A tree language of a fixed type τ is any set of terms of type τ. We consider here a binary operation +n on the set Wτ (Xn) of all n-ary terms of type τ, which results in semigroup (Wτ (Xn), +n). We characterize languages which are idempotent with respect to this binary operation, and look at varieties of tree languages containing idempotent languages. We also compare properties of semigroup homomorphisms from (𝒫(Wτ (Xn));+n) to (𝒫(Wτ (Xm));+m) with properties of homomorphisms between the corresponding absolutely free algebras ℱτ (Xn) and ℱτ (Xm).
The Institut für Nukleare Entsorgung (INE) at the Forschungszentrum Karlsruhe (FZK), Germany, has constructed and is operating a beamline at the synchrotron source ANKA dedicated to actinide speciation investigations related to nuclear waste disposal as well as applied and basic actinide research. Experiments on nuclides not suited as nuclear fuel with activities up to 106 times the limit of exemption inside a safe and flexible containment concept are now possible. The design is for a multi-purpose beamline, i.e., a number of methods (XAFS, surface sensitive and spatially resolved techniques) are envisaged on one and the same sample, with X-ray energies from 2472 eV (SK edge) to 23220 eV (RhK edge). The commissioning of the INE-Beamline was officially completed in September 2005 and meanwhile regular user operation has been started. Here we present a description of this new facility and examples for X-ray absorption studies on actinides and homologues performed during the beamline commissioning phase.
In 2009 K. Denecke and J. Koppitz proved that for a monoid ℳ of hypersubstitutions M-solid positive varieties of tree languages correspond to M-solid ordered pseudovarieties. In this paper, we will characterize M-solid ordered pseudovarieties in a similar way in which in  M-solid varieties, in  M-solid quasivarieties, in  M-solid pseudovarieties and in  M-solid algebraic systems were characterized. The main idea is to show, that we have two Galois-connections and a conjugate pair of additive closure operators. Then we can apply the general theory of conjugate pairs of additive closure operators.
Sorption of trivalent Cm onto γ-Al2O3 is investigated by time-resolved laser fluorescence spectroscopy (TRLFS). The pH dependent sorption of Cm(III) is followed at constant ionic strength of 0.1 M NaClO4 under argon atmosphere in the pH range between 3.5 and 13.2 at a total Cm(III) concentration of 2.5×10-7 mol/L. Three different surface-sorbed Cm(III) species appearing at different pH are identified by their emission spectra with peak maxima at 600.6 nm, 602.5 nm, and 605.7 nm using an excitation wavelength of λex=396.6 nm. No variation of the emission decay is observed for the three sorbed species (constant lifetimes of 110 μs). The pH dependent species distribution obtained from peak deconvolution of emission spectra is in agreement with earlier Eu/Cm sorption studies and sorbed species are assigned to >Al−O−Cm(OH)x(2-x)(H2O)5-x inner-sphere complexes. Indirect Cm excitation via energy transfer from the solid to the metal ion at λex=355 nm yields emission bands significantly shifted compared to spectra obtained at λex=396.6 nm. We interpret this observation as a hint for the existence of Cm inner-sphere complexes bound to different γ-Al2O3 surface sites. The exact nature of those species is presently not known, but they likely involve Cm interaction with Al(OH)3 phases at the solid surface which may even dominate the solid surface chemistry. Complementary EXAFS measurements are performed with Lu and Gd, taken as chemical homologues of the trivalent actinides. EXAFS for Gd/Lu(III) sorbed onto γ-Al2O3 at pH=6 identifies a single oxygen coordination shell with a high degree of disorder. For Gd this shell consists of 9±1.5 atoms at a 2.45±0.02 Å distance. A coordination number of 7±1.5 and a Lu−O distance of 2.28±0.02 Å is found in the Lu-samples. Those values are quite close to what is known for the respective aquo ions. The large asymmetry in the coordination shell, however, suggests inner-sphere complexation. This is in agreement with TRLFS results showing clearly the existence of inner-sphere surface complexes where the first coordination shell of the trivalent metal ions consists of 5H2O/OH- entities. Together with EXAFS data, a metal ion coordination to four oxygen atoms belonging to the γ-alumina surface is concluded. Both spectroscopic studies indicate a certain variability of surface binding sites for trivalent metal ions.
The Lu(III) sorbed species onto synthetic hydrous ferric oxide (HFO), commonly called ferrihydrite, has been identified. Characterization of the synthetic 2-line HFO shows that its synthesis is reproducible. Potentiometric titration of freshly synthesized HFO, modeled using the constant capacity model (κ1=0.5 F/m2) in the FITEQL code, yields a specific surface area Sa of 360±35 m2/g (N2-BET), a site density Nd of 2.86 sites/nm2 (concentration of hydroxyl groups, Ns=1.71×10-3 mol sites/g HFO), and acidity constants pKa1}int=6.37 and pKa2}int=9.25.
Evaluation of chemical sorption data reveals the presence of two different Lu surface sorbed species, dependent on pH; a monodendate species forms at low pH and a polydentate species at pH>5. Satisfactory fits to the sorption data are obtained using a combination of monodentate and bidentate surface species. The combination of species is chosen, based on extended X-ray absorption fine structure (EXAFS) results. The sorption constants obtained from these fits are pKs=-1.89(±0.1) and pKs=-1.69(±0.1) for the monodentate species ≡FeOLu(H2O)52+ for fits to the pH edge and to the isotherm at pH°5.9, respectively. A value of pKs=3.69(±0.01) is found for the bidentate species ≡ Fe(O)2Lu(H2O)5+ for both fits. EXAFS analysis of sorption samples prepared at 4.5<pH<8 shows that Lu is surrounded by a single first shell of 7±1 oxygen atoms, at a distance of (2.30±0.01) Â in all samples. A second coordination shell of Fe neighboring atoms at a distance of (3.38±0.01) Â is observed for sorption samples pH≥5.5. This distance is associated with the formation of a bidendate complex with bonding via edge sharing to iron octahedra. The samples prepared at pH<5.1 show no Fe shell, as expected for monodentate coordination. No evidence for surface precipitation and no noticeable difference between wet paste and dried powder samples is found.