Tris(oxalato)phosphorus acid and its lithium salt

The conversion of three equivalents of anhydrous oxalic acid with phosphorus pentachloride yields tris(oxalato)phosphorus acid 1, which crystallizes from diethyl ether solutions as protonated diethyl ether complex [(Et2O)2H](+)[P(C2O3)3)]-. The superacidic compound can be used as catalyst for Friedel-Crafts-type reactions. Upon neutralization with lithium hydride, the lithium salt Li[P(C2O3)3] 2 is obtained, which is highly soluble in aprotic solvents and which exhibits a wide voltage window. Thus, the lithium compound is a promising candidate as electrolyte for high performance non-aqueous batteries.     

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.     

Synthesis, spectroscopy, and X-ray structure of the polymer catena-[bis(azido-N)-copper(II)-μ-bis(2-benzimidazolyl)butane]

The title compound, catena-[bis(azido-N)-copper(II)-(bis(2-benzimidazolyl)butane), [Cu(C₁₈H₁₈N₄)(N₃)₂]_n, was obtained from the reaction of the ligand bis(2-benzimidazolyl)butane and Cu(N₃)₂. The x-ray crystal structure is reported. The compound crystallizes in the monoclinic space group P2₁/c with a = 8.2524(10), b = 12.765(5), c = 9.1125(15) Å, = 106.423(12)°, Z = 2. The Cu(II) ions are square-planar coordinated with trans-oriented end-on binding azido ligands. The structure is a polynuclear chain with the benzimidazole bridging at each end. In addition a N_(ligand)-H···N_(azido) H-bridge [N_(ligand)···N_(azido) = 2.994(7) Å] is present, resulting in a pseudo 2-dimensional lattice. The characteristic azido infrared vibrations are found at 2060 and 2077 cm^–1 (_as(N₃)) and 1284 and 1297 cm^–1 ((N₃)).     

Asymptotic singular behaviour of inhomogeneous cosmologies in Einstein-Maxwell-dilaton-axion theory

We present the study of exact inhomogeneous cosmological solutions to a four-dimensional low energy limit of string theory containing non-minimal interacting electromagnetic, dilaton and axion fields. We focus at Einstein-Rosen solutions of Einstein-Maxwell-dilaton-axion equations. Several cases are analyzed and some of them have asymptotically velocity-term dominated (AVTD) singularities.     

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.     

Über Strukturen in ionotropen Gelen

Ohne Zusammenfassung