Some exact solutions for nonlinear desorptive diffusion

The existence is pointed out of a class of exact solutions for desorption which can be obtained by means of a simple inversion method. This method is related to that proposed by Philip (1960) for sorption and redistribution and it consists of the inversion of the diffusivity equation of Matano (1933) and Bruce and Klute (1952). Some of the exact solutions can be useful in the study of problems encountered in flow in porous media.

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Résumé On démontre l'existence d'une classe de solutions exactes pour le problème de désorption qui peuvent être obtenues par une méthode d'inversion. Cette méthode correspond à la méthode proposée par Philip (1960) pour sorption et rédistribution, et elle consiste de l'inversion de l'équation pour la diffusivité de Matano (1933) et de Bruce et Klute (1952). Quelques unes de ces solutions peuvent être utiles dans l'étude du mouvement de fluides en milieux poreux.

     

Der Sättigungsdruck von NbBr5 und Tal5

Sublimation Pressure of NbBr₅, NbI₅, and TaI₅ The sublimation pressure of NbBr₅, NbI₅ and TaI₅ has been determined by a spectralphotometric method: . The vapour pressure of NbI_5,1 is equal to log \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm P}\,{\rm = }\, - \frac{{4653}}{{\rm T}}\, + \,5.43 $\end{document}. All the pressure are given in atm. The melting point of NbI₅ is 673 ± 1 K.     

Quadratische Räume unendlicher Dimension und partielle Isomorphismen

Ohne Zusammenfassung     

Regularity of Backward Stochastic Volterra Integral Equations in Hilbert Spaces

This article investigates backward stochastic Volterra integral equations in Hilbert spaces. The existence and uniqueness of their adapted solutions is reviewed. We establish the regularity of the adapted solutions to such equations by means of Malliavin calculus. For an application, we study an optimal control problem for a stochastic Volterra integral equation driven by a Hilbert space-valued fractional Brownian motion. A Pontryagin-type maximum principle is formulated for the problem and an example is presented.     

Remarks on the <Emphasis Type="Italic">k</Emphasis>-error linear complexity of <Emphasis Type="Italic">p</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>-periodic sequences

Recently the first author presented exact formulas for the number of 2 ⁿ -periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity and upper and lower bounds for the expected k-error linear complexity, k ≥ 2, of a random 2 ⁿ -periodic binary sequence. A crucial role for the analysis played the Chan–Games algorithm. We use a more sophisticated generalization of the Chan–Games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the 1-error linear complexity for p ⁿ -periodic sequences over prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of p ⁿ -periodic sequences over .      

High temperature liquid chromatography hyphenated with ESI-MS and ICP-MS detection for the structural characterization and quantification of halogen containing drug metabolites

In this paper we describe the hyphenation of high temperature liquid chromatography with ICP-MS and ESI-MS for the characterization of halogen containing drug metabolites. The use of temperature gradients up to 200°C enabled the separation of metabolites with low organic modifier content. This specific property allowed the use of detection methods that suffer from (significant) changes in analyte response factors as a function of the organic modifier content such as ICP-MS. Metabolites of two kinase inhibitors (SB-203580-Iodo and MAPK inhibitor VIII) produced by bacterial cytochrome P450 BM3 mutants and human liver microsomes were identified based on high resolution MS(n) data. Quantification was done using their normalized and elemental specific response in the ICP-MS. The importance of these kinds of quantification strategies is stressed by the observation that the difference of the position of one oxygen atom in a structure can greatly affect its response in ESI-MS and UV detection.     

Physical Properties of Superbulky Lanthanide Metallocenes: Synthesis and Extraordinary Luminescence of [EuII(CpBIG)2] (CpBIG=(4‐nBu‐C6H4)5‐Cyclopentadienyl)

The superbulky deca‐aryleuropocene [Eu(Cp^BIG)₂], Cp^BIG=(4‐nBu‐C₆H₄)₅‐cyclopentadienyl, was prepared by reaction of [Eu(dmat)₂(thf)₂], DMAT=2‐Me₂N‐α‐Me₃Si‐benzyl, with two equivalents of Cp^BIGH. Recrystallizyation from cold hexane gave the product with a surprisingly bright and efficient orange emission (45 % quantum yield). The crystal structure is isomorphic to those of [M(Cp^BIG)₂] (M=Sm, Yb, Ca, Ba) and shows the typical distortions that arise from Cp^BIG???Cp^BIG attraction as well as excessively large displacement parameter for the heavy Eu atom (U_eq=0.075). In order to gain information on the true oxidation state of the central metal in superbulky metallocenes [M(Cp^BIG)₂] (M=Sm, Eu, Yb), several physical analyses have been applied. Temperature‐dependent magnetic susceptibility data of [Yb(Cp^BIG)₂] show diamagnetism, indicating stable divalent ytterbium. Temperature‐dependent ¹⁵¹Eu Mössbauer effect spectroscopic examination of [Eu(Cp^BIG)₂] was examined over the temperature range 93–215 K and the hyperfine and dynamical properties of the Eu^II species are discussed in detail. The mean square amplitude of vibration of the Eu atom as a function of temperature was determined and compared to the value extracted from the single‐crystal X‐ray data at 203 K. The large difference in these two values was ascribed to the presence of static disorder and/or the presence of low‐frequency torsional and librational modes in [Eu(Cp^BIG)₂]. X‐ray absorbance near edge spectroscopy (XANES) showed that all three [Ln(Cp^BIG)₂] (Ln=Sm, Eu, Yb) compounds are divalent. The XANES white‐line spectra are at 8.3, 7.3, and 7.8 eV, for Sm, Eu, and Yb, respectively, lower than the Ln₂O₃ standards. No XANES temperature dependence was found from room temperature to 100 K. XANES also showed that the [Ln(Cp^BIG)₂] complexes had less trivalent impurity than a [EuI₂(thf)_x] standard. The complex [Eu(Cp^BIG)₂] shows already at room temperature strong orange photoluminescence (quantum yield: 45 %): excitation at 412 nm (24270 cm^?1) gives a symmetrical single band in the emission spectrum at 606 nm (ν_max=16495 cm^?1, FWHM: 2090 cm^?1, Stokes‐shift: 2140 cm^?1), which is assigned to a 4f⁶5d¹→4f⁷ transition of Eu^II. These remarkable values compare well to those for Eu^II‐doped ionic host lattices and are likely caused by the rigidity of the [Eu(Cp^BIG)₂] complex. Sharp emission signals, typical for Eu^III, are not visible.     

Hypersingularities in three-dimensional crack configurations in composite laminates

Three-dimensional crack configurations in composite laminates are studied by means of the Scaled Boundary Finite Element Method (SBFEM) particularly regarding stress singularities and their associated deformation modes. The SBFEM is an efficient semi-analytical method that permits solving linear elastic mechanical problems. Only the boundary needs to be discretized while the problem is considered analytically in the direction of the dimensionless radial coordinate pointing from the scaling center to the boundary . An important advantage is that it requires no additional effort for the characterization of existing stress singularities. The situation of two meeting inter-fiber cracks is investigated in detail, considering different materials and fiber / crack orientations. It is shown that in three-dimensional crack configurations in composite laminates so-called hypersingularities can occur, i.e. stress singularities which are even stronger than the classical crack singularity. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)