Uber die hemisphärische Funktion

Ohne Zusammenfassung     

Finite element approximation of a problem with a nonlinear Newton boundary condition

The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition. The existence and uniqueness of the solution of the continuous problem is established with the aid of the monotone operator theory. The main attention is paid to the investigation of the finite element approximation using numerical integration for the computation of nonlinear boundary integrals. The solvability of the discrete finite element problem is proved and the convergence of the approximate solutions to the exact one is analysed. Received April 15, 1996 / Revised version received November 22, 1996     

Kinetics of the bulk polymerization of dioxolane in the presence of water

The polymerization of dioxolane initiated by the ～Si^⊕HSO ion pair is greatly influenced by water which changes the overall polymerization rate. Particularly great changes are brought about at certain higher conversions (whose values are also a function of an initial concentration of water). The polymerization practically stops at these conversions and the system appears to be close to a monomer—polymer equilibrium. It is shown that the equation V_overall = f([H₂O]), which describes the dependence of the overall rate of polymerization on the concentration of water and which was originally derived for the polymerization of trioxane, holds also for the polymerization of dioxolane. The decrease of water concentration during the polymerization was measured and the observed equilibrium was shown to be a kinetic phenomenon.     

Multivariate control charts: Control charts for calibration curves

The proposed multivariate control charts for p-dimensional vectors are an extension of the conventional control charts for one variable. The controlling quantity is the Mahalanobis distance of vector x from the central value vector x..: D=(x-x..)^T-1.(x-x..), where is the covariance matrix estimate. The quantity D has Hotelling's T² distribution. A PC program was set up for the automatic graphical construction of such charts. The program draws the sequential chart of the quantity D as well as the position of the vectors x in the p dimensional control ellipsoid in the axes of the principal components. In this way a control chart was developed for the calibration curve in the photometric determination of Fe³⁺ with sulfosalicylic acid. Vector x was formed by absorbance values for the calibration curve points (p=5). The chart can assist in detection of even small disturbances of the calibration curve.     

Reaction and transport effects in the heterogeneous systems for lean gas purification

Sorption of hydrogen chloride gas by active soda and that of hydrogen sulfide gas by calcium oxide are explored by experiment as promising means of removing these detrimental contaminants from fuel gas: active Na₂CO₃ was prepared by the calcination of commercial NaHCO₃ at 200 °C; reactive CaO was formed by decomposing a fine-grained, high-calcium limestone at 830 °C. Techniques with a differential reactor were employed to explore the rate of reaction of HCl with Na₂CO₃ at 500 °C and that of H₂S with CaO at 800 °C. Time-resolved data on the sorbents’ conversion were collected as a function of mean particle size in the range between 0.285 and 1.12 mm. The surface reaction constants, deduced via the tractable model from the initial reaction rates of the two reactions, slightly increase with the increasing particle size. The proposed correlations enable to interpolate or cautiously extrapolate to other isotropic, irregularly shaped solids. The effective diffusivities educed by means of the model from the experimental curves decrease significantly with the increasing conversion and are affected by the particle size in both sorptions. The developed reaction rate equations can conveniently be applied to the design and simulation of the deep dechloridization and the bulk desulfurization of hot producer gas.     

Anoxic granulated biomass and its storage

Laboratory experiments involving shutdown and repeated start-up of a denitrification USB reactor with granulated anoxic biomass were conducted in order to find suitable conditions for a safe storage period of the biomass. Anoxic granulated biomass stored under anaerobic conditions for a half year period at 6°C and for a half month period at 18–20°C retained its activity and granular morphology. Storage of anoxic granules under anaerobic conditions for a half year period at 18–20°C led to the loss of the biomass original activity and a significant portion of the granules disintegrated. Anoxic granulated biomass stored for a one and a half month period under endogenous anoxic conditions at 18–20°C retained its activity and granular morphology. A two month storage under endogenous anoxic conditions at 18–20°C was too long and the shutdown of the reactor had to be followed by repeated anoxic granulation. Minimum loading of the USB reactor with N-NO₃ to maintain endogenous anoxic conditions in the sludge bed was in the range of 0.06–0.1 kg of N-NO₃ per m³ per day. Restart of the USB reactor can be accelerated by an addition of anaerobic granulated biomass.     

Computer simulation of the uncertainty of analytical results

Uncertainty is an important quality parameter of any analytical result. Estimating the uncertainty of analytical procedures can be rather difficult in many instances. Computer simulation based on multiple repetition of calculation of the resulting quantity while varying slightly the input parameters is an alternative option. The input parameters for the various computation runs are composed of two terms: the constant mean value and the error, obtained as the product of the standard uncertainty of the parameter in question and a random number with the normal distribution N(0.1). This approach can also serve to optimize measuring procedures, as demonstrated on an example of the determination of lead in biological materials by isotope dilution mass spectrometry. The accuracy of the optimized method was tested by analysis of some CRMs, the robustness of the method was examined, and the detection limit (10 ng/g Pb) and repeatability (4 ng/g Pb) were determined. Received: 30 September 1998 / Revised: 3 December 1998 / Accepted: 8 December 1998