable manifolds, but also of its derivative. In addition,we give a characterization of the stable manifolds in termsof the maximal exponential growth rate that is allowed, we discusshow the manifolds vary with the perturbations, and we discusstheir equivariance with respect to a sequence of linear operators.     

A quantum mechanical strategy to investigate the structure of liquids: the cases of acetonitrile, formamide, and their mixture

A computational strategy based on quantum mechanical (QM) calculations and continuum solvation models is used to investigate the structure of liquids (either neat liquids or mixtures). The strategy is based on the comparison of calculated and experimental spectroscopic properties (IR-Raman vibrational frequencies and Raman intensities). In particular, neat formamide, neat acetonitrile, and their equimolar mixture are studied comparing isolated and solvated clusters of different nature and size. In all cases, the study seems to indicate that liquids, even when strongly associated, can be effectively modeled in terms of a shell-like system in which clusters of strongly interacting molecules (the microenvironments) are solvated by a polarizable macroenvironment represented by the rest of the molecules. Only taking into proper account both these effects can a correct picture of the liquid structure be achieved.     

Solvation in pure liquids: what can be learned from the use of pairs of indicators?

The solvation of six solvatochromic probes in a large number of solvents (33-68) was examined at 25 degrees C. The probes employed were the following: 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenyl pyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr(2), respectively. Of these, MePMBr is a novel compound. They can be grouped in three pairs, each with similar pK(a) in water but with different molecular properties, for example, lipophilicity and dipole moment. These pairs are formed by RB and MePM; QB and MePMBr; WB and MePMBr(2), respectively. Theoretical calculations were carried out in order to calculate their physicochemical properties including bond lengths, dihedral angles, dipole moments, and wavelength of absorption of the intramolecular charge-transfer band in four solvents, water, methanol, acetone, and DMSO, respectively. The data calculated were in excellent agreement with available experimental data, for example, bond length and dihedral angles. This gives credence to the use of the calculated properties in explaining the solvatochromic behaviors observed. The dependence of an empirical solvent polarity scale E(T)(probe) in kcal/mol on the physicochemical properties of the solvent (acidity, basicity, and dipolarity/polarizability) and those of the probes (pK(a), and dipole moment) was analyzed by using known multiparameter solvation equations. For each pair of probes, values of E(T)(probe) (for example, E(T)(MePM) versus E(T)(RB)) were found to be linearly correlated with correlation coefficients, r, between 0.9548 and 0.9860. For the mercyanine series, the values of E(T)(probe) also correlated linearly, with (r) of 0.9772 (MePMBr versus MePM) and 0.9919 (MePMBr(2) versus MePM). The response of each pair of probes (of similar pK(a)) to solvent acidity is the same, provided that solute-solvent hydrogen-bonding is not seriously affected by steric crowding (as in case of RB). We show, for the first time, that the response to solvent dipolarity/polarizability is linearly correlated to the dipole moment of the probes. The successive introduction of bromine atoms in MePM (to give MePMBr, then MePMBr(2)) leads to the following linear decrease: pK(a) in water, length of the phenolate oxygen-carbon bond, length of the central ethylenic bond, susceptibility to solvent acidity, and susceptibility to solvent dipolarity/polarizability. Thus studying the solvation of probes whose molecular structures are varied systematically produces a wealth of information on the effect of solute structure on its solvation. The results of solvation of the present probes were employed in order to test the goodness of fit of two independent sets of solvent solvatochromic parameters.     

Sequential Production of Amylolytic and Lipolytic Enzymes by Bacterium Strain Isolated from Petroleum Contaminated Soil

Amylases and lipases are highly demanded industrial enzymes in various sectors such as food, pharmaceuticals, textiles, and detergents. Amylases are of ubiquitous occurrence and hold the maximum market share of enzyme sales. Lipases are the most versatile biocatalyst and bring about a range of bioconversion reactions such as hydrolysis, inter-esterification, esterification, alcoholysis, acidolysis, and aminolysis. The objective of this work was to study the feasibility for amylolitic and lipolytic production using a bacterium strain isolated from petroleum contaminated soil in the same submerged fermentation. This was a sequential process based on starch and vegetable oils feedstocks. Run were performed in batchwise using 2% starch supplemented with suitable nutrients and different vegetable oils as a lipase inducers. Fermentation conditions were pH 5.0; 30 degrees C, and stirred speed (200 rpm). Maxima activities for amyloglucosidase and lipase were, respectively, 0.18 and 1,150 U/ml. These results showed a promising methodology to obtain both enzymes using industrial waste resources containing vegetable oils.     

High pressure solubility data of carbon dioxide in (tri-iso-butyl(methyl)phosphonium tosylate + water) systems

Ionic liquids are attracting great attention nowadays due to their interesting properties which make them useful in a broad range of applications including reaction media or separation/capture of environmentally hazardous gases such as carbon dioxide. In many cases, for practical and/or economical reasons, the use of aqueous solutions of ILs would be preferable to their use as pure compounds.In this work, high pressure equilibrium data for the {carbon dioxide (CO₂) + tri-iso-butyl(methyl)phosphonium tosylate [iBu₃MeP][TOS] + water system were measured at temperatures ranging from (276 to 370) K and pressures up to 100 MPa. Measurements were performed using a high-pressure cell with a sapphire window that allows direct observation of the liquid–vapour transition. Mixtures with different IL concentrations were studied in order to check the influence of the amount of IL on the solubility of CO₂ in the aqueous mixture.The results show that the presence of IL enhances the solubility of CO₂ in the (IL + water) system revealing a salting-in effect of the IL on the solubility of CO₂. The appearance of a three phase region was observed for IL concentrations higher than 4 mol% of IL in water when working at pressures between 4 and 8 MPa and temperatures between (280 and 305) K. In this range, the upper limit of the VLE region observed is shown to increase with the temperature being almost independent of the IL initial concentration in the mixture.