The generation and classification of tile-k-transitive tilings of the Euclidean plane,the sphere and the hyperbolic plane

Algorithms based on the theory of Delaney-Dress symbols are discussed that can be used to recursively produce all possible equivariant types of tile-k-transitive tilings of the Euclidean plane, the sphere and the hyperbolic plane, for any (reasonable)k. A number of results can be obtained using computer implementations of the algorithms.     

Chern-Simons theory with finite gauge group

We construct in detail a 2+1 dimensional gauge field theory with finite gauge group. In this case the path integral reduces to a finite sum, so there are no analytic problems with the quantization. The theory was originally introduced by Dijkgraaf and Witten without details. The point of working it out carefully is to focus on the algebraic structure, and particularly the construction of quantum Hilbert spaces on closed surfaces by cutting and pasting. This includes the Verlinde formula. The careful development may serve as a model for dealing with similar issues in more complicated cases.The first author is supported by NSF grant DMS-8805684, an Alfred P. Sloan Research Fellowship, a Presidential Young Investigators award, and by the O'Donnell Foundation. The second author is supported by NSF grant DMS-9207973     

Etude des conditions d'accès au triazino-1,2,4-[4,5-b] indazole

1,2,4-Triazino[4,5-b]indazol-1(2H)one and its derivatives were prepared by transposition of 3-[2-(-1,3,4-oxadiazolyl)]indazole or by ring closure of indazole ethoxymethylidenehydrazides. The synthesis of 1,2,3,4-tetrahydro-l,2,4-triazino[4,5-b]indazole-1,4-dione was achieved by cyclising the N-carbethoxyhydrazide of indazole-3-carboxylic acid and the synthesis of 1,2,4-triazino-[4,5-b]indazol-4(3H)one was made by cyclising the N-carbethoxy-hydrazone of indazole-3-carboxaldehyde. The Oxydation of 1,2,4-triazino[4,5-b]indazole-l(2H)thione gave 1,2,4-triazino-[4,5-b]indazoles. Nmr spectral data are reported.     

Polymeric flocculants processing by accelerated electron beams and microwave heating

Results obtained by accelerated electron beam, microwave and simultaneous microwave and electron beam application in the chemistry of acrylamide and acrylic acid copolymers (polymeric flocculants used for wastewater treatment) are presented. Comparative results concerning the molecular weight and Huggins’ constant for the acrylamide and acrylic acid copolymers obtained by classical heating, microwave heating, electron beam irradiation and simultaneous microwave and electron beam treatment are reported. Microwave heating produces high water solubility of the polymeric flocculants but median molecular weight values. Electron beam irradiation gives high molecular weight values but associated with a cross-linked structure (poor water solubility) while microwave energy addition to electron beam energy gives simultaneously high molecular weight values and high water solubility.     

Stereochemically controlled synthesis of unsaturated acids via diphenylphosphinoyl (Ph2PO) -ketoacids

Acylation of phosphine oxide anions with derivatives of cyclic anhydrides or oxidative cleavage of cyclic allyl phosphine oxides gives Ph₂PO-ketoacids: reduction, separation of diastereoisomers, and completion of the Horner-Wittig reaction gives single isomers ($\text{E}$) or ($\text{Z}$) of unsaturated acids.     

Formation and structure of self-assembled monolayers of alkanethiolates on palladium

The adsorption of n-alkanethiols onto polycrystalline thin films of palladium containing a strong (111) texture produces well-organized, self-assembled monolayers. The organization of the alkane chains in the monolayer and the nature of the bonding between the palladium and the thiol were studied by contact angle measurements, optical ellipsometry, reflection absorption infrared spectroscopy (RAIRS), and X-ray photoelectron spectroscopy (XPS). The XPS data reveals that a compound palladium-sulfide interphase is present at the surface of the palladium film. The RAIR spectra, ellipsometry data, and wetting properties show that the palladium-sulfide phase is terminated with an organized, methyl-terminated monolayer of alkanethiolates. The local molecular environment of the alkane chains transitions from a conformationally disordered, liquidlike state to a mostly all-trans, crystalline-like structure with increasing chain length (n = 8-26). The intensities and dichroism of the methylene and methyl stretching modes support a model for the average orientation of an ensemble of all-trans-conformer chains with a tilt angle of approximately 14-18 degrees with respect to the surface normal and a twist angle of the CCC plane relative to the tilt plane of approximately 45 degrees. The SAMs are stable in air, although the sulfur present at the surface oxidizes in air over a period of 2-5 days at room temperature. The differences in chain organization between SAMs formed by microcontact printing and by solution deposition are also examined by RAIRS and XPS.     

Application of laser ablation–inductively coupled plasma-mass spectrometry (LA–ICP–MS) to investigate trace metal spatial distributions in human tooth enamel and dentine growth layers and pulp

Human tooth enamel provides a nearly permanent and chronological record of an individuals nutritional status and anthropogenic trace metal exposure during development; it might thus provide an excellent bio archive. We investigated the micro-spatial distribution of trace metals (Cu, Fe, Mg, Sr, Pb, and Zn) in 196×339 m² raster pattern areas (6.6×10⁴ m²) in a deciduous tooth using laser ablation-inductively coupled plasma-mass spectrometry (LA–ICP–MS). Ablated areas include prenatal and postnatal enamel, the neonatal line, the dentine–enamel junction (DEJ), dentine, and the dentine–pulp junction. Topographic variations in the surface elemental distribution of lead, zinc, strontium, and iron intensities in a deciduous tooth revealed heterogeneous distribution within and among regions. ⁴³Ca normalized elemental intensities showed the following order: Sr>Mg>>Zn>Pb>Fe>Cu. Elevated zinc and lead levels were present in the dental pulp region and at the neonatal line. This study demonstrates the ability of LA–ICP–MS to provide unique elemental distribution information in micro spatial areas of dental hard tissues. Elemental distribution plots could be useful in decoding nutrition and pollution information embedded in their bio apatite structure.Presented in part at the 2002 Winter Conference on Plasma Spectrochemistry, Scottsdale, AZ, January 6–12, 2002. The poster was selected as an outstanding poster presentation.     

Detailed analysis of α,ω-bis(4-hydroxybutyl) poly(dimethylsiloxane) using GPC-MALDI TOF mass spectrometry

In this study the prepolymer alpha,omega-bis(4-hydroxybutyl) poly(dimethylsiloxane), used in the formulation of oxygen permeable films, is evaluated by gel permeation chromatography (GPC) combined with matrix assisted laser desorption ionization (MALDI) time of flight (TOF) mass spectrometry (MS). Two unexpected mass distributions are observed in the mass spectra. Reaction schemes for the formation of these distributions are proposed. A solution phase trimethylsilane end group modification was performed on the prepolymer to determine whether the unexpected mass distributions occur as impurities from synthesis or as artifacts from the MS process. Evaluation of the TMS modified prepolymer indicates the unexpected mass distributions indeed occur as impurities from the synthetic procedure. Average molecular weight values are determined by traditional GPC, direct MALDI-TOF MS, and GPC-MALDI-TOF MS methods and the results are compared.