Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to the editor-in-chieX Chandler Davis.     

Synthesis of silylene-vinylene oligomers via catalytic polycondensation of divinyldimethylsilane

Acyclic diene polymerization (ADP) of divinyldimethylsilane in the presence of ruthenium RuCl₂(PPh₃)₃ and rhodium [RhCl(cod)]₂ catalysts led predominantly to linear silylene-vinylene oligomers (M_n = 1510 and M_w/M_n = 1.19) if the ruthenium catalyst was used or to mixture of cyclic and linear oligomers if rhodium complex was catalyst. © 1996 John Wiley & Sons, Inc.     

A new synthetic approach to 5-dethia-4-methyl-5-oxacephems

Starting from (l)-ethyl lactate and 4-vinyloxy-azetidin-2-one the diastereomeric (4S,6R)- and (4S,6S)-4-methyl-5-oxa-3-methylene and 3-oxo-cephams were obtained. The formation of the cepham skeleton proceeds with a diastereomeric excess up to 80%, depending on catalyst and reaction conditions. For comparison, the corresponding racemic cephams lacking a methyl at C-4 or with a gem-dimethyl group at C-4 were synthesized.     

Phase transitions in the atomic, electronic, and magnetic subsystems of LaSrMnO films versus the synthesis temperature

The evolution of the cluster structure in amorphous LaSrMnO films as synthesis temperature T _s increases from 20 to 300°C is considered. Two order-disorder phase transitions with different scale parameters are observed. One of them, the aggregation of disordered atoms into small (～20 Å) amorphous clusters at T _s = 100°C, shows up as a sharp increase in the intensity of diffuse X-ray scattering (diffuse halo 1) with a simultaneous suppression of incoherent (background) scattering. At T _s > 150°C, disordering dominates (I _incoh = I _max) until the next stage of ordering sets in at T _s = 250?300°C. At this stage, the crystalline phase forms from large (>100 Å) crystalline clusters. This amorphous-crystalline phase transition is characterized by the appearance of Debye lines and a reduction of the halo intensity. The structural phase transition to long-range order is accompanied by a decrease in the LaSrMnO resistivity from 10¹⁰ to 10 Ω cm and a change from the tunneling mechanism of conductivity involving metallic clusters (which is typical of granulated systems) to the hopping mechanism with a hop variable length following the Mott law ρ ～ exp(T ^?1/4). In the magnetic subsystem, the paramagnetic-ferromagnetic phase transition occurs.     

On the Fefferman class of metrics associated with a three-dimensional CR space

We derive the explicit forms of Fefferman's metric for a Cauchy-Riemann space admitting a solution of the tangential Cauchy-Riemann equation and of the corresponding Weyl tensor. We show that its Petrov type is 0 in the case of the hyperquadric or N in all other cases, and that the Fefferman class of metrics does not contain any nonflat solution of Einstein's vacuum equations with cosmological constant.Work supported in part by the Polish Ministry of Science and Higher Education, Research Problem CPBP 01.03.