Rigidity of circle domains whose boundary hasσ-finite linear measure

Summary Let be a circle domain in the Riemann sphere whose boundary has -finite linear measure. We show that is rigid in the sense that any conformal homeomorphism of onto any other circle domain is equal to the restriction of a Möbius transformation. Previously, Kaufman and Bishop have independently found examples of non-rigid circle, domains whose boundary is a Cantor set of (Hausdorff) dimension one.Oblatum 19-VI-1992 & 2-IV-1993Supported by NSF and Sloan Foundation     

Modelling of the processes of ultrafine SiO2 production under thermal plasma conditions

The production of ultrafine silica particles is examined by modelling the processes in a flow plasma reactor. The model is based on the authors' experimental data on silica sand processing by use of thermal arc plasma. The free-molecular coagulation is assumed to be the dominant process for particle growth. This is carried out at fast cooling of the vapour, during its mixing with oxygen. The particle size distribution functions are calculated, and the influence of the chemical monomer generation and the mixing on their behavior is investigated. Comparison of the calculated and the experimental mean particle size is made.List of symbols C _nl collision frequency function, cm³/s - d _m mean median diameter, nm - F _LN(d) integral form of the particle size distribution function,% - g(t) mixing function - k Boltzmann's constant - k ₁,k,k rate coefficients, cm³/s - k ₂,k ₃ rate coefficiens, cm⁶/s - m mass of the monomer, g - M number of groups - T absolute temperature, K - T ₀ temperature of the hot vapour, K - T _E temperature of SiO₂ condensation, K - t time, s - t _m mixing time, s - t _c colling time, s - z ₀ monomer concentration, cm^–3 - z _n ,z _l concentrations of particles in groups, cm^–3 - z _n total number concentration of particles (n=0, 1, M), cm^–3 - z _n /(z _n )(log d _n+1 –logd _n) differential form of particle size distribution function - w _i reaction rates (i=1, 2, 3), cm^–3/s - , cooling rates, K/s - coefficient of proportionality - _SiO conversion rate of SiO,% - coefficient determined from the cooling rate, s^–1 - mass density of the particles, g/cm³ - standard deviation The authors gratefully acknowledge Prof. L. S. Polak from the Institute of Petrol Chemical Synthesis, Russian Academy of Science, for helpful discussions.     

The structure of magnesium alanate

Mg(AlH(4))(2) was produced as a nanocrystalline powder by metathesis of NaAlH(4) and MgCl(2). Starting with a structure estimation which was developed from an evaluation of FTIR data and comparison of structural properties of two solvent adducts, quantum chemical calculations were performed on the density functional theory (DFT) level. The calculated atomic positions were used to simulate an X-ray powder diffraction pattern, based on a trigonal unit cell. The simulated pattern was congruent to experimental data. Thus, magnesium alanate exhibits a CdI(2) layer structure, the layers being formed by Mg atoms occupying the Cd sites and AlH(4) tedrahedra occupying the sites of the iodine atoms in CdI(2).     

A new color of the synthetic chameleon methoxyallene: synthesis of trifluoromethyl-substituted pyridinol derivatives: an unusual reaction mechanism, a remarkable crystal packing, and first palladium-catalyzed coupling reactions

Addition of lithiated methoxyallene to pivalonitrile afforded after aqueous workup the expected iminoallene 1 in excellent yield. Treatment of this intermediate with silver nitrate accomplished the desired cyclization to the electron-rich pyrrole derivative 2 in moderate yield. Surprisingly, trifluoroacetic acid converted iminoallene 1 to a mixture of enamide 3 and trifluoromethyl-substituted pyridinol 4 (together with its tautomer 5). A plausible mechanism proposed for this intriguing transformation involves addition of trifluoroacetate to the central allene carbon atom of an allenyl iminium intermediate as crucial step. Enamide 3 is converted to pyridinol 4 by an intramolecular aldol-type process. A practical direct synthesis of trifluoromethyl-substituted pyridinols 4, 10, 11, and 12 starting from typical nitriles and methoxyallene was established. Pyridinol 10 shows an interesting crystal packing with three molecules in the elementary cell and a remarkable helical supramolecular arrangement. Trifluoromethyl-substituted pyridinol 4 was converted to the corresponding pyridyl nonaflate 13, which is an excellent precursor for palladium-catalyzed reactions leading to pyridine derivatives 14-16 in good to excellent yields. The new synthesis of trifluoromethyl-substituted pyridines disclosed here demonstrates a novel reactivity pattern of lithiated methoxyallene which is incorporated into the products as the unusual tripolar synthon B.     

Direct calculation of interconversion barriers in dynamic chromatography and electrophoresis: Isomerization of captopril

Dynamic capillary electrophoresis (DCE) and direct calculation of the rate constants of isomerization has been applied to determine the cis-trans isomerization barriers of the angiotensin-converting enzyme inhibitor captopril. The separation of the rotational cis-trans isomeric drug has been performed in an aqueous 50 mM borate buffer at pH 9.3. Interconversion profiles featuring plateau formation, peak-broadening, and peak coalescence were observed. To determine the rate constants of the forward and backward reaction (k(cis-->trans) and k(trans-->cis)) of the isomerization process in dynamic capillary electrophoresis, a novel straightforward calculation method using the experimental parameters plateau height, h(plateau), peak width at half height w(h), the total migration times of the cis-trans isomers t(R) and the electroosmotic break-through time t(0) as well as the peak ratio of the cis-trans isomers is presented for the first time. From temperature dependent measurements the rate constants k(cis-->trans) and k(trans-->cis) and the kinetic activation parameters DeltaG( not equal), DeltaH( not equal), and DeltaS( not equal) of the cis-trans isomerization of captopril were obtained. From the activation parameters the isomerization barriers of captopril at 37 degrees C under basic conditions were calculated to be DeltaG( not equal) (cis-->trans) = 90.3 kJ.mol(-1)and DeltaG( not equal) (trans-->cis) = 90.0 kJ.mol(-1*).