Bis(pyrazolyl)(thioimidazolyl)borate ligands: the missing member in the N3...S3 scorpionate series

The anionic bis(pyrazolyl)(thioimidazolyl)borate ligands BpMt(R) with R = tert-butyl and isopropyl were obtained as their potassium salts by reacting potassium tris(pyrazolyl)borate with the corresponding thioimidazoles in the melt at 150 degrees C. They were applied to form some tetrahedral zinc complexes and identified by the crystal structures of (BpMt(t-Bu))ZnCl and (BpMt(i-Pr))Zn-SC(6)H(4)-p-Cl.     

Der Zwei-Quadrate-Satz von Fermat - eine Studie zur Heuristik des Beweisens

Dieser Beitrag hat seinen Ursprung in Veranstaltungen zur Heuristik im Rahmen meiner Tätigkeit in der fachdidaktischen Ausbildung von Gymnasiallehrern an der hiesigen RWTH. Mehr und mehr habe ich dabei die Überzeugung gewonnen, dass es notwendig ist, Lehramtskandidaten historische, heuristische und pädagogische Aspekte wichtiger mathematischer Inhalte erfahren zu lassen, die innerhalb der fachlichen Ausbildung nicht oder nicht genügend Berücksichtigung finden können und die aber im Hinblick auf den späteren Beruf wesentlich sind. Es wird hiermit weniger für eine Behandlung des Zwei-Quadrate-Satzes in der Schule - wenngleich sehr erwünscht - plädiert, wohl aber könnte dieses Thema Bestandteil eines fachdidaktischen Seminars oder Proseminars sein. Die Einschränkung im obigen Zitat von Hardy war natürlich eine zusätzliche didaktische Herausforderung. Den Gutachtern danke ich für ihre Ermutigung sowie für zahlreiche Verbesserungsvorschläge und Hinweise auf Unklarheiten und Fehler. Ebenso danke ich Herrn Artmann sehr, der eine frühere Fassung gelesen und konstruktiv kritisiert hat.Einige Grafiken wurden mit der dynamischen Mathematiksoftware GEONExT erzeugt. GEONExT ist unter der Adresse http: //geonext.de frei erhältlich.     

Strong field quantum path control using attosecond pulse trains

We show that attosecond pulse trains have a natural application in the control of strong field processes. In combination with an intense infrared laser field, the pulse train can be used to microscopically select a single quantum path contribution to a process that would otherwise consist of several interfering components. We present calculations that demonstrate this by manipulating the time-frequency properties of high order harmonics at the single atom level. This quantum path selection can also be used to define a high resolution attosecond clock.     

SUBPOL: a novel SUcrose-Based Polymer support for solid-phase peptide synthesis and affinity chromatography applications

A novel SUcrose-Based Polymer support (SUBPOL) with tailored morphology suitable for the use in solid-phase peptide synthesis (SPPS) is described, and its application as a hydrophilic affinity matrix for the specific removal of fibrinogen from human plasma is demonstrated. After suspension polymerization of partly methacrylated 2,1':4,6-di-O-isopropylidene sucrose and subsequent removal of the protecting groups, hydrophilic spherical polymer beads were obtained. The morphology of the resulting resin was controlled by variation of the porogen as well as the average degree of substitution with respect to the methacryloyl groups of the monomer mixture. After introduction of amino groups for a permanent attachment of immobilized peptide ligands, prevention of unintended esterification during SPPS was achieved by silylation of remaining hydroxy groups. Alternatively, a Rink amide linker was introduced prior to SPPS to allow cleavage and subsequent analysis of the peptide assembled on the SUBPOL resins. Two hexapeptides of sequence kwiivw and hffflw, consisting of d-amino acids, as well as a 19-mer peptide corresponding to the sequence GSGVRGDFGSLAPRVARQL of the VP1 protein from the foot-and-mouse disease virus (FMDV) were successfully prepared both manually or in a semi-automated process on SUBPOL resins according to the Fmoc/tBu strategy. Yields and purities were comparable to peptides prepared on commercially available polystyrene resins. A specific affinity adsorbent containing the fibrinogen-binding pentapeptide GPRPK was prepared by SPPS on SUBPOL resins of different morphology, and the strong impact of the affinity matrix on adsorption performance was demonstrated.     

Duality-Induced Reflections and CPT

The linear particle-antiparticle conjugation C and position space reflection P aswell as the antilinear time reflection T are shown to be inducible by theself-duality of representations for the operation groups SU(2), SL(C²), and R forspin, Lorentz transformations, and time translations, respectively. The definitionof a color-compatible linear CP-reflection for quarks as self-duality induced isimpossible since triplet and antitriplet SU(3)-representations are not linearlyequivalent.     

Synthesis of Cyclic Peptides by Photochemical Decarboxylation of N‐Phthaloyl Peptides in Aqueous Solution

The synthesis of a variety of cyclic peptides from N‐phthaloyl‐protected di‐, tri‐, tetra‐, and pentapeptides with different aminocarboxylic acid tethers by photodecarboxylation – initiated by intramolecular electron transfer – has been explored in aqueous media. The progress and the chemoselectivity of the follow‐up processes after CO₂ extrusion were traced by the respective pH/time‐profiles, as well as by the overall change in pH after completion of the reaction. The competition between cyclization and simple oxidative decarboxylation depends on spacer length and geometry, H‐bonding interaction between the electron accepting phthalimide C?O groups and amide H‐atoms, as well as the geometric reorganization coupled with the radical combination step and the formation of the lactam rings. With progressing reaction, hydrolysis of the phthalimide chromophore becomes an increasingly important side reaction due to the constant increase in pH. The use of phosphate‐buffered aqueous media consequently improved the cyclization yields. The ground‐state interactions between amide groups and the terminal COO^? group with the imide C?O groups were studied for the model system [N‐(phthaloyl)glycyl]sarcosine ( 1 ) by NMR spectroscopy where the amide (E/Z)‐equilibrium depends on the presence of carboxylate vs. free carboxylic acid, demonstrating the role of H‐bonding and metal coordination.