On Stöhr-Voloch's proof of Weil's theorem

LetX be a smooth, projective curve of genusg defined over a finite field. Then there exists a finite extension fieldk=F _q such that, for all sufficiently largen, (1)X imbeds in P ⁿ in such a way that the set of pointsx ofX mapped via Frobenius into the osculating hyperplane ofX atx is the support of a positive divisor and (2) the numberN of points inX(k) satisfies

Approximate neutrality of large-Z ions

LetN(Z) denote the number of electrons which a nucleus of chargeZ can bind in non-relativistic quantum mechanics (assuming that electrons are fermions). We prove thatN(Z)/Z1 asZ.Research partially supported by the NSERC under Grant NA7901 and by the USNSF under Grants DMS-8416049 and PHY 85-15288-A01     

Multi-iron wells-Dawson heteropolytungstates. Electrochemical probing of siderophoric behavior in sandwich-type complexes

The demetalation process of 10 multi-iron Wells-Dawson polyoxometalates is studied by cyclic voltammetry and controlled potential coulometry. Eight sandwich-type complexes (alphaalphaalphaalpha-Na(16)[(NaOH(2))(2)(Fe(III))(2)(X(2)W(15)O(56))(2)], alphaalphabetaalpha-Na(14)[(NaOH(2))(Fe(III)OH(2))(Fe(III))(2)(X(2)W(15)O(56))(2)], alphabetabetaalpha-Na(12)[(Fe(III)OH(2))(2)(Fe(III))(2)(X(2)W(15)O(56))(2)], and alphabetabetaalpha-Na(14)[(Mn(II)OH(2))(2)(Fe(III))(2)(X(2)W(15)O(56))(2)] (where X = P(V) or As(V))) and two monomeric complexes (alpha-Na(11)[(P(2)(Fe(III)Cl)(2)(Fe(III)OH(2))W(15)O(59))] and alpha-Na(11)[(As(2)(Fe(III)Cl)(2)Fe(III)OH(2))W(15)O(59))]) were selected for this study. All 10 complexes show Fe(III) waves which are well-separated from the redox activity of the W(VI) centers. At room temperature and under mild conditions, iron release from the complexes is observed upon reduction of the Fe(III) centers. This release is controlled by the ionic strength of the medium, the nature and concentration of the anions present in the supporting electrolyte, and by the pH of the solution. This behavior parallels those described for most siderophores which depend on the same parameters.     

Easy preparation of cobalt corrole and hexaphyrin and isolation of new oligopyrroles in the solvent-free condensation of pyrrole with pentafluorobenzaldehyde

[reaction: see text] Following the discovery that meso-substituted corroles are formed in solvent-free condensation of pyrrole with aldehydes, we demonstrate that a small variation in the methodology is suitable for facile synthesis of cobalt(III) corrole and hexaphyrin. These compounds, as well as three noncyclic products, were fully characterized by spectroscopy and X-ray crystallography.     

Highly conjugated p-quinonoid pi-extended tetrathiafulvalene derivatives: a class of highly distorted electron donors

A new class of pi-extended TTF-type electron donors (11 a-c) has been synthesized by Wittig-Horner olefination of bianthrone (9) with 1,3-dithiole phosphonate esters (10 a-c). In cyclic voltammetry experiments, donors 11 a-c reveal a single, electrochemically irreversible oxidation-yielding the corresponding dicationic products-at relatively low oxidation potentials (approximately 0.7-0.8 V). Theoretical calculations, performed at the DFT level (B3 P86/6-31 G*), predict a highly-folded C(2h) structure for 11 a. In the ground state, the molecule adopts a double saddle-like conformation to compensate the steric hindrance. The calculations suggest that the intramolecular charge transfer associated with the HOMO-->LUMO transition is responsible for an absorption band observed above 400 nm. While the radical cation 11 a*+ retains the folded C(2h) structure predicted for the neutral molecule as the most stable conformation, the dication 11 a(2+) has a fully aromatic D(2) structure, formed by an orthogonal 9,9'-bianthryl central unit to which two singly-charged dithiole rings are attached. The drastic conformational changes that compounds 11 undergo upon oxidation account for their electrochemical properties. By means of pulse radiolysis measurements, radical-induced one-electron oxidation of 11 a-c was shown to lead to the radical cation species (11 a-c*+), which were found to disproportionate with generation of the respective dication species (11 a-c(2+)) and the neutral molecules (11 a-c).     

Direct preparation and structure determination of tertiary and secondary amine boranes from primary or secondary amine boranes

New secondary and tertiary amine borane derivatives were prepared in a one-pot reaction starting from primary amine boranes. The reaction involves treatment of an amine borane with 2 equivalents of s-BuLi at −78 °C. In general, mixtures of mono and di metallated products were obtained. Alkyl iodides and benzyl chloride reacted with the lithiated amine, but aldehydes and ketones were reduced. Conversion was high as determined by NMR, but moderate to low yields were obtained after chromatography, possibly due to decomposition on silica. Crystal structures were obtained for the compounds 3a, 3b and 3c.     

Copolymerization behavior of vinylimidazolium salts

Copolymerization studies of cationic monomers have been reported in the literature to yield wide variations in reactivity ratios and Q–e values, depending on the comonomer and the nature of the solvent. In this work are presented the copolymerization characteristics of a variety of vinylimidazolium salts in both water and ethanol solution. From these studies, the effect of solvent polarity, of substitution at the imidazolium 2-position, of the type of counterion, and of the hydrophilic–hydrophobic character of the monomeric salts could be ascertained. The results of the study are consistent with other related investigations, in that solvent polarity and comonomer both strongly affected copolymerization.