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.     

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.     

Variations of the elastic constants of InSb near the covalent-metallic transition

Abstract

The pulse-echo-overlap method was used to measure the longitudinal and transverse wave velocities in single-crystal (100) and (111) samples of InSb up to 3 GPa at room temperature. The peculiar variations of the elastic constants were observed near the covalent-metallic transition.     

Synthesis of Poly(amidoamine) Dendrimer with a Diphenyl Diselenide Core

Abstract

We succeeded in the synthesis of a novel poly(amidoamine) dendrimer having diphenyl diselenide at the core. Modification of the dendrimer diselenide by the reaction with glucono-δ-lactone in methanol gave a water-soluble dendrimer diselenide having chiral terminal groups. The structures of dendrimers were satisfactorily confirmed by MAIDI-TOF MS spectrometry, elemental analysis, and NMR spectroscopy. Interestingly, induced circular dichroism (ICD) of the interaction between the diphenyl diselenide core and D-gluconamide periphery of the dendrimer was observed at 300 nm.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.

GRAPHICAL ABSTRACT     

Prehomogeneous vector spaces and ergodic theory II

We apply M. Ratner's theorem on closures of unipotent orbits to the study of three families of prehomogeneous vector spaces. As a result, we prove analogues of the Oppenheim Conjecture for simultaneous approximation by values of certain alternating bilinear forms in an even number of variables and certain alternating trilinear forms in six and seven variables.

     

Enhanced photon generation in a Nb/n-InGaAs/p-InP superconductor/semiconductor-diode light emitting device

We experimentally demonstrate Cooper pairs' drastic enhancement of the band-to-band radiative recombination rate in a semiconductor. Electron Cooper pairs injected from a superconducting electrode into an active layer by the proximity effect recombine with holes injected from a p-type electrode. The recombination of a Cooper pair with p-type carriers dramatically increases the photon generation probability of a light-emitting diode in the optical-fiber communication band. The measured radiative decay time rapidly decreases with decreasing temperature below the superconducting transition temperature of the niobium electrodes. Our results indicate the possibility to open up new interdisciplinary fields between superconductivity and optoelectronics.