Some Inequalities for Superharmonic Functions on Graphs

An inequality for superharmonic functions on Riemannian manifolds due to S.Y. Cheng and S-T. Yau is adapted to the setting of graphs. A number of corollaries are discussed, including a Harnack inequality for graphs having at most quadratic growth and satisfying a certain connectedness condition.     

Extracting metabolite ions out of a matrix background by combined mass defect,neutral loss and isotope filtration

Mass defect, neutral loss and isotope filtration techniques were applied to electrospray ionization mass spectrometry (ESI‐MS) data obtained for in vivo and in vitro samples of drug metabolism studies. A combination of these post‐acquisition processing techniques was shown to be more powerful than the use of one of these tools alone for the detection in complex matrices of metabolites of candidate drugs with a characteristic isotope pattern (e.g. containing bromine, chlorine, or a high proportion of radiolabeled drug (¹²C/¹⁴C)) or characteristic neutral losses. In combination with ‘all‐in‐one’ data acquisition this methodology is able to perform software‐driven constant neutral loss scanning for an unlimited number of mass differences at any time after analysis. Highly selective MS chromatograms were obtained with excellent correlation with their corresponding radiochromatograms. Copyright © 2009 John Wiley & Sons, Ltd.     

Indépendance algébrique sur les T-modules

We study the transcendence degree (of the values at algebraic points) of the coordinate functions of a given one parameter subgroup on a simple g dimensional T-module. In such a situation, we obtain a lower bound for this transcendence degree depending on g and on the growth order of the parameter subgroup. As a particular case, one gets the finite characteristic analogue of a result of Siegel on the algebraic independence for the values of the classical Bessel function. Résumé. Nous obtenons une minoration du degré de transcendance d'un ensemble de valeurs en des points algébriques des fonctions coordonnées d'un sous-groupe à un paramètre d'un T-module simple, en fonction de l'ordre de croissance de ces dernières et de la dimension du T-module. Un cas particulier de ce résultat permet d'obtenir en caractéristique finie un analogue d'un résultat de Siegel sur l'indépendance algébrique des valeurs de la fonction de Bessel usuelle.     

Oxidative degradation of nitrogen-containing organic compounds: vaccum-ultraviolet (VUV) photolysis of aqueous solutions of 3-amino 5-methylisoxazole

The oxidative degradation of 3-amino 5-methyl isoxazole initiated by the VUV photolysis of water at 172 nm has been studied. Mineralization of CO₂, H₂O, NO ₃ ^– and NH ₄ ⁺ is more efficient when reductive conditions (argon saturated solutions) are favoured. Formation of compounds which cannot be completely oxidised to CO₂ is observed. Experiments performed under strictly oxidative conditions show higher yields of these inert compounds and, hence, incomplete mineralization. Cyanide was formed in concentrations lower than 5×10^–5 mol/l. In alkaline aqueous solutions, cyanide is completely transformed into CO ₃ ^2– , NH ₄ ⁺ and NO ₃ ^– during the irradiation time needed to mineralize the isoxazole. Therefore, cyanide does not present a potential risk for the use of the VUV photolysis for isoxazole degradation. Similarly, organic nitrogen is converted into both, NO ₃ ^– and NH ₄ ⁺ . The relative concentrations of the two ions depend on total irradiation time, oxygen saturation and reactor geometry. A sequence of reactions is proposed and discussed.Dedicated to Professor Dr. Dieter Klockow on the occasion of his 60th birthday     

Growth by laser ablation of Ti-based oxide films with different valency states

x La_2/3+yTiO_3-δ perovskite (with δ≤0.5) were deposited by the laser ablation technique from Li_0.33La_0.56TiO₃ targets. Their growth onto MgO substrateswas studied as a function of the oxygen pressure. For films grown in vacuum (10^-6 mbar), a La_0.63TiO_2.5 composition was obtained, meaning that Ti³⁺ alone is present in the films, while Li ions are not incorporated under these conditions. This material shows good electric conductivity (ρ=500 mΩ cm). By contrast, insulating films with a Li_0.1La_0.70TiO₃ composition corresponding to the Ti⁴⁺ species were obtained at high oxygen pressures (>0.05 mbar). For all conditions, textured films were grown with different orientations depending on the temperature and the oxygen pressure. Received: 10 September 1997/Accepted: 24 November 1997     

Stationary axisymmetric solutions of three-dimensional Einstein gravity

Einstein theory in three space-time dimensions is studied in the stationary, rotationally symmetric regime. Explicit interior solutions for various types of matter sources are found and their properties discussed.