Fondements d'une théorie générale de la courbure linéaire

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Ueber Spectralapparate und Spectralanalyse

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Effect of the temperature on the physical properties of pure 1-propyl 3-methylimidazolium bis(trifluoromethylsulfonyl)imide and characterization of its binary mixtures with alcohols

In this paper, physical properties of a high purity sample of the ionic liquid 1-propyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [PMim][NTf₂], and its binary mixtures with methanol, ethanol, 1-propanol, and 2-propanol were measured at atmospheric pressure. The temperature dependence of density, refractive index and speed of sound (293.15 to 343.15) K and dynamic viscosity (298.15 to 343.15) K were studied at atmospheric pressure by conventional techniques for the pure ionic liquid. For its mixtures with alcohols, density, speed of sound, and refractive index were measured at T = 298.15 K over the whole composition range. The thermal expansion coefficient of the [PMim][NTf₂] was calculated from the experimental results using an empirical equation, and values of the excess molar volume, excess refractive index, and excess molar isentropic compressibility for the binary systems at the above mentioned temperature, were calculated and fitted to the Redlich–Kister equation. The heat capacity of the pure ionic liquid at T = 298.15 K was determined using DSC.     

Analysis of Schrödinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case

In this article, we consider the problem of optimal approximation of eigenfunctions of Schrödinger operators with isolated inverse square potentials and of solutions to equations involving such operators. It is known in this situation that the finite element method performs poorly with standard meshes. We construct an alternative class of graded meshes, and prove and numerically test optimal approximation results for the finite element method using these meshes. Our numerical tests are in good agreement with our theoretical results.Copyright © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1130–1151, 2014     

Quantitative monitoring of an activated sludge reactor using on-line UV-visible and near-infrared spectroscopy

The performance of an activated sludge reactor can be significantly enhanced through use of continuous and real-time process-state monitoring, which avoids the need to sample for off-line analysis and to use chemicals. Despite the complexity associated with wastewater treatment systems, spectroscopic methods coupled with chemometric tools have been shown to be powerful tools for bioprocess monitoring and control. Once implemented and optimized, these methods are fast, nondestructive, user friendly, and most importantly, they can be implemented in situ, permitting rapid inference of the process state at any moment. In this work, UV-visible and NIR spectroscopy were used to monitor an activated sludge reactor using in situ immersion probes connected to the respective analyzers by optical fibers. During the monitoring period, disturbances to the biological system were induced to test the ability of each spectroscopic method to detect the changes in the system. Calibration models based on partial least squares (PLS) regression were developed for three key process parameters, namely chemical oxygen demand (COD), nitrate concentration (N-NO₃⁻), and total suspended solids (TSS). For NIR, the best results were achieved for TSS, with a relative error of 14.1% and a correlation coefficient of 0.91. The UV-visible technique gave similar results for the three parameters: an error of ~25% and correlation coefficients of ~0.82 for COD and TSS and 0.87 for N-NO₃⁻. The results obtained demonstrate that both techniques are suitable for consideration as alternative methods for monitoring and controlling wastewater treatment processes, presenting clear advantages when compared with the reference methods for wastewater treatment process qualification.     

Osmotic coefficients of binary mixtures of four ionic liquids with ethanol or water at T = (313.15 and 333.15) K

Measurements of osmotic coefficients of BmimCl (1-butyl-3-methylimidazolium chloride) and HmimCl (1-hexyl-3-methylimidazolium chloride) with ethanol and EmimEtSO₄ (1-ethyl-3-methylimidazolium ethylsulfate) and EmpyEtSO₄ (1-ethyl-3-methylpyridinium ethylsulfate) with water at T = (313.15 and 333.15) K are reported in this work. Vapour pressure and activity results of the studied binary systems are obtained from experimental measurements. The results for the osmotic coefficients are correlated using the extended Pitzer model modified by Archer and the modified NRTL (MNRTL) model. The standard deviations obtained with both models are also given. The parameters obtained with the extended Pitzer model of Archer are used to calculate the mean molal activity coefficients.