Über eine Abbildung der Ebene auf eine gewisse Kummer'sche Fläche

Ohne Zusammenfassung     

Nickel as a chemical modifier for sensitivity enhancement and fast atomization processes in electrothermal atomic absorption spectrometric determination of cadmium in biological and environmental samples.

A systematic study of the efficiency of protons, Ni, Pd and Th as chemical modifiers for the determination of cadmium by electrothermal atomic absorption spectrometry (ETAAS) using fast temperature programs was made for platform atomization. A comparison was made in terms of the salt type, absorbance-time profiles and elimination of the sodium chloride interference. The results were adapted to develop a method for the ETAAS determination of cadmium in biological and environmental samples. The highest sensitivity to determine cadmium in biological and environmental samples was obtained using nickel (together with protons) as a chemical modifier. The accuracy of the method was tested by the determination of cadmium in different certified reference materials. The best detection limit and the characteristic mass of Cd were found to be 0.03 ng mL(-1) and 0.35 pg, respectively.     

Comparison of Several Calibration Procedures for Glass Electrodes in Proton Concentration

Several reported procedures for calibrating glass electrodes in proton concentration are compared. Some recommendations for non-experts are also given. The examined procedures can be classified into two broad categories, namely: those based on direct potential difference measurements of solutions of known proton concentration and those that use one or several pH standards to calibrate the electrode and subsequently measure the pH of solutions containing known proton concentrations. With a single buffer, the two types of procedures lead to equivalent results. However, if two pH buffers are used, the slope of the calibration graph in proton concentration will differ from the real electrode slope to an extent proportional to the difference between the liquid junction potentials of the two buffers. Therefore, any other method is preferable under these circumstances.     

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A Kind of direct methods is presented for the solution of optimal control problems with state constraints.These methods are sequential quadratic programming methods.At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and Linear approximations to constraints is solved to get a search direction for a merit function.The merit function is formulated by augmenting the Lagrangian funetion with a penalty term.A line search is carried out along the search direction to determine a step length such that the merit function is decreased.The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadrade programming methods.     

Higher-Order Simple Lie Algebras

It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to be satisfied by the antisymmetric tensors (or higher-order “structure constants”) which characterise the Lie algebra cocycles. This analysis allows us to present a classification of the higher-order simple Lie algebras as well as a constructive procedure for them. Our results are synthesised by the introduction of a single, complete BRST operator associated with each simple algebra. Received: 3 June 1996 / Accepted: 8 November 1996