Bifunctional diphosphorus Lewis acids from cyclodiphosphadiazanes

The quantitative displacement of triflate groups in 1,3-ditriflato-2,4-bis(2,6-dimethylphenyl)cyclodiphospha-2,4-diazane by DMAP (4-dimethylaminopyridine) or Me(3)P gives dicationic complexes containing bifunctional diphosphorus Lewis acceptors.     

Herstellung von 1,2,4‐Trithiolan‐, 1,2,4,5‐Tetrathian‐ sowie 1,2,3,5,6‐Pentathiepan‐S‐oxiden und deren Reaktionen mit (Ph3P)2Pt(η2‐C2H4). Kristallstrukturanalyse von 3,3,5,5‐Tetraphenyl‐1,2,4‐trithiolan‐1‐oxid

Metal Complexes of Functionalized Sulfur‐containing Ligands. XVII Synthesis of S ‐Oxides of 1,2,4‐Trithiolane, 1,2,4,5‐Tetrathiane as well as 1,2,3,5,6‐Pentathiepane, and their Reactions with (Ph₃P)₂Pt(η²‐C₂H₄). X‐Ray Structure Analysis of 3,3,5,5‐Tetraphenyl‐1,2,4‐trithiolane 1‐oxide 3,3,5,5‐Tetraphenyl‐1,2,4‐trithiolan ( 1 ) was oxidized using m‐chloroperbenzoic acid to give, selectively, the 3,3,5,5‐tetraphenyl‐1,2,4‐trithiolane 1‐oxide ( 2 ). 2 was characterized structurally. The reaction of octamethyl tetrathiadispiro[3.2.3.2]dodecane‐2,9‐dione ( 3 ) with trifluoroperacetic acid at –50 °C yielded the corresponding 5‐oxide 4 . Oxidation of octamethyl pentathiadispiro[3.3.3.2]tridecane‐2,9‐dione ( 5 ) with m‐chloroperbenzoic acid at 0 °C gave the 12‐oxide 6 . Treatment of 2 with two equivalents of (Ph₃P)₂Pt(η²‐C₂H₄) ( 7 ) afforded a mixture (1 : 1) of the complexes (Ph₃P)₂PtSCPh₂S ( 8 ) and (Ph₃P)₂Pt(η²‐Ph₂C=S=O) ( 9 ), respectively.     

Natural convection flow with solidification between two vertical plates filled with a porous medium

Quasi-steady solidification between two vertical flat plates filled with a saturated porous medium has been investigated. The medium is homogeneous and isotropic. The convection flow of liquid takes place in the porous medium in the variable space between the two walls. One of the vertical walls is set to a temperature lower than the solidification temperature of the medium and therefore a frozen crust is formed on this wall. The second wall has a high temperature then the fusion temperature of the medium. The problem has been simplified by assuming laminar flow and the Brinkman and the Oberbeck–Bousinesq’s approximations. The results are presented in terms of the velocity for different properties of the porous medium. Various velocities are displayed in dependence of the Rayleigh and Darcy numbers. The study indicates that asymmetric boundary conditions have an important effect on the temperature and flow field. In addition, the growth of the thickness of the frozen layer with time has been derived from a simple analytical solution of the interface energy equation.     

Generation of femtosecond pulses by two-photon pumping supercontinuum-seeded collinear traveling wave amplification in a dye solution

Visible femtosecond (fs) laser pulses have been obtained in a dye solution with a very simple traveling wave collinear configuration. A femtosecond Ti:sapphire laser (790 nm) pumps the dye solution by two-photon absorption and simultaneously generates supercontinuum, which seeds a light-amplification mechanism. Cross-correlation frequency-resolved optical gating measurements reveal a chirped structure in the dye pulse. The shortest pulse duration achieved is 170 fs and the overall energy efficiency of the process is typically 25%. Received: 22 March 2001 / Revised version: 4 July 2001 / Published online: 19 September 2001     

Sequences—Basic elements for discrete mathematics

Sequences are fundamental mathematical objects with a long history in mathematics. Sequences are also tools for the development of other concepts (e. g. the limit concept), as well as tools for the mathematization of real-life situations (e. g. growth processes). But, sequences are also interesting objects in themselves, with lots of surprising properties (e. g. Fibonacci sequence, sequence of prime numbers, sequences of polygonal numbers). Nowadays, new technologies provide the possibility to generate sequences, to create symbolic, numerical and graphical representations, to change between these different representations. Examples of some empirical investigation are given, how students worked with sequences in a computer-supported environment.     

Spectral parameters for quantitative mobility contrast in NMR imaging of solid polymers

Different procedures based on parameters of the wideline NMR absorption spectrum are presented to obtain localized molecular mobility contrast for imaging of solid polymers. For this purpose a ¹H-NMR imaging technique with magic sandwich echoes is used for acquiring localized wideline spectra. With samples composed of polystyrene and high impact strength polystyrene, and polycarbonate and low density polyethylene a spatial difference in NMR absorption spectrum lineshape and linewidth is displayed. Furthermore, the spatial distribution of rigid and mobile domains in a heterogeneous polymer can be derived from the NMR spectral components. It is demonstrated that a van Vleck moment analysis can be performed from spatially resolved magic echo decays. The second (M₂) and fourth (M₄) moments of the rigid components show considerable variation with the spatial composition of the investigated samples.     

Studies on cyclic dipeptides, II. Methylated modifications ofcyclo-[Phe-His]

Summary Synthesis of seven new cyclic dipeptides and their conformational analysis based on¹HNMR spectra is reported as well as their application as models to elucidate the mechanism of cyclic dipeptide catalysis in enantioselective mandelonitrile formation. Further evidence is presented to support the view that a highly ordered supramolecular complex of dipeptides acts as catalyst.

---

Untersuchungen an cyclischen Dipeptiden, 2. Mitt.: Methylierte Derivate von cyclo-[Phe-His]

Zusammenfassung Es wird die Synthese sieben neuer cyclischer Dipeptide, ihre Konformationsanalyse (basierend auf¹H-NMR-Daten) und ihre Anwendung als Modelle zur Aufklärung des Mechanismus der dipeptidkatalysierten enantioselektiven Mandelsäurenitrilsynthese beschrieben. Weitere Hinweise zur Stützung der Annahme, daß ein hoch geordneter supramolekularer Komplex aus Dipeptiden für die Katalyse ausschlaggebend ist, werden vorgelegt.