Improved error estimates for mixed finite-element approximations for nonlinear parabolic equations: The discrete-time case

This article treats mixed finite-element methods for second-order quasilinear parabolic equations. A fully discrete scheme is presented and L₂-error estimates are established. The convergence of both the function value and the flux is demonstrated. In a previous paper, Part I the author introduced powerful numerical methods for dealing with parabolic problems. The technique used here is an extension of the continuous-time results for the discrete-time case. © 1994 John Wiley & Sons, Inc.     

Isolierung und Nachweis basischer Arzneimittel in der Toxikologie

Zusammenfassung Zu den schwierigsten Aufgaben der toxikologischen Analyse gehört die rasche und sichere Isolierung und Identifizierung organischer Basen aus dem Untersuchungsmaterial. Mit einem entsprechenden Extraktionsverfahren oder durch Fällung mit Tetraphenylborat in einem systematischen Analysengang können sehr günstige Ausbeuten erzielt werden. Die Reinigung der Rohextrakte oder -fällungen erfolgt prinzipiell mittels Dünnschichtchromatographie. Aus den Tetraphenylboratkomplexen werden dabei auf den Kieselgelschichten die reinen Basen in Freiheit gesetzt. An Hand derR _f- Wert-Tabellen ist eine Identifizierung möglich, wobei Substanzen mit gleichemR _f- Wert durch fraktionierte Extraktion bei verschiedenem p_H getrennt werden können. Eine weitere Identifizierung kann mit Hilfe der UV-Spektren erfolgen.

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Summary Among the most difficult problems of toxicological analysis are the rapid and reliable isolation and identification of organic bases from the material under examination. Very satisfactory yields can be obtained by means of a suitable extraction procedure or through precipitation with tetraphenyl borate in a systematic scheme of analysis. The purification of the crude extracts or precipitates is accomplished fundamentally by thin layer chromotography. The pure bases are liberated on the silica layers from the tetraphenyl borate complexes. An identification is possible through reference toR _f- tables; substances with likeR _f value can be separated by fractional extraction at different p_H values. A further identification can be made with the aid of UV spectra.

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Résumé L'isolement rapide et sûr des bases organiques dans une substance à l'étude et leur identification représentent l'un des problèmes les plus difficiles de l'analyse toxicologique. On peut atteindre des rendements très satisfaisants avec un procédé d'extraction analogue ou par précipitation par le tétraphénylborure dans un processus d'analyse systématique. La purification de l'extrait brut ou des produits de précipitation s'effectue principalement au moyen de la chromatographie en couche mince. Les bases pures sont libérées des complexes au tétraphénylborure en opérant sur couches en gel de silice. On peut faire une identification en se servant des valeurs desR _f figurant dans les tables, ce qui permet de séparer les substances de mêmeR _f par extraction fractionnée à des p_H différents. Une identification plus poussée peut avoir lieu à l'aide des spectres UV.

     

Some existence results for quasilinear elliptic equations in a finite cylinder

We study the existence of solutionsu in the finite cylinderS _a=(?a, a)×ω of the quasilinear elliptic equation $$\sum\limits_{i,j = 1}^n {a_{i,j} (x)\partial _{i,j} u + f(x,u,\nabla u) = 0} $$ with Dirichlet boundary condition on flat parts of σS _a and Neumann condition on the curved parts. In this paper, we focus on the technicality caused by the “corners” ofS _a. We prove the existence of such solutions provided that suitable sub and super solutions are known and under the condition that the coefficientsa _1,i,i#1 vanish on the corners. We also prove a more general result in ?².     

The use of Omega Chrome Fast Blue 2G in the microdetermination of some metals

Summary Omega Chrome Fast Blue 2G has been found to be a suitable indicator for the detection of the equivalence point of calcium, magnesium and manganese in the presence of cadmium, nickel, and aluminium, when they are masked by the addition of cyanide or triethanolamine. It is also a suitable indicator for the back titration of aluminium using calcium or magnesium as a back titrant.This dye has also been found to be a suitable reagent for the colorimetric determination of calcium, magnesium, manganese and thorium.     

Characterization of the new Bi∼6.2Cu∼6.2O8(PO4)5 oxyphosphate; a disordered compound containing 2- and 3-O(Bi, Cu)4 tetrahedra—wide polycationic ribbons

The present work is dedicated to the XRD, ED and HREM characterization of a new bismuth copper oxyphosphate Bi_∼6.2Cu_∼6.2O₈(PO₄)₅ (a=11.599(2)Å, , c=37.541(5)Å, R₁=0.0755, Rw₂₌0.174, G.S Pn2₁a). The relatively long size of its c parameter is due to the arrangement along this direction of two kinds of ribbon-like polycations formed by edge sharing O(Bi, Cu)₄ tetrahedra. The existence of such cations is characterized by the b∼5.2 Å value intrinsic to the ribbons structure and commonly found in bismuth oxyphosphate materials. In the title compound, 2-tetrahedra wide [Bi_∼2.4Cu_∼3.6O₄]^6.4+ and 3-tetrahedra wide [Bi_∼5Cu_∼3O₆]⁹⁺ ribbons are isolated by phosphate groups and alternate along c. The interstitial site created between two different sizes ribbons is occupied by Cu²⁺ cations disordered over several close crystallographic sites. The mixed Bi³⁺/Cu²⁺ nature of certain edge-of-ribbons positions induces a disorder over several configurations of the phosphate groups. The concerned oxygen atoms form the environment of the disordered interstitial Cu²⁺ cations which occupy tunnels formed by the phosphate anions. The high-resolution electron microscope study enables a precise correlation between the observed images and the refined crystal structure, evidencing the polycations visualization. Furthermore, this material being the second example of partially disordered compound similar chemical system, some topological rules can be deduced. The b-axis doubling was observed by ED and HREM and is assigned to the ordering of interstitial Cu²⁺ within tunnels cations. A partial intra-tunnel ordering was also observed.     

Etude par RMN du 13C d'un heterocycle derive du dibora-2,4 diazaro-1,3 benzene et du borazine correspondant

¹³C NMR spectra and complete assignment by means of coupled spectra and off resonance experiments, are reported for a new kind of organoboron heterocycle and the related borazine (o-CH₃C₆H₄NBCH₃)₃; π-charge densities, obtained from LCAO-MO Hückel calculations, are in reasonable agreement with experimental chemical shifts for the former compound.     

Kinetics of calcium phosphate reduction by carbon

A fundamental study was made on the reduction of calcium phosphate by carbon. The mechanism of reduction was presented on applying different additions. Both silica and alumina increased the extent of reduction but with variable rates. The activation energies were calculated on the basis of first-order reactions. The phases formed during reduction were investigated by X-ray analysis.     

Emulsion liquid membrane extraction of fission products promoted by polyvalent and organic acids

Emulsion liquid membranes (ELM) with di-2-ethylhexylphosphoric acid in n-alkane, and dipicrylamine and cobalt(III) dicarbollide in nitrobenzene stabilized in double emulsions by SPAN 80/85 surfactant were used for preconcentration of radioactive fission products (¹³⁷Cs,⁹⁰Sr,¹³⁹Ce, and¹⁵²Eu) from slightly acidic nitrate solutions. The efficiency of sulfuric, phosphotungstic and silicotungstic acids as stripping agents, and picric acid as the bulky anion additive was investigated. A group separation of the fission products is possible by the ELM technique and can be considered for their removal from waste water solutions.