An ore-type condition for the existence ofk-factors in graphs

Letk be a positive integer, and letG be a graph of ordern withn 4k – 5,kn even and minimum degree at leastk. We prove that if the degree sum of each pair of nonadjacent vertices is at leastn, thenG has ak-factor.     

Self-avoiding walk in five or more dimensions I. The critical behaviour

We use the lace expansion to study the standard self-avoiding walk in thed-dimensional hypercubic lattice, ford5. We prove that the numberc _n ofn-step self-avoiding walks satisfiesc _n ~A ⁿ , where is the connective constant (i.e. =1), and that the mean square displacement is asymptotically linear in the number of steps (i.e.v=1/2). A bound is obtained forc _n(x), the number ofn-step self-avoiding walks ending atx. The correlation length is shown to diverge asymptotically like (^––Z)^1/2. The critical two-point function is shown to decay at least as fast as x^–2, and its Fourier transform is shown to be asymptotic to a multiple ofk ^–2 ask0 (i.e. =0). We also prove that the scaling limit is Gaussian, in the sense of convergence in distribution to Brownian motion. The infinite self-avoiding walk is constructed. In this paper we prove these results assuming convergence of the lace expansion. The convergence of the lace expansion is proved in a companion paper.Supported by the Nishina Memorial Foundation and NSF grant PHY-8896163.Supported by NSERC grant A9351     

Highly sensitive chiral shift reagent bearing two zinc porphyrins

A new type of chiral receptor (R,R)- or (S,S)-1b with C(2) symmetry was synthesized. An induced-fit type of binding behavior of 1b for diamines was revealed by CD spectroscopy. NMR studies demonstrated that 1b can function as a highly sensitive chiral shift reagent for the determination of the enantiomeric purity of chiral diamines, aziridine, and isoxazoline at the microgram level. [structure: see text]     

Preparation of dehydrated powder of hemoglobin vesicles

The carbonyl hemoglobin (CO-Hb), which was used to prevent denaturation (metHb) during the preparation of samples, was encapsulated into lipid vesicles constituted from unsaturated phospholipid, cholesterol and unsaturated fatty acid. Unsaturated components were polymerized by γ-irradiation to enhance the stability of bilayer membrane. An aqueous dispersion of resulting Hb vesicles was freeze-dried in the presence of saccharides (50–200 mM) to obtain a dehydrated powder of Hb vesicles. Change in the vesicle size, the leakage of encapsulated Hb and the oxidation of Hb to metHb were not observed. Therefore, the long-term storage of Hb vesicles can be realized as a dry powder.     

Simultaneous analysis of tea catechins, caffeine, gallic acid, theanine and ascorbic acid by micellar electrokinetic capillary chromatography

A micellar electrokinetic capillary chromatography (MEKC) method for the simultaneous analysis of five tea catechins, theanine, caffeine, gallic acid and ascorbic acid has been developed. The catechins are (-)-epicatechin, (+)-catechin, (-)-epigallocatechin, (-)-epicatechin gallate and (-)-epigallocatechin gallate. p-Nitrophenol serves as both reference and internal standard. All the components are separated within 13 min with a 57 cm uncoated fused-silica column. On-column detection was carried out at 200 nm. This method has been used to measure these compounds in fresh tea leaves and tea liquor. The limit of detection for all analytes ranged from 1 to 20 microg/ml.     

Cloning, sequencing, and functional analysis of the biosynthetic gene cluster of macrolactam antibiotic vicenistatin in Streptomyces halstedii

Vicenistatin, an antitumor antibiotic isolated from Streptomyces halstedii, is a unique 20-membered macrocyclic lactam with a novel aminosugar vicenisamine. The vicenistatin biosynthetic gene cluster (vin) spanning approximately 64 kbp was cloned and sequenced. The cluster contains putative genes for the aglycon biosynthesis including four modular polyketide synthases (PKSs), glutamate mutase, acyl CoA-ligase, and AMP-ligase. Also found in the cluster are genes of NDP-hexose 4,6-dehydratase and aminotransferase for vicenisamine biosynthesis. For the functional confirmation of the cluster, a putative glycosyltransferase gene product, VinC, was heterologously expressed, and the vicenisamine transfer reaction to the aglycon was chemically proved. A unique feature of the vicenistatin PKS is that the loading module contains only an acyl carrier protein domain, in contrast to other known PKS-loading modules containing certain activation domains. Activation of the starter acyl group by separate polypeptides is postulated as well.     

Aqueous phase behavior of a 1-O-phytanyl-beta-D-xyloside/water system. Glycolipid-based bicontinuous cubic phases of crystallographic space groups Pn3m and Ia3d

Temperature- and concentration-dependent aqueous phase diagram of a novel alkylglycoside, 1-O-phytanyl-beta-D-xyloside (beta-Xyl(Phyt)), was studied using small-angle X-ray scattering, polarizing optical microscopy, and differential scanning calorimetry. The phases found in this system include an Lc phase, an Lalpha phase, an HII phase, two inverted cubic phases of crystallographic space groups Pn3m and Ia3d, and a fluid isotropic phase, FI. The phase diagram of the beta-Xyl(Phyt)/water system is similar to that for the 1-monooleylglycerol (MO)/water system, suggesting that the phase behavior is largely determined by the overall molecular shape rather than the details of surfactant molecular structure. Moreover, the structural parameters of the beta-Xyl(Phyt) liquid crystals are also similar to those of the MO/water, due primarily to the similar molecular dimensions of two molecules. As compared to the MO/water system, however, the beta-Xyl(Phyt)/water system displays a lower value of TK ( approximately 8.(5) degrees C) and a wider temperature window for the mesophases (8.(5)-120 degrees C). Moreover, beta-Xyl(Phyt) is chemically more robust than MO, as the ether linkage is more stable against hydrolysis than the ester linkage and the phytanyl chain is fully saturated.     

Crystalline orientation of the InN films prepared by atmospheric pressure halide chemical vapor deposition

The structural analysis of the hexagonal InN film prepared on a Si(100) substrate by the AP-HCVD technique using InCl₃ and NH₃ as starting materials were carried out by the X-ray pole figure analysis. The deposited films consist of the hexagonal InN pillar crystals. It was found that the pillar crystals, which have random rotation around the 100 axis, were grown at an angle of 70–90° to the substrate.     

Biodegradable Phosphorylcholine Polymer Hydrogels Cross‐Linked with Vinyl‐Functionalized Polyphosphate

A vinyl‐functionalized polyphosphate (PIOP) was synthesized by ring‐opening polymerization of 2‐isopropyl‐2‐oxo‐1,3,2‐dioxaphospholane and 2‐(2‐oxo‐1,3,2‐dioxaphosphoroyloxyethyl methacrylate) with triisobutylaluminum as an initiator. The number‐averaged molecular weight of the PIOP was 1.2 × 10⁴. The average number of vinyl groups in the PIOP is 2.20. Transparent hydrogels were prepared by the radical polymerization of 2‐methacryroyloxyethyl phosphorylcholine with PIOP as a cross‐linking reagent. These hydrogels may have many applications in the biomedical field because of their biodegradability and biocompatibility.

Synthetic route of PIOP.     

Synthesis of α-(aminomethylene)-9H-purine-6-acetic acid derivatives

α-(Aminornethylene)-9H-purine-6-acetamide ( 3a ) and the corresponding ethyl acetate 9 have been synthesized by catalytic hydrogenation of 6-cyanomethylenepurine derivatives 2 and 7 which were obtained by the substitution of 6-chloropurine derivatives with α-cyanoacetamide and ethyl cyanoacetate, respectively. Substitution of α-(aminomethylene)-9-(tetrahydrofuran)-9H-purine-6-acetamide ( 3b ) with amines gave the corresponding N-alkyl- and N-arylamines 5 , which were treated with acid to give N-substituted α-(aminomethylene)-9H-purine-6-acetamides 6 . Substitution of 9 with amines gave the corresponding N-alkyl- and N-aryl substituted amines 10 .