Factoring of positive definite functions on semigroups

No abstract. June 15,1999     

Ionic conductivity of pure and doped Li3N

The ionic conductivity of Li₃N crystals doped with various metal ions (magnesium, copper and aluminum) or hydrogen has been investigated. The metal ions have a negative effect on the conductivity whereas hydrogen increases it. The intrinsic Li⁺ ionic conductivity of pure Li₃N is (2·-4)×10^-4Ω^-1cm^-1 at room temperature with an activation energy of 0.26?0.27 eV. Doping with hydrogen to a maximum level of 0.5?1.0 atom% results in a conductivity of 6×10^-3Ω^-1cm^-1 and an activation energy which has been lowered to 0.20 eV. A model is proposed for the action of hydrogen whereby the Li-N bonds next to an NH^2- group are weakened thereby facilatating the creation of Li⁺ Frenkel defects and the vacancy migration. Hydrogen-doped Li₃N is termed an enhanced intrinsic conductor.     

Method of moments on semigroups

If ( _j ) is a sequence of measures onR ^k having momentss _n ( _j ) of all ordersnN ₀ ^k and if for eachnN ₀ ^k the sequence (s _{n j} )) _jN converges to somet _n R then some subsequence of ( _j ) converges weakly to a measure with moments of all orders satisfyings _n ()=t _n for allnN^0/k . Thisindeterminate method of moments and the continuity theorems in probability theory suggest a common generalization, dealing with a commutative semigroupS, with involution and a neutral element, and measures on the dual semigroupS ^* ofcharacters on S—hermitian multiplicative complex functions not identically zero. In this setting, a continuity theorem holds for measures on the set of bounded characters,⁽²⁾ and an indeterminate method of moments whenS is finitely generated.⁽²⁾ The latter result is generalized in the present paper to the case of arbitraryS. This leads to a generalization of Haviland's criterion for theK-moment problem, and to a continuity theorem for the so-called perfect semigroups.     

Calculation of the nonlinear electric susceptibility of benzene

We calculate the various components of the third-order nonlinear electric susceptibility of the benzene molecule, starting from a CNDO wavefunction. Our theoretical result for the space-fixed nonlinear third-order susceptibility is 6.15 × 10^?36 esu, the corresponding experimental value is 1.58 × 10^?36 esu. We also estimate the contributions from the σ and π electrons to the total susceptibility.     

Hybrid composites of monodisperse pi-conjugated rodlike organic compounds and semiconductor quantum particles

Composite materials of quantum particles (Q-particles) arranged in layers within crystalline powders of pi-conjugated, rodlike dicarboxylic acids are reported. The synthesis of the composites, either as three-dimensional crystals or as thin films at the air-water interface, comprises a two-step process: 1) The preparation of the Cd salts 6 (Cd), 8 (Cd) or Pb salts 6 (Pb), 8 (Pb) of the oligo(p-phenyleneethynylene)dicarboxylic acids 6 (H), 8 (H), in which the metal ions are arranged in ribbons and are separated by the long axis of the organic molecules, as demonstrated by X-ray powder diffraction analysis of the solids and grazing incidence X-ray diffraction analysis of the films on water. 2) Topotactic solid/gas reaction of these salts with H(2)S to convert the metal ions into Q-particles of CdS or PbS embedded in the organic matrix that consists of the acids 6 (H) and 8 (H). These hybrid materials have been characterized by X-ray photoelectron spectroscopy and transmission electron microscopy.     

Transition metal-catalyzed hetero-[5 + 2] cycloadditions of cyclopropyl imines and alkynes: dihydroazepines from simple,readily available starting materials

The first example of a transition metal-catalyzed hetero-[5 + 2] cycloaddition reaction is described. Use of cyclopropyl imines as five-atom components, an alkyne as a two-carbon component, and a Rh(I) catalyst enables a new route to dihydroazepines. This new hetero-[5 + 2] cycloaddition works well with aldimines, ketimines, and with substituted cyclopropanes and affords the desired dihydroazepines in excellent yields as single regioisomers. Use of serial imine formation/aza-[5 + 2] cycloaddition generates the desired dihydroazepines in one operation from three commercially available starting materials. The reaction has been scaled to give gram quantities of dihydroazepine.     

Interactions and dispersion stability of aluminum oxide colloidal particles in electroless nickel solutions in the presence of comb polyelectrolytes

The effect of comb polyelectrolytes on the dispersion stability of colloidal alumina particles in DI water and commercial electroless nickel (EN) solutions was investigated. Adsorption of polyelectrolytes and major EN components onto colloidal alumina was assessed by TGA, chemical analysis, and zeta potential measurements. Zeta potential measurements were made during titrations of comb-polyelectrolyte-stabilized dispersions with EN solutions to full ionic strength for the first time. The compilation of titration curves made with varying amounts of comb polyelectrolytes provides high resolution and novel insight into the particle/surfactant/EN systems. Continuous decrease in particle/EN components surface interactions with the increase in comb polyelectrolyte coverage is observed. Laser diffraction measurements reveal steric stabilization of nano- and submicronmeter alumina dispersions in both DI water and EN solutions with >7 wt% and >2 wt% comb polyelectrolyte, respectively.