On-line determination of mercury in river water at the German monitoring station Schnackenburg/Elbe

A monitor is described which provides the on-line determination of mercury in river water at concentrations from 20 to 1000 ng/L. The measurement includes an on-line digestion with Br^–/BrO₃ ^– and UV-radiation. Each determination is controlled by an on-line addition of 50 and 100 ng/L mercury carried out by pre-dilution of a 500 and 1000 ng/L stock solution using sequential injection analysis (SIA). One cycle of analysis takes 20 min and results in nine signals. A five days stand-alone operation has been performed successfully. Details are also published at web page: “http/www.rzbd.fh-hamburg.de/¶～prmercol”     

Three Saponins, a Steroid, and a Flavanol Glycoside from Achyrantes aspera

Summary.  Three bisdesmosidic saponins, 20-hydroxyecdysone, and quercetin-3-O-β-D-galactoside were isolated from the methanol extract of the aerial parts of Achyranthes aspera L. (Amaranthaceae). Their structures were established on the basis of NMR spectroscopic analysis; the complete ¹H and ¹³C assignments of the compounds were achieved by means of 2D NMR studies. Received July 21, 1999. Accepted August 26, 1999     

On a hybrid boundary element method

Summary. In this paper we study a symmetric boundary element method based on a hybrid discretization of the Steklov–Poincaré operator well suited for a symmetric coupling of finite and boundary elements. The representation used involves only single and double layer potentials and does not require the discretization of the hypersingular integral operator as in the symmetric formulation. The stability of the hybrid Galerkin discretization is based on a BBL–like stability condition for the trial spaces. Numerical examples confirm the theoretical results. Received December 15, 1997 / Revised version received December 21, 1998/ Published online November 17, 1999     

The peridynamic model in non-local elasticity theory

The peridynamic model is described and an overview of some recent results concerning the analysis of the peridynamic equation of motion is given. Moreover, its numerical solution is discussed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A unified expression of elastic–plastic notch stress–strain calculation in bodies subjected to multiaxial cyclic loading

In this paper, a simplified thermodynamics analysis of cyclic plastic deformation is performed in order to establish an energy transition relation for describing the elastic–plastic stress and strain behavior of the notch-tip material element in bodies subjected to multiaxial cyclic loads. Based on the thermodynamics analysis, it is deduced that in the case of elastic–plastic deformation, Neuber’s rule inevitably overestimates the actual stress and strain at the notch tip, while the equivalent strain energy density (ESED) method tends to underestimate the actual notch-tip stress and strain. According to the actual energy conversion occurring in the notch-tip material element during cyclic plastic deformation, a unified expression for estimating the elastic–plastic notch stress–strain responses in bodies subjected to multiaxial cyclic loads is developed, of which Neuber’s rule and the ESED method become two particular cases, i.e. upper and lower bound limits of the notch stress and strain estimations. This expression is verified experimentally under both proportional and non-proportional multiaxial cyclic loads and a good agreement between the calculated and the measured notch strains has been achieved. It is also shown that in the case of multiaxial cyclic loading, the unified expression distinctly improves the accuracy of the notch-tip stress–strain estimations in comparison with Neuber’s rule and the ESED method. The unified expression of the notch stress–strain calculation developed in this paper can thus provide a more logical approximate approach for estimating the elastic–plastic notch-tip stress and strain responses of components subjected to lengthy multiaxial cyclic loading histories for local strain approach-based fatigue-crack-initiation life prediction.     

On the stability of the $L_2$ projection in fractional Sobolev spaces

Summary.   In this paper we prove the stability of the projection onto the finite element trial space of piecewise polynomial, in particular, piecewise linear basis functions in for . We formulate explicit and computable local mesh conditions to be satisfied which depend on the Sobolev index s. In conclusion we prove a stability condition needed in the numerical analysis of mixed and hybrid boundary element methods as well as in the construction of efficient preconditioners in adaptive boundary and finite element methods. Received October 14, 1999 / Revised version received March 24, 2000 / Published online October 16, 2000     

Commutative Nilpotent Extensions of Commutative C*-Algebras Split

It is proved that every commutative, nilpotent extension ofa commutative C*-algebra splits topologically. 1991 MathematicsSubject Classification 46J40.     

Supervisory control of hybrid systems based on model abstraction and guided search

This paper addresses the task of computing supervisory controllers by which hybrid systems with nonlinear continuous dynamics are driven into goal sets while safety specifications are met. For this class of systems, the (conservatively approximative) determination of reachable states is an important but also a computationally expensive step of the controller synthesis. This contribution proposes a technique aiming at reducing the reach set computation by using abstract models and guided search. For a discrete abstraction of the hybrid model, candidate paths are determined as possible controlled evolutions which fulfill the given specifications. A validation scheme comprising three different techniques is applied to determine whether the candidate path represents a feasible control strategy for the hybrid system. If the specification is violated, the abstract model is refined according to the validation result. The iterative application of the determination of candidate paths, the path validation and the model refinement steers the search for a control strategy such that often only a relatively small part of the reachable state space has to be explored. The synthesis procedure is illustrated for two examples.