Given a word w over a finite alphabet, we consider, in three special cases, the generalised star-height of the languages in which w occurs as a contiguous subword (factor) an exact number of times and of the languages in which w occurs as a contiguous subword modulo a fixed number, and prove that in each case it is at most one. We use these combinatorial results to show that any language recogn...

Let I be an ideal of a Noetherian ring R. The Rees algebra of I is the graded R-algebra ⊕k=0Ik. The study of the properties of Rees algebras (and of the other blow-up algebras) has attracted the attention of many researchers in the last three decades. For a detailed account of the theories that have been developed and of the results that have been proved, the reader should consult the monograph...

Despite the increasing use of rare earth elements (REEs) and oxides (REOs) in various technologies, the information on their ecotoxicological hazard is scarce. Here, the effects of La3+, Ce3+, Pr3+, Nd3+, Gd3+, CeO₂, and eight doped REOs to marine bacteria Vibrio fischeri and freshwater protozoa Tetrahymena thermophila were studied in parallel with REO dopant metals (Co2+, Fe3+, Mn2+, Ni2+, Sr2...

A sensitive mass spectrometric analysis method based on the microwave plasma technique is developed for the fast detection of trace rare earth elements (REEs) in aqueous solution. The plasma was produced from a microwave plasma torch (MPT) under atmospheric pressure and was used as ambient ion source of a linear ion trap mass spectrometer (LTQ). Water samples were directly pneumatically nebuliz...

The Möbius inversion formula, introduced during the 19th century in number theory, was generalized to a wide class of monoids called locally finite such as the free partially commutative, plactic and hypoplactic monoids for instance. In this contribution are developed and used some topological and algebraic notions for monoids with zero, similar to ordinary objects such as the (total) algebra o...

Dynamics of confined water has interesting implications in the organization and function of molecular assemblies such as membranes. A direct consequence of this type of organization is the restriction imposed on the mobility of the constituent structural units. Interestingly, this restriction (confinement) of mobility couples the motion of solvent (water) molecules with the slow moving molecule...

In this paper we continue a classical work of Schützenberger on codes with bounded synchronization delay. He was interested to characterize those regular languages where the groups in the syntactic monoid belong to a variety H. He allowed operations on the language side which are union, intersection, concatenation and modified Kleene-star involving a mapping of a prefix code of bounded synchron...

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...

In this paper we show that the Rees algebra can be made into a functor on modules over a ring in a way that extends its classical definition for ideals. The Rees algebra of a module M may be computed in terms of a “maximal” map f from M to a free module as the image of the map induced by f on symmetric algebras. We show that the analytic spread and reductions of M can be determined from any emb...

Objectives: To provide initial evidence for the construct, concurrent, and predictive validity of the TeamReferent Attributions Measure in Sport (the TRAMS). Design: Cross-sectional in Studies 1 and 2, and multiple time points in Study 3. Method: Study 1 required participants (N 1⁄4 500) to complete the TRAMS for their “least successful” and “most successful” performances in the preceding three...