Finite Hurwitz braid group actions for Artin groups

We prove that (with two possible exceptions) the Hurwitz braid group action on the sequence of standard generators of an irreducible Artin group has a finite orbit if and only if the Artin group is of finite type (i.e., the corresponding Coxeter group is finite).     

Doppeltangenten einer Curven ter Ordnung

Ohne Zusammenfassung     

Analytical formulas for the velocity field induced by an infinitely thin vortex ring

Three different analytical solutions are presented for a potential vortex ring using three different streamfunctions. Verification studies confirm that all three approaches are valid. It is found that the solution obtained using the Biot–Savart law is the most efficient method due to its simplicity. It is shown that all analytical results are accurate to within machine accuracy and sample calculations are included. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparing adult mathematical literacy with PISA students: results of a pilot study

In Germany, very little empirical data about the mathematical competence of adults is available. The aim of this study is to test the level of mathematical competence in an adult sample. For this purpose, a mathematics test was constructed using the PISA mathematics framework as a guideline. The test consisted of fourteen public items from the mathematics test in PISA 2000. The study was implemented by carrying out house visits (Germany). The sample was comprised of 64 adults (90% women, age: 41 years). The test results were scaled in the metric of PISA 2000. Compared with the average German student competencies in PISA 2000, the average competency in the adult sample was on the same level as the fifteen-year-old comprehensive secondary school student (at a German Gymnasium). Further analysis shows that the mathematics competency level in the adult sample is positively connected to the individual vocational education degree.     

Medicinal Organometallic Chemistry: Designing Metal Arene Complexes as Anticancer Agents

The field of medicinal inorganic chemistry is rapidly advancing. In particular organometallic complexes have much potential as therapeutic and diagnostic agents. The carbon‐bound and other ligands allow the thermodynamic and kinetic reactivity of the metal ion to be controlled and also provide a scaffold for functionalization. The establishment of structure–activity relationships and elucidation of the speciation of complexes under conditions relevant to drug testing and formulation are crucial for the further development of promising medicinal applications of organometallic complexes. Specific examples involving the design of ruthenium and osmium arene complexes as anticancer agents are discussed.     

Genetically Encoded Bioluminescent Indicator for ERK2 Dimer in Living Cells

In this study, a genetically encoded bioluminescent indicator for ERK2 dimer was developed with the split Renilla luciferase complementation method, in which the formation of ERK2 dimer induces a spontaneous emission of bioluminescence in living cells. In response to extracellular stimuli, such as epidermal growth factor (EGF) or 17β‐estradiol (E2), extracellular signal‐regulated kinase 2 (ERK2) is phosphorylated by its upstream kinase MEK, and also phosphorylates its substrates in various regions of the cell, including the nucleus. Phosphorylated ERK2 is led to form its dimer, thereby transporting itself into the nucleus. We demonstrated with the indicator that stimulation with EGF or E2 induces the formation of ERK2 dimer in living MCF‐7 cells. The dynamics of this dimer formation was examined and discussed.     

Weak Attractive Ligand–Polymer and Related Interactions in Catalysis and Reactivity: Impact,Applications, and Modeling

The notion of weak attractive ligand–polymer interactions is introduced, and its potential application, importance, and conceptual links with “cooperative” ligand–substrate interactions are discussed. Synthetic models of weak attractive ligand–polymer interactions are described, in which intramolecular weak C? H???F? C interactions (the existence of which remains contentious) have been detected by NMR spectroscopy and neutron and X‐ray diffraction experiments. These C? H???F? C interactions carry important implications for the design of catalysts for olefin polymerization, because they provide support for the practical feasibility of ortho‐F???H_β ligand–polymer contacts proposed for living Group 4 fluorinated phenoxyimine catalysts. The notion of weak attractive noncovalent interactions between an “active” ligand and the growing polymer chain is a novel concept in polyolefin catalysis.