Perturbations of positive semigroups on AM-spaces

We consider positive perturbations of positive semigroups on AM-spaces and prove a result which is the dual counterpart of a famous perturbation result of Desch in AL-spaces. As an application we present unbounded perturbations of the shift semigroup.     

Solvent Effects on the NMR Chemical Shifts of Imidazolium-Based Ionic Liquids and Cellulose Therein

The interactions of ionic liquids (IL) with solvents usually used in liquid-state nuclear magnetic resonance (NMR) spectroscopy are studied. The ¹H- and ¹³C-NMR chemical shift values of 1-n-butyl-3-methyl (BM)- and 1-ethyl-3-methyl (EM)-substituted imidazolium (IM) -chlorides (Cl) and -acetates (Ac) are determined before and after diluting with deuterated solvents (DMSO-d₆, D₂O, CD₃OD, and CDCl₃). The dilution offers structural modifications of the IL due to the solvents capacity to ionization. For further investigation of highly viscous cellulose dopes made of imidazolium-based IL, solid-state NMR spectroscopy enables the reproducibility of liquid-state NMR data of pure IL. The correlation of liquid- and solid-state NMR is shown on EMIM-Ac and cellulose/EMIM-Ac dope (10 wt %).     

The Transitive Minimum Manhattan Subnetwork Problem in 3 dimensions

We consider the Minimum Manhattan Subnetwork (MMSN) Problem which generalizes the already known Minimum Manhattan Network (MMN) Problem: Given a set P of n points in the plane, find shortest rectilinear paths between all pairs of points. These paths form a network, the total length of which has to be minimized. From a graph theoretical point of view, a MMN is a 1-spanner with respect to the L₁ metric. In contrast to the MMN problem, a solution to the MMSN problem does not demand L₁-shortest paths for all point pairs, but only for a given set R⊆P×P of pairs. The complexity status of the MMN problem is still unsolved in ≥2 dimensions, whereas the MMSN was shown to be NP-complete considering general relations R in the plane. We restrict the MMSN problem to transitive relations R_T (Transitive Minimum Manhattan Subnetwork (TMMSN) Problem) and show that the TMMSN problem in 3 dimensions is NP-complete.     

Using Goffman's concepts to explore collaborative interaction processes in elementary school mathematics

The present paper describes the combined implementation of two approaches which are based on the work of Erving Goffman and focus on the analysis of the interactional participation structures. Our aim is to examine the ways that differing interpretations of the ongoing interactions may lead the students to adopt differing roles, which in turn affects the process of negotiating and establishing shared meanings. For this purpose we analyse the interaction processes in one ‘expert’ group within the ‘Jigsaw’ form of cooperation (Aronson, 1978 Aronson, E. 1978. The jigsaw classroom, Beverly Hills, CA: Sage.  [Google Scholar]), decomposing the participants’ roles according to their interactional status and their interpersonal effect. Our analysis points out the different roles that emerge in the process of collaborative interaction, and the influence of these roles on group achievement and individual learning possibilities.     

Crystal Growth and Structure Determination of Pigment Orange 82

The crystal structure of the important industrial orange pigment PO82, major part of the BASF Colors & Effects^® product Sicopal^® Orange K/L 2430, was solved from combined X‐ray single crystal, X‐ray and neutron powder diffraction, ¹¹⁹Sn Mössbauer spectroscopy, transmission electron microscopy, electron diffraction, and chemical analyses. The structure contains Keggin type clusters composed of four [M₃O₁₃] trimers consisting each of three MO₆ octahedra that share edges and one common oxygen atom connecting the trimers to the central ZnO₄ tetrahedron. The octahedrally coordinated metal atom position is mixed occupied by Ti⁴⁺, Sn⁴⁺, and Zn²⁺. Adjacent Keggin clusters share vertices and are further interconnected to four ZnO₄ tetrahedra. This framework of interconnected MO₆ octahedra and ZnO₄ tetrahedra contains channels along [110], in which the Sn²⁺ cations are located.     

Reactions with a Metalloid Tin Cluster {Sn10[Si(SiMe3)3]4}2−: Ligand Elimination versus Coordination Chemistry

Chemistry that uses metalloid tin clusters as a starting material is of fundamental interest towards understanding the reactivity of such compounds. Since we identified {Sn₁₀[Si(SiMe₃)₃]₄}^2? 7 as an ideal candidate for such reactions, we present a further step in the understanding of metalloid tin cluster chemistry. In contrast to germanium chemistry, ligand elimination seems to be a major reaction channel, which leads to the more open metalloid cluster {Sn₁₀[Si(SiMe₃)₃]₃}^? 9 , in which the Sn core is only shielded by three Si(SiMe₃)₃ ligands. Compound 9 is obtained through different routes and is crystallised together with two different countercations. Besides the structural characterisation of this novel metalloid tin cluster, the electronic structure is analysed by ¹¹⁹Sn Mössbauer spectroscopy. Additionally, possible reaction pathways are discussed. The presented first step into the chemistry of metalloid tin clusters thus indicates that, with respect to metalloid germanium clusters, more reaction channels are accessible, thereby leading to a more complex reaction system.     

Highly sensitive and rapid determination of tacrolimus in peripheral blood mononuclear cells by liquid chromatography–tandem mass spectrometry

After solid organ transplantation, tacrolimus is given to prevent rejection. Therapeutic drug monitoring is used to reach target concentrations of tacrolimus in whole blood. Because the site of action of tacrolimus is the lymphocyte, and tacrolimus binds ~80% to erythrocytes, the intracellular tacrolimus concentration in lymphocytes is possibly more relevant. For this purpose, we aimed to develop, improve and validate a UPLC–MS/MS method to measure tacrolimus concentrations in isolated peripheral blood mononuclear cells (PBMCs). PBMCs were isolated using a Ficoll separation technique, followed by a washing step using red blood cell lysis. A cell suspension of 50 μL containing 1 million PBMCs was used in combination with MagSiMUS‐TDM^PREP. To each sample we added 30 μL lysis buffer, 20 μL reconstitution buffer containing ¹³C²H₄‐tacrolimus as internal standard, 40 μL MagSiMUS‐TDM^PREP Type I Particle Mix and 175 μL Organic Precipitation Reagent VI for methanol‐based protein precipitation. A 10 μL aliquot of the supernatant was injected into the UPLC–MS/MS system. The method was validated, resulting in high sensitivity and specificity. The method was linear (r² = 0.997) over the range 5.0–1250 pg/1 × 10⁶ PBMCs. The inaccuracy was <5% and the imprecision was <15%. The washing steps following Ficoll isolation could be performed at either room temperature or on ice, with no effect of the temperature on the results. A method for the analysis of tacrolimus concentrations in PBMCs was developed and successfully validated. Further research will be performed to investigate the correlation between concentrations in PBMCs and clinical outcome.