Establishing order in planar subdivisions

A planar subdivision is the partition of the plane induced by an embedded planar graph. A representation of such a subdivision isordered if, for each vertexv of the associated graphG, the (say) clockwise sequence of edges in the embedding ofG incident withv appears explicitly.The worst-case complexity of establishing order in a planar subdivision, i.e., converting an unordered representation into an ordered one, is shown to be (n + log (G)), wheren is the size (number of vertices) of the underlying graphG and (G) is (essentially) the number of topologically distinct embeddings ofG in the plane.This work was supported by the National Science and Engineering Research Council of Canada under Grant A3583. A preliminary version of this paper appeared in theProceedings of the Third Annual ACM Symposium on Computational Geometry.     

On the large order behavior of Φ 4 4

We continue the rigorous study of the large order behavior of the perturbation series for the ⁴ model in 4 dimensions started in [1]. In this paper we prove a result announced in [1]. We show that the exact radius of convergence of the Borel transform of the renormalized perturbation series for ₄ ⁴ is greater than or equal to the expected value given by the position of the first renormalon [2]. This result holds for any vector (²)² model withN components, and makes use of the Lipatov bound of [1]. This result is based on a partial resummation of counterterms similar to the one of [3], but in a phase-space analysis of the renormalized series.     

Large area bolometers for millimeter-wave power calibration

An accurate monolithic power meter has been developed for millimeter-wave applications. The detector is a large-area Bismuth bolometer, integrated on a fused-Quartz substrate. It simply measures the temperature change caused by the absorption of millimeter-wave radiation. The power meter is simple to fabricate, inexpensive, and can be easily calibrated using a low-frequency network. The measured responsivity for a 50 bolometer, with an area of 1×1cm, at a bias of 1V. and a video modulation of 100Hz, is 1mV/W. The noise spectrum exhibits a 1/f rolloff till 1KHz, and is limited by the Johnson noise for higher frequencies. The NEP of the detector is 3WHz^–1/2 at a video modulation of 1KHz. It is possible to decrease the current NEP by fabricating bolometers with higher responsivities. Possible application areas are absolute power calibration and localized power density measurements at millimeter and submillimeter wavelengths.     

Monotone Chemical Reaction Networks

We analyze certain chemical reaction networks and show that every solution converges to some steady state. The reaction kinetics are assumed to be monotone but otherwise arbitrary. When diffusion effects are taken into account, the conclusions remain unchanged. The main tools used in our analysis come from the theory of monotone dynamical systems. We review some of the features of this theory and provide a self-contained proof of a particular attractivity result which is used in proving our main result.     

Self-assembly of a hydrophobic groove

Heptakis(2,6-di-O-methyl)-β-cyclodextrin interacts with 5,15-diphenylporphine to produce a 2:1 complex in dimethyl sulfoxide. This complex possesses a hydrophobic groove that circumscribes the metal binding site of the porphyrin moiety.     

Restricted rotation about the boron---nitrogen bond in aminoboranes

The application of variable temperature ¹³C NMR to the study of a series of chlorodialkylaminophenylboranes has enabled G values for the rotational barrier, about the boron---nitrogen bond, to be determined.     

Diastereoselective [4+2] annulation of vinyl carbodiimides with N-alkyl imines. Asymmetric synthetic access to the batzelladine alkaloids

A diastereoselective [4+2] annulation of vinyl carbodiimides with chiral N-alkyl imines has been developed to access the stereochemically rich tricyclic core of the batzelladine alkaloids. Its application to the asymmetric synthesis of batzelladine D permitted the use of long-range, directed hydrogenation and stereoselective intramolecular iodoamination as additional key steps to establish the remaining stereocenters within the natural product with excellent stereocontrol.     

The crystal and molecular structure of 1,1,1,3,3,3-hexaphenyl-1,3-disilapropane

Crystals of the title compound H₂C(SiPh₃)₂ are triclinic, space group P$\text{1}$, with a = 9.290(2), b = 12.128(4), c = 16.882(4) Å, α = 62.08(1), β = 106.88(1), γ = 117.28(2)° and Z = 2. The central skeletal angle SiCSi is 128.8(7)°. The structures of the molecules H₂C(SiR₃)₂ (R = H, CH₃, and Ph) are compared and discussed: a simple model for the skeletal geometry of species H₂C(MR₃)₂ is proposed, and tested against experimental data and theoretical calculations.     

Evaluation of gas chromatography-tandem quadrupole mass spectrometry for the determination of organochlorine pesticides in fats and oils

A gas chromatography-tandem quadrupole mass spectrometry multi-residue method for the analysis of 19 organochlorine pesticides in fats and oils has been developed. Gel permeation chromatography was employed to remove lipid material prior to GC-MS/MS analysis. Average recoveries of the pesticides spiked at 10 and 50 microg kg(-1) into fish oil, pork fat, olive oil and hydrogenated vegetable oil were typically in the range 70-110% with relative standard deviations generally less than 10%. Calculated limits of detection are between 0.1 and 2.0 microg kg(-1) and results obtained for the analysis of proficiency test materials are in good agreement with assigned values. The higher selectivity of the GC-MS/MS compared to electron capture detection and GC-MS in selective ion monitoring mode allowed unambiguous identification and confirmation of all the target pesticides at low microg kg(-1) levels in fats and oils in a single analysis.     

Effects of sugar inhibition on cellulases and β-glucosidase during enzymatic hydrolysis of softwood substrates

A quantitative approach was taken to determine the inhibition effects of glucose and other sugar monomers during cellulase and β-Glucosidase hydrolysis of two types of cellulosic material: Avicel and acetic acid-pretreated softwood. The increased glucose content in the hydrolysate resulted in a dramatic increase in the degrees of inhibition on both β-Glucosidase and cellulase activities. Supplementation of mannose, xylose, and galactose during cellobiose hydrolysis did not show any inhibitory effects on β-Glucosidase activity. However, these sugars were shown to have significant inhibitory effects on cellulase activity during cellulose hydrolysis. Our study suggests that high-substrate consistency hydrolysis with supplementation of hemicellulose is likely to be a practical solution to minimizing end-product inhibition effects while producing hydrolysate with high glucose concentration.