Splitting of n-fold rotationally symmetric graphs

R. A. Davidson's rules for splitting an n-fold rotationally symmetric graph can be derived from a unitary transformation on the adjacency matrix. The McClelland and D'Amato rules are special cases with n = 2 and n = 3, respectively.     

Taxumairols X--Z,new taxoids from Taiwanese Taxus mairei

In addition to 19-dydroxybaccatin III, 1beta-hydroxy-5 alpha-deacetylbaccatin I, taxayuntin G and 13-O-deacetyltaxumairol Z (4), three new taxane diterpenoids, taxumairols X (1), Y (2), Z (3) have been isolated from extracts of the Formosan Taxus mairei (LEMEE & LEVL.) S. Y. HU. Compounds 1-2 belong to the 11(15-->1)-abeo-taxane system, having a tetrahydrofuran ring at C-2, C-3, C-4 and C-20. The new compound 3 and 4, which was misidentified previously are derivatives of 11(15-->1)-abeo-taxane with an intact oxirane system. The structures of compounds 1-4 were elucidated on the basis of extensive two dimensional (2D)-NMR analysis.     

Infrared and electronic spectra of copper (II) complex of maleonitriledithiolate and 4,4'-dimethyl-2, 2'-bipyridine and their theoretical studies

The molecular structure and binding, as well as infrared and electronic spectroscopic properties for the title complex Cu(mnt)(dmbpy)(mnt(2-)=maleonitriledithiolate, dmbpy=4,4'-dimethyl-2,2'-bipyridine) were studied in this paper. With semi-empirical PM3 and non-empirical DFT (B3LYP/6-311G*) methods, the molecular geometry of the complex was optimized and corresponding vibrational spectra in the gaseous state were obtained. The calculated results derived from DFT were more reasonable than those from PM3. The point group of Cu(mnt)(dmbpy) in isolated gaseous state was C(2), in which Cu(II) adopted a distorted tetrahedral geometry and the dihedral angle between the N(2)Cu and S(2)Cu planes was about 29.814 degrees. And a complete assignment to the IR spectra of such a complicated molecule was exhibited. With ZINDO/S method an electronic spectrum was calculated. The results showed that the calculated values generally agreed with the observed ones. And a detailed explain was made on its electronic spectra.     

Ruthenium-catalyzed cyclization of 3-en-1-ynyl imines with nucleophiles via tandem 5-exo-dig cyclization and nucleophilic addition

Treatment of 3-en-1-ynyl imines with TpRuPPh₃(CH₃CN)₂PF₆ catalyst (1 mol %) in DCE (50 °C, 6 h) effected catalytic cyclization with suitable nucleophiles and gave functionalized pyrroles in good yields. The reaction mechanism is proposed to proceed via (2-pyrrolyl)carbenoid intermediates derived from 5-exo-dig cyclization. This catalytic reaction works well with various nucleophiles, including water, alcohols and anilines.     

Synthesis, crystal structure and magnetic property of a new nickel selenite chloride: Ni5(SeO3)4Cl2

The new nickel selenite chloride, Ni₅(SeO₃)₄Cl₂, was obtained by high-temperature solid state reaction of NiCl₂, Ni₂O₃ and SeO₂ in a 1:2:4 molar ratio at 700 °C in an evacuated quartz tube. Its structure was established by single-crystal X-ray diffraction. Ni₅(SeO₃)₄Cl₂ crystallizes in the triclinic system, space group P-1 (No. 2) with cell parameters of a=8.076(2), b=9.288(2), c=9.376(2) Å, α=101.97(3), β=105.60(3), γ=91.83(3)° and Z=2. All nickel(II) ions in Ni₅(SeO₃)₄Cl₂ are octahedrally coordinated by selenite oxygens or/and chloride anions (([Ni(1)O₅Cl], [Ni(2)O₄Cl₂], [Ni(3)O₅Cl], [Ni(4)O₆] and [Ni(5)O₄Cl]). The structure of the title compound features a condensed three-dimensional (3D) network built by Ni(II) ions interconnected by SeO₃²⁻ anions as well as Cl⁻ anions. Magnetic property measurements show strong antiferromagnetic interaction between nickel(II) ions.     

On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations

Summary This paper is a continuation of our previous work [10] on projection methods. We study first existing higher order projection schemes in the semidiscretized form for the Navier-Stokes equations. One error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent Neumann boundary condition satisfied by the pressure approximations. We then propose a penalty-projection scheme for which we obtain improved error estimates.This work is partially supported by NSF grant MS-8802596.