Filament sets, aposyndesis, and the decomposition theorem of Jones

Applications of the work introduced by the authors in a recent article, Filament sets and homogeneous continua, are given to aposyndesis and local connectedness. The aposyndetic decomposition theorem of Jones is generalized to spaces with the property of Kelley.

     

The Hyers-Ulam stability of nonlinear recurrences

We show some Hyers-Ulam type stability results for some nonlinear recurrences in metric spaces.     

Identification of the Isomeric Dideutero p-Benzoquinones by 13C-H and 13C-D Coupling Constants

2,5- and 2,6-dideuterobenzoquinone-1,4 were prepared by a direct catalytic (NaBD₄/PdCl₂) exchange of bromine in the corresponding dibromo derivatives and the subsequent oxidation with Ag₂O. The structure of the products was unambiguously established by proton-carbon and deuteron-carbon splitting pattern of their NMR spectra.     

Photocatalytic properties of Ta-doped TiO2

Ionics - This work reports the effect of tantalum (0.1–1 at.% Ta) on the photocatalytic performance of TiO2 annealed at 1373 and 1673 K in air. It was shown that addition of...     

A novel hydroxy functionalized polyester obtained by ring opening copolymerization of L‐lactide with a pyrolysis product of cellulose

A hydroxylactone ((1R,5S)‐1‐hydroxy‐3,6‐dioxabicyclo [3.2.1] octan‐2‐one, abbreviated as LAC) obtained from catalytic pyrolysis of cellulose was investigated as a monomer in the synthesis of polyesters by ring‐opening polymerization (ROP) with L ‐lactide. Although stannous octoate resulted inactive, ROP initiated by zirconium (IV) acetylacetonate afforded novel copolyesters from LAC and lactide mixtures in the bulk at 110 °C. Copolymers were obtained with different LAC content (from 19 to 45%) with a random microstructure as established by detailed NMR analysis. FTIR spectrometry confirmed the presence in the polymer chain of the OH groups originally present in LAC, which do not react during polymerization due to steric hindrance and inter/intramolecular hydrogen bonding. Reaction with trichloroacetylisocyanide proved that OH groups of the polyesters can be readily derivatized. The application of LAC as a comonomer enables the insertion of the alcohol functionality in polylactide avoiding protection/deprotection steps and potentially expanding the realm of biomaterials affordable from carbohydrate feedstock. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 247–257, 2009     

High-efficiency coupling structure for a single-line-defect photonic-crystal waveguide

We present the design and fabrication of a planar structure for coupling light from a multimode feed waveguide into a single-line-defect photonic-crystal waveguide. Finite-difference time-domain calculations predict a coupling efficiency of greater than 90%, and preliminary experimental results indicate successful coupling through a single-line-defect photonic-crystal waveguide. Device design, fabrication, and characterization are presented.     

Novel and elegant modes of SbF3 coordination in the complexes with azacrown ethers

Synthesis and single-crystal X-ray structures are recorded for three adducts of SbF₃ with different azacrown ethers. [SbF₃·H₂O·L₁], 1, (L₁ = 12,13-benz-1,10-di(azamethyl)-4,7-dioxacyclotetradecane-1,14-dione), triclinic, , a = 11.234(2), b = 11.691(2), c = 8.869(2) Å, = 94.66(3), = 113.12(3), = 67.82(3)°, Z = 2. [SbF₃Cl·H₂O·(HL₂)], 2, (L₂ = monoaza-18-crown-6), orthorhombic, P2₁2₁2₁, a = 8.763(2), b = 13.003(3), a = 16.836(3) Å, Z = 4. [(SbF₃)₂Cl₂·(H₂L₃)], 3, (L₃ = 1,10-diaza-18-crown-6), triclinic, , a = 8.284(2), b = 9.016(2), c = 9.134(2) Å, = 82.92(3), = 65.24(3), = 63.38(3)°, Z = 1. All three structures include SbF₃ neutral molecules in the pyramidal mode and the antimony second coordination sphere is completed up to six in different fashions. In 1 the dimeric (SbF₃)₂ adducts are made up due to the involvement of the symmetry-related fluorine atom in coordination. The distorted octahedron is then completed by water molecule and carbonyl oxygen of L₁. The neutral molecules are joined by coordination and hydrogen bonds in the infinite ribbons. 2 and 3 are both comprised of neutral and charged species also bounded via coordination and hydrogen bonds. L₂ and L₃ in the complexes adopt the form of single and double-charged cations, respectively. The inorganic backbone unites the neutral SbF₃ molecules and chloride anions in the alternative mode. The sixth coordination site in the antimony polyhedron is completed by the water molecule in 2 and the ethereal oxygen atom in 3. Alignment of the inorganic entities within the structures of 2 and 3 is strikingly similar. Hydrogen bonding patterns are discussed.     

Anisochronism of large geminal groups in the 1H and 13C nuclear magnetic resonance spectra

The role of steric factors in magnetic non-equivalence anisochronism of complex geminal groups and of their fragments in compounds of the general formula RCH(Ph)CH(COOR′)₂ has been investigated. CMR anisochronism is more sensitive to conformational and other steric changes than is PMR.