On the Shintani zeta function for the space of binary quadratic forms

Partially supported by NSF Grant DMS-8803085, DMS-8610730     

Synchronized sailing of two camphor boats in polygonal chambers

The synchronized self-motion of two camphor boats on polygonal water chambers was investigated. The two boats synchronously moved depending on the number of corners in the polygon by changing the distance between the two boats through the corners. We regard the self-motion of a camphor boat as an oscillator; i.e., one cycle on the polygonal chamber corresponds to 2pi. Phase-locked synchronization at a phase difference of 2pi/3, which corresponds to the length of one side of the chamber, was observed with a triangular chamber. Two types of synchronized motion at phase differences of pi/2 and pi, which correspond to the length of one and two sides of the chamber, respectively, were observed with a square chamber. These characteristic features of synchronized self-motion were qualitatively reproduced by a numerical calculation that regarded the surface tension as the driving force and the number of corners in the chamber as a velocity-regulating mechanism. We believe that the present system may be a simple model of synchronization which depends on the geometry of the system.     

Synthesis of fluoride garnets {Na3}[M3+2](Li3)F12 (M = Al,Cr, and Fe) from aqueous solution and their properties

The garnet-type fluorides, Na₃M₂Li₃F₁₂ (M = Al, Cr, and Fe) were synthesized as the coprecipitates of ～1 to 10 μm powders from HF solutions. The garnet structures were always obtained under acidic conditions. The incorporation of water molecules into the structure of the Cr and Fe garnets was observed. After heat treatment at 300°C, very small unknown peaks were observed in the X-ray powder pattern in addition to the garnet phase which had a slightly smaller value of the lattice constant than that of hydrous garnets. From the measurement of magnetic properties and Mössbauer effects, the Fe and Cr garnets were found to be paramagnetic with both ions in the trivalent state. Presentation of infrared spectra of the garnets is also included.     

Solvents inducing oxidation of hydroxylamines

Hydroxylamines gradually undergo oxidation to their oximes on being dissolved in organic solvent (e.g. methanol). This phenomenon was followed by (1)H-NMR and liquid chromatography-mass spectrometry (LC-MS). The oxidation rate was estimated from the peak area observed on the mass chromatogram at the protonated molecule or fragment ion on LC-atmospheric pressure chemical ionization (APCI)-MS. The results showed that the oxidation rate of hydroxylamines depended on the solvent type.     

Engineered biosynthesis of plant polyketides: chain length control in an octaketide-producing plant type III polyketide synthase

The chalcone synthase (CHS) superfamily of type III polyketide synthases (PKSs) produces a variety of plant secondary metabolites with remarkable structural diversity and biological activities (e.g., chalcones, stilbenes, benzophenones, acrydones, phloroglucinols, resorcinols, pyrones, and chromones). Here we describe an octaketide-producing novel plant-specific type III PKS from aloe (Aloe arborescens) sharing 50-60% amino acid sequence identity with other plant CHS-superfamily enzymes. A recombinant enzyme expressed in Escherichia coli catalyzed seven successive decarboxylative condensations of malonyl-CoA to yield aromatic octaketides SEK4 and SEK4b, the longest polyketides known to be synthesized by the structurally simple type III PKS. Surprisingly, site-directed mutagenesis revealed that a single residue Gly207 (corresponding to the CHS's active site Thr197) determines the polyketide chain length and product specificity. Small-to-large substitutions (G207A, G207T, G207M, G207L, G207F, and G207W) resulted in loss of the octaketide-forming activity and concomitant formation of shorter chain length polyketides (from triketide to heptaketide) including a pentaketide chromone, 2,7-dihydroxy-5-methylchromone, and a hexaketide pyrone, 6-(2,4-dihydroxy-6-methylphenyl)-4-hydroxy-2-pyrone, depending on the size of the side chain. Notably, the functional diversity of the type III PKS was shown to evolve from simple steric modulation of the chemically inert single residue lining the active-site cavity accompanied by conservation of the Cys-His-Asn catalytic triad. This provided novel strategies for the engineered biosynthesis of pharmaceutically important plant polyketides.     

Effects of carbonyl and aldehyde groups in the graft copolymerization of methyl methacrylate on cellulose with a ceric salt

Graft copolymerization of methyl methacrylate on cellulosic materials of various carbonyl and aldehyde contents with the use of a ceric salt as an initiator was studied. It was found that the concentration of the ceric salt which gives the maximum per cent grafting is in good agreement with the equivalent of total carbonyl content in the cellulosic material, and the number of grafted chains in copolymers is roughly proportional to it. However, the molar ratio of the number of grafted chains to total carbonyl content is quite small, being approximately 1:50, and the graft copolymerization can be explained kinetically on the assumption that the number of radicals produced on cellulose by the ceric salt leading to branching is very much smaller than the number of radicals destroyed by the ceric salt, and growing radicals can be stabilized by the termination reaction with the ceric salt or with a cellulose radical. Although both aldehyde and carbonyl groups contribute to the formation of grafted chains, the former are effective mainly at low concentrations of the ceric salt; both groups participate in the production of graft copolymers showing the maximum per cent grafting.     

Emulsifier-free emulsion polymerization of tetrafluoroethylene by radiation. I. Effects of reaction conditions on the polymerization rate and polymer molecular weight

The radiation-induced emulsifier-free emulsion polymerization of tetrafluoroethylene was carried out at an initial pressure of 2–25 kg/cm², temperature of 30–110°C, and under a dose rate of 0.57 × 10⁴?3.0 × 10⁴ rad/hr. The rate of polymerization was shown to be proportional to 1.0 and 1.3 powers of the dose rate and initial pressure, respectively, and is maximal at about 70°C. The molecular weight of polytetrafluoroethylene (PTFE) lies in the range of 10⁵?10⁶, increases with reaction time in the early stage of polymerization, and is maximal at 70°C but is almost independent of the dose rate. An interesting discovery is that PTFE, a hydrophobic polymer, forms as a stable latex in the absence of emulsifier. When PTFE latex coagulates during polymerization under certain conditions, the polymerization rate decreases, probably because polymerization proceeds mainly on the polymer particle surface. The observed rate acceleration and successive increase in polymer molecular weight may be due to slow termination of propagating radicals in the rigid PTFE particles.     

Emulsifier-free emulsion polymerization of tetrafluoroethylene by radiation. III. Simultaneous formation of hydrofluoric acid

Simultaneous formation of hydrofluoric acid (HF) in the radiation-induced polymerization of tetrafluoroethylene (TFE) was investigated. HF concentration in PTFE latex was determined mainly by conductometric titration with 0.01 and 0.001N NaOH. The amount of HF formed is almost independent of agitation speed and the amount of n-hexadecane added and is maximal at ca. 70°C corresponding to the rate of polymerization. The rate of HF formation increases with the initial pressure of TFE monomer and dose rate and decreases with polymerization or TFE consumption. This fact suggests that HF is formed mainly by TFE reactions and not by the degradation of PTFE. The mechanism of HF formation in this reaction system in the absence of oxygen is shown in the following two schemes: scheme I is the reaction of TFE with primary radicals (OH·, H·, e) from the radiolysis of water; scheme II is the reaction of water with the species from the radiolysis of TFE. On the assumption that HF is formed only according to scheme I, the G value of HF formation G(HF)_calc can be calculated as 11.25. All observed G values G(HF)_obs are larger than G(HF)_calc. When the polymerization is carried out at 20 kg/cm² under various dose rates, G(HF)_obs increases with the dose rate. When the polymerization is carried out at 3.0 × 10⁴ rad/hr under various pressures, G(HF)_obs decreases with the decrease in pressure from 20 to 2 kg/cm² and is fairly close to G(HG)_calc at 2 kg/cm². This indicates that HF formation is due mainly to scheme II at high pressure (in the presence of enough TFE) and to scheme I as the pressure is lowered.