[1] The rare earth elements (REEs) with their systematically varying properties are powerful tracers of continental inputs, particle scavenging intensity and the oxidation state of seawater. However, their generally low ( pmol/kg) concentrations in seawater and fractionation potential during chemical treatment makes them difficult to measure. Here we report a technique using an automated precon...

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A combined procedure for separating Lu, Hf, Sm, Nd, and rare earth elements (REEs) from a single sample digest is presented. The procedure consists of the following five steps: (1) sample dissolution via sodium peroxide sintering; (2) separation of the high field strength elements from the REEs and other matrix elements by a HF-free anion-exchange column procedure; (3) purification of Hf on a c...

Fix a finite semigroup S and let a1, . . . , ak , b be tuples in a direct power S. The subpower membership problem (SMP) for S asks whether b can be generated by a1, . . . , ak. For combinatorial Rees matrix semigroups we establish a dichotomy result: if the corresponding matrix is of a certain form, then the SMP is in P; otherwise it is NP-complete. For combinatorial Rees matrix semigroups wit...

We study enumerative and homological properties of the Rees product of the cubical lattice with the chain. We give a bijective proof that the Möbius function of this poset can be expressed as n times the permanent of a matrix. This gives a new bijective proof of Jonsson’s result that the Möbius function of the Rees product of the Boolean algebra with the chain is given by a derangement number. ...

We survey results concerning automatic structures for semigroup constructions, providing references and describing the corresponding automatic structures. The constructions we consider are: free products, direct products, Rees matrix semigroups, Bruck-Reilly extensions and wreath products.

We study enumerative and homological properties of the Rees product of the cubical lattice with the chain. We give several explicit formulas for the Möbius function. The last formula is expressed in terms of the permanent of a matrix and is given by a bijective proof. Résumé. Nous étudions des propriétés énumératives et homologiques du produit de Rees du treillis cubique avec la chaı̂ne. Nous do...