Pin c and Lipschitz Structures on Products of Manifolds

The topological condition for the existence of a pin ^c structure on the product of two Riemannian manifoldsis derived and applied to construct examples of manifolds havingthe weaker Lipschitz structure, but no pin ^c structure.An example of a five-dimensional manifold with this property is given;it is pointed out that there are no manifolds of lower dimension withthis property.     

Kinetic stabilization of primary hydrides of main group elements. The synthesis of an air-stable, crystalline arsine and silane

Two new, "user-friendly" derivatives of triptycene containing AsH(2) and SiH(3) fragments were synthesized. Both solids are crystalline, air-stable compounds characterized by elevated melting points and resistance toward moisture. The highly reactive As-H and Si-H bonds are protected by the presence of the surrounding phenylene hydrogen atoms, which ensure a remarkable kinetic stabilization of these primary hydrides. After X-ray irradiation of a single crystal of triptycenesilane, a persistent silyl radical was trapped and characterized.     

Self-catalytic Michael reaction of enolizable carbonyl compounds. A facile route to α-methylene-δ-valerolactones

Various dicyclohexylammonium 2-phosphono-5-oxoalkanoates 3 were prepared by the Michael reaction of enolizable carbonyl compounds with the acrylate 1. The corresponding 2-phosphono-5-oxoalkanoic acids 4 were converted into α-phosphono-δ-valerolactones 6. The products were shown to be useful substrates for the synthesis of α-methylene-δ-valerolactones 7 by the Horner-Wadsworth-Emmons reaction.     

Regioselective pyridination of m-benziporphyrin

[reaction: see text] Reaction of tetraaryl-m-benziporphyrin with pyridine and silver tetrafluoroborate yields 22-pyridiniumyl-m-benziporphyrin as the only substitution product. This compound is further rearranged to a fused m-benziphlorin containing a 4a-azafluorene fragment. A mechanism involving a high-valent silver complex is proposed for the pyridination reaction.     

Equal treatment, symmetry and Banzhaf value axiomatizations

The Banzhaf value is the only value satisfying the equal treatment, dummy player and marginal contributions conditions and neutrality of some linear operators on the spaces of games. Under some of these neutrality assumptions, equal treatment can be replaced by even weaker conditions. For linear values having the dummy player property, equal treatment is equivalent to symmetry. All these properties together imply the marginal contributions condition, but in some Banzhaf value axiomatizations marginal contributions cannot be a substitute for linearity. Received: December 1997/Revised version: May 2001     

Propagation of the radiation field excited on discontinuities of optical waveguides

Numerical and semi-analytical techniques widely used to model the complicated structure of the radiation field excited on sharp and smooth discontinuities of a dielectric slab are reviewed. Comparative analysis of the radiation field modelling by the fast Fourier transformation-beam propagation method (FFT-BPM) and the finite difference(FD)-BPM is presented. Propagation of a higher-order mode through the cut-off cross-section of smooth and sharp discontinuities is simulated numerically by the FD-BPM, the total field is analysed using the leaky mode approach.     

Synthesis and characterization of quasi-two-coordinate transition metal dithiolates M(SAr*)2 (M = Cr, Mn, Fe, Co, Ni, Zn; Ar* = C6H3-2,6(C6H2-2,4,6-Pri3)2

A sequence of first row transition metal(II) dithiolates M(SAr)(2) (M = Cr(1), Mn(2), Fe(3), Co(4), Ni(5) and Zn(6); Ar = C(6)H(3)-2,6-(C(6)H(2)-2,4,6-Pr(i)(3))(2)) has been synthesized and characterized. Compounds 1-5 were obtained by the reaction of two equiv of LiSAr with a metal dihalide, whereas 6 was obtained by treatment of ZnMe(2) with 2 equiv of HSAr. They were characterized by spectroscopy, magnetic measurements, and X-ray crystallography. The dithiolates 1, 2, and 4-6 possess linear or nearly linear SMS units with further interactions between M and two ipso carbons from C(6)H(2)-2,4,6-Pr(i)(3) rings. The iron species 3, however, has a bent geometry, two different Fe-S distances, and an interaction between iron and one ipso carbon of a flanking ring. The secondary M-C interactions vary in strength in the sequence Cr(2+) approximately Fe(2+) > Co(2+) approximately Ni(2+) > Mn(2+) approximately Zn(2+) such that the manganese and zinc compounds have essentially two coordination but the chromium and iron complexes are quasi four and three coordinate, respectively. The geometric distortions in the iron species 3 suggested that the structure represents the initial stage of a rearrangement into a sandwich structure involving metal-aryl ring coordination. The bent structure of 3 probably also precludes the observation of free ion magnetism of Fe(2+) recently reported for Fe{C(SiMe(3))(3)}(2). DFT calculations on the model compounds M(SPh)(2) (M = Cr-Ni) support the higher tendency of the iron species to distort its geometry.     

Amplification of changes of a thin film's macromolecular structure into macroscopic reaction-diffusion patterns

A reaction-diffusion process induced from a micronetwork geometry amplifies changes in the molecular structure of a thin gel film into macroscopic readout patterns. When the gel undergoes a helix-to-coil phase transition, the patterns formed by RD switch from symmetry-broken to symmetric ones. Theoretical analysis explains how the system reconfigures internally in response to mass transfer between the applied network and the probed film.     

Conformational flexibility of nickel(II) benziporphyrins

(1)H NMR spectra of three paramagnetic Ni(II) complexes of benziporphyrins have been investigated in a broad temperature range. For the m- and p-benziporphyrin complexes, the line widths of certain signals exhibit an unusual temperature dependence characteristic of a dynamic process. This behavior is interpreted in terms of an equilibrium in which one of the forms is present at a very small concentration and cannot be observed directly. For the benziporphodimethene complex, the two exchanging forms are present at comparable concentrations and can yield separate signals in the slow exchange limit. To account for the observed exchange process, a mechanism is proposed involving the motion of the phenylene moiety. This hypothesis is further explored with DFT modeling, which indicates that the postulated conformers are thermally accessible.