A stannaethene with a planar environment of the tricoordinated tin and carbon atoms

Addition of the diarylstannylene R″₂Sn (R″ = 2−^tBu−4,5,6-Me₃C₆H) to the cryptodiborylcarbene (Me₃Si)₂C(B^tBu)₂C furnishes the stannaethene (Me₃Si)₂C(B^tBu)₂C=SnR″₂ (10). The X-ray structure analysis of 10 reveals a strictly planar environment of the tricoordinated tin and carbon atoms and a slight twisting of the Sn=C double bond.     

Plancherel Inversion as Unified Approach to Wavelet Transforms and Wigner Functions

We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. We first prove that a Plancherel inversion formula, well known for Bruhat functions on the group, holds for a much larger class of functions. This result allows us to view the wavelet transform as essentially the inverse Plancherel transform. The wavelet transform of a signal is an L²-function on an appropriately chosen group while the Wigner function is defined on a coadjoint orbit of the group and serves as an alternative characterization of the signal, which is often used in practical applications. The Plancherel transform maps L²-functions on a group unitarily to fields of Hilbert-Schmidt operators, indexed by unitary irreducible representations of the group. The wavelet transform can essentially be looked upon as a restricted inverse Plancherel transform, while Wigner functions are modified Fourier transforms of inverse Plancherel transforms, usually restricted to a subset of the unitary dual of the group. Some known results on both Wigner functions and wavelet transforms, appearing in the literature from very different perspectives, are naturally unified within our approach. Explicit computations on a number of groups illustrate the theory. Communicated by Gian Michele Graf submitted 05/06/01, accepted: 19/09/02     

Systematic investigations of the photocatalytic alkyne-nitrile heterotrimerisation to pyridine

The photocatalytic heterocyclotrimerisation of ethyne and nitrile initiated by cobalt(I) complexes was studied. General mechanistic features as proposed for the ‘dark’ reaction were found to apply as well under photolytic conditions albeit with modifications. The results suggest that the irradiated light accelerates that stage of reaction, leading to the organometallic species which is believed to be the common intermediate for the formation of pyridine and benzene. The rate of pyridine production is linear dependent from nitrile concentration. Benzene formation may be minimised by keeping the ethyne concentration low. An alternative mechanism, based on the initial coordination of nitrile at cobalt is not confirmed. A novel gas buret system was used, which allowed automatic feed of ethyne under isobaric conditions and to monitor all reactants simultaneously on-line.     

Smoothness of subdivision surfaces at extraordinary points

A stationary subdivision scheme such as Catmull and Clark's is described by a matrix iteration around an extraordinary point. We show how higher order smoothness of a limiting surface obtained by a stationary subdivision algorithm for tri- or quadrilateral nets depends on the spectral properties of the matrix and give necessary and sufficient conditions. The results are also useful to construct subdivision algorithms for surfaces of any smoothness order at extraordinary points. This revised version was published online in August 2006 with corrections to the Cover Date.     

Precision spectroscopy at heavy ion ring accelerator SIS300

Unique spectroscopic possibilities open up if a laser beam interacts with relativistic lithium-like ions stored in the heavy ion ring accelerator SIS300 at the future Facility for Antiproton and Ion Research FAIR in Darmstadt, Germany. At a relativistic factor γ = 36 the ²P_1/2 level can be excited from the ²S_1/2 ground state for any element with frequency doubled dye-lasers in collinear geometry. Precise transition energy measurements can be performed if the fluorescence photons, boosted in forward direction into the X-ray region, are energetically analyzed with a single crystal monochromator. The hyperfine structure can be investigated at the ²P_1/2−²S_1/2 transition for all elements and at the ²P_3/2−²S_1/2 transition for elements with Z≤50. Isotope shifts and nuclear moments can be measured with unprecedented precision, in principle even for only a few stored radioactive species with known nuclear spin. A superior relative line width in the order of 5·10⁻⁷ may be feasible after laser cooling, and even polarized external beams may be prepared by optical pumping.     

Linear and Hyperbranched Poly(arylene ether)s from a New Semifluorinated AB Monomer

A new trifluoromethyl-activated AB monomer has been successfully synthesized by Pd-initiated coupling of 4-bromo anisole with 4-fluoro-3-trifluoromethylphenylboronic acid followed by demethylation. The monomer leads to a semifluorinated poly(arylene ether) by nucleophilic displacement polymerization reaction. The AB monomer has been further copolymerized with a corresponding AB ₂ monomer to form the corresponding semifluorinated hyperbranched (hb) poly(arylene ether). The resulting linear and hb poly(arylene ether)s exhibited weight average molecular weight of 75700 and 144100 g/mol, respectively. The hb copolymer exhibited better solubility in different organic solvents compared to the linear poly(arylene ether). The polymers showed excellent thermal stability up to 522°C at 10% wt loss in air and glass transition temperatures as high as 187°C. The mechanical properties of the linear poly(arylene ether) film 1a exhibited tensile strength at break of 89 MPa, elongation at break of up to 3% and a Young’s modulus value of 2.66 GPa. The films of the polymers were hydrophobic in nature and showed water contact angle as high as 93.6°.