A new differential calculus on a complex banach space with application to variational problems of quantum theory

It is proved that a semilinear function on a complex banach space is not differentiable according to the usual definition of differentiability in the calculus on banach spaces. It is shown that this result makes the calculus largely inapplicable to the solution of variational problems of quantum mechanics. A new concept of differentiability called semi-differentiability is defined. This generalizes the standard concept of differentiability in a banach space and the resulting calculus is particularly suitable for optimizing real-valued functions on a complex banach space and is directly applicable to the solution of quantum mechanical variational problems. As an example of such application a rigorous proof of a generalized version of a result due to Sharma (1969) is given. In the course of this work a new concept of prelinearity is defined and some standard results in the calculus on banach spaces are extended and generalized into more powerful ones applicable directly to prelinear functions and hence yielding the standard results for linear functions as particular cases.     

Multiplicity results for periodic solutions of second order ODEs with asymmetric nonlinearities

We prove various results on the existence and multiplicity of harmonic and subharmonic solutions to the second order nonautonomous equation , as or where is a smooth function defined on a open interval The hypotheses we assume on the nonlinearity allow us to cover the case (or ) and having superlinear growth at infinity, as well as the case (or ) and having a singularity in (respectively in ). Applications are given also to situations like (including the so-called ``jumping nonlinearities'). Our results are connected to the periodic Ambrosetti - Prodi problem and related problems arising from the Lazer - McKenna suspension bridges model.

     

The effect of acidity behaviour of Y zeolites on the catalytic degradation of polyethylene

Thermogravimetric (TGA) and differential scanning calorimetric (DSC) analyses were used to investigate the effect of the acidity behaviour of Y zeolites on the catalytic degradation of polyethylene (PE). The acidity behaviour of these zeolites was modified by ion exchange treatments. Two Y zeolites with similar Si/Al atomic ratios were subjected to an ion exchange treatment using NaNO₃ for H-form (HY) and NH₄NO₃ for Na-form (NaY). The activity and the deactivation behaviour of the Y zeolites were determined in the samples by TGA measurements, using a polymer/catalyst ratio of 9:1. The sample residues obtained after an isothermic TGA, were analysed by DSC, in order to evaluate the crystallinity of each mixture. The HY zeolite, which has the strongest acidity, reduced the onset temperature resulting in more rapid degradation of the polymer. It is shown that the ion exchange treatment over Y zeolites enhances the selective catalytic degradation of polymer in detriment of the rapid deactivation.     

Determination of the performance of glass electrodes in aqueous solutions in the physiological ph range and at the physiological sodium ion concentration

A method for testing glass electrodes in the physiological pH range (6.4–7.6) and at the physiological sodium ion concentration (0.15 mol l^-1), based on indirect comparison of potentials with the hydrogen gas electrode, is developed according to a scheme described earlier. The hydrogen ion sensitivity and the sodium ion error of a glass electrode can be determined with three different aqueous solutions of amine buffers and their hydrochlorides; two of these have different pH values and one also contains a sodium salt (at the higher pH value). A cell without a liquid/liquid junction, containing silver/silver chloride reference electrodes, is used at 37° C. The accuracy of both determinations is ±0.2 mV (±0.003 pH). The results for some commercial glass electrodes tested with this method are presented.     

On the self-aggregation and fluorescence quenching aptitude of surfactant ionic liquids

The aggregation behavior in aqueous solution of a number of ionic liquids was investigated at ambient conditions by using three techniques: fluorescence, interfacial tension, and (1)H NMR spectroscopy. For the first time, the fluorescence quenching effect has been used for the determination of critical micelle concentrations. This study focuses on the following ionic liquids: [Cnmpy]Cl (1-alkyl-3-methylpyridinium chlorides) with different linear alkyl chain lengths (n=4, 10, 12, 14, 16, or 18), [C12mpip]Br (1-dodecyl-1-methylpiperidinium bromide), [C12mpy]Br (1-dodecyl-3-methylpyridinium bromide), and [C12mpyrr]Br (1-dodecyl-1-methylpyrrolidinium bromide). Both the influence of the alkyl side-chain length and the type of ring in the cation (head) on the CMC were investigated. A comparison of the self-aggregation behavior of ionic liquids based on 1-alkyl-3-methylpyridinium and 1-alkyl-3-methylpyridinium cations is provided. It was observed that 1-alkyl-3-methylpyridinium ionic liquids could be used as quenchers for some fluorescence probes (fluorophores). As a consequence, a simple and convenient method to probe early evidence of aggregate formation was established.     

Emerging trends in metal oxide electrocatalysis: Bifunctional oxygen catalysis,synergies and new insights from in situ studies

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Ionic Liquids in Polyethylene Glycol Aqueous Solutions: Salting-in and Salting-out Effects

Changes of the fluid phase behaviour of polyethylene glycol (PEG) aqueous solutions – viz. critical solution temperature shifts at atmospheric pressure – were produced by the addition of different ionic liquids, namely 1-ethyl-3-methylimidazolium ethyl sulfate and 1-alkyl-3-methylimidazolium chloride (alkyl = ethyl to decyl). The addition of ionic liquids with long alkyl chains improves the solubility of PEG in water (salting-in effect), whereas the impact of short-chain ionic liquids is usually the contrary (salting-out effect). The results are interpreted taking into account the kosmotropic (water-structuring) or chaotropic (water-structure-breaking) nature of ionic liquids, as compared to other inorganic salts.