Interassociates of the bicyclic semigroup

An interassociate of a semigroup \((S,\cdot )\) is a semigroup \((S, *)\) such that for all \(a, b, c \in S\), \(a\cdot (b*c)=(a\cdot b) *c\) and \(a*(b\cdot c)=(a*b) \cdot c\). We investigate the bicyclic semigroup C and its interassociates. In particular, if p and q are the generators of the bicyclic semigroup and m and n are fixed nonnegative integers, the operation \(a*_{m,n} b= aq^mp^n b\) is known to be an interassociate. We show that for distinct pairs (m, n) and (s, t), the interassociates \((C, *_{m,n})\) and \((C, *_{s,t})\) are not isomorphic. We also generalize a result regarding homomorphisms on C to homomorphisms on its interassociates.     

Adaptive optimal control of Signorini’s problem

In this article, we present a-posteriori error estimations in context of optimal control of contact problems; in particular of Signorini’s problem. Due to the contact side-condition, the solution operator of the underlying variational inequality is not differentiable, yet we want to apply Newton’s method. Therefore, the non-smooth problem is regularized by penalization and afterwards discretized by finite elements. We derive optimality systems for the regularized formulation in the continuous as well as in the discrete case. This is done explicitly for Signorini’s contact problem, which covers linear elasticity and linearized surface contact conditions. The latter creates the need for treating trace-operations carefully, especially in contrast to obstacle contact conditions, which exert in the domain. Based on the dual weighted residual method and these optimality systems, we deduce error representations for the regularization, discretization and numerical errors. Those representations are further developed into error estimators. The resulting error estimator for regularization error is defined only in the contact area. Therefore its computational cost is especially low for Signorini’s contact problem. Finally, we utilize the estimators in an adaptive refinement strategy balancing regularization and discretization errors. Numerical results substantiate the theoretical findings. We present different examples concerning Signorini’s problem in two and three dimensions.     

Destillation

Ohne Zusammenfassung     

Novel use of a fiber-optic-based on-line trichloroethylene sensor in a column retardation experiment

A newly developed fiber-optic-based trichloroethylene (TCE) sensor previously described [F.P. Milanovich, S.B. Brown, B.W. Colston, Jr., P.F. Daley and K. Langry, Talanta, 41 (1994) 2189], was used to provide analyses of TCE in laboratory tests of retardation of TCE in ground water. The sensor enabled inexpensive real time analyses of TCE in retardation tests conducted in a sand-filled flow-through column. The simultaneous data analysis of TCE, (18)O and Cl(-) breakthrough curves enabled the calculation of an estimated retardation coefficient which was found to be in good agreement with that predicted by the octanol/water partitioning K(d) method. The fiber-optic sensor was demonstrated to be a fast and reliable method for conducting on-line laboratory analyses of TCE at the parts per billion level in a small volume of contaminated water, thus providing excellent temporal resolution of the data as well as minimizing volatile losses during sample collection and analysis.     

Trace metals analysis in estuarine and seawater by ICP-MS using on line preconcentration and matrix elimination with chelating resin

The main difficulties of trace metals analysis in estuarine and seawater stem from their very low concentration (mug/l to sub-mug/l), and, by contrast, the high salt content (up to 38 g/l in the Mediterranean Sea). ICP-MS allows multi-elemental analysis and offers great sensitivity, but may be strongly affected by matrix effects induced by high salt contents (> 1 g/l). To perform trace metals analysis both in riverine, estuarine and seawater, we have developed a hyphenated method: ion chelation chromatography coupled on-line with ICP-MS. Iminodiacetate resin, Metpac CC-1 (Dionex), was used to concentrate most of the trace metals, and to separate them from alkaline and alkaline-earth metals. Behaviour of 17 elements (Pb, Cu, Cd, Ni, U, Cr, Mn, Al, Co, Ga, In, Zn, V, Tl, Bi, Ag and Sn) towards the resin was qualitatively investigated. A method validation, partly derived from AFNOR standard XPT 90-210, was carried out on 12 elements (Pb, Cu, Cd, Ni, U, Cr, Mn, Al, Co, Ga, Bi and In). Replicate measurements of multi-elemental standard solutions were used to check linearity, and to determine repeatability and detection limits. Method accuracy was then assessed by analysing two certified materials: a synthetic freshwater (SRM 1643d), and a natural filtered coastal seawater (NRCC CASS-3). An application assay of natural samples from the Rh?ne river (France) was eventually carried out, and the analytical results were found to be consistent with previous works.     

H3PO4 — etching of {001}-faces of InP, (GaIn)P,GaP, and Ga(AsP)

This paper shows that hot H₃PO₄ is a suitable etchant for the production of dislocation etch pits on {001}-InP, (InGa)P, GaP, Ga(AsP), and {111}-GaP. The effects upon etch pit morphology of the misorientation of samples and the type of dislocations are investigated in detail.