Polygonal heat conductors with a stationary hot spot

We consider a convex polygonal heat conductor whose inscribed circle touches every side of the conductor. Initially, the conductor has constant temperature and, at every time, the temperature of its boundary is kept at zero. The hot spot is the point at which temperature attains its maximum at each given time. It is proved that, if the hot spot is stationary, then the conductor must satisfy two geometric conditions. In particular, we prove that these geometric conditions yield some symmetries provided the conductor is either pentagonal or hexagonal. This research was partially supported by Grants-in-Aid for Scientific Research (B) (# 12440042) and (B) (# 15340047) of Japan Society for the Promotion of Science, and by a Grant of the Italian MURST.     

Deracemization of 1,2-diol monotosylate derivatives by a combination of enzymatic hydrolysis with the Mitsunobu inversion using polymer-bound triphenylphosphine

The deracemization of 1,2-diol monotosylate derivatives is achieved by the sequential combination of enzymatic hydrolysis and Mitsunobu inversion using a polymer-bound triphenylphosphine. After the lipase-catalysed hydrolysis of the racemic 2-acetoxyhexyl tosylate, the subsequent Mitsunobu reaction without separation causes an inversion of the resulting (R)-alcohol to give the (S)-enantiomer of the acetate as a single product. In particular, the reaction using the polymer-bound triphenylphosphine also proceeds smoothly, and the product is easily separated by filtration from the polymer-bound reagent and its by-products. This deracemization process is applicable to the preparation of several optically active 1,2-diol monotosylates.     

Living cationic polymerization of 2‐adamantyl vinyl ether

Living cationic polymerization of 2‐adamantyl vinyl ether (2‐vinyloxytricyclo[3.3.1.1]^3,7decane; 2‐AdVE) was achieved with the CH₃CH(OiBu)OCOCH₃/ethylaluminum sesquichloride/ethyl acetate [CH₃CH(OiBu)OCOCH₃/Et_1.5AlCl_1.5/CH₃COOEt] initiating system in toluene at 0 °C. The number‐average molecular weights (M_n's) of the obtained poly(2‐AdVE)s increased in direct proportion to monomer conversion and produced the polymers with narrow molecular weight distributions (MWDs) (M_w/M_n = ～1.1). When a second monomer feed was added to the almost polymerized reaction mixture, the added monomer was completely consumed and the M_n's of the polymers showed a direct increase against conversion of the added monomer. Block and statistical copolymerization of 2‐AdVE with n‐butyl vinyl ether (CH₂?CH? O? CH₂ CH₂CH₂CH₃; NBVE) were possible via living process based on the same initiating system to give the corresponding copolymers with narrow MWDs. Grass transition temperature (T_g) and thermal decomposition temperature (T_d) of the poly(2‐AdVE) (e.g., M_n = 22,000, M_w/M_n = 1.17) were 178 and 323 °C, respectively. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1629–1637, 2008     

Characteristic responses of a semiconductor gas sensor depending on the frequency of a periodic temperature change

A novel gas-sensing system based on a dynamic nonlinear response is reported to enhance the selectivity toward sample gases using a single detector. A periodic temperature change was applied to a semiconductor gas sensor and the resulting conductance of the sensor was evaluated by fast Fourier transformation (FFT). The dynamic nonlinear response to the sample gases was further characterized depending on the frequency of the temperature change. The characteristic sensor response under the application of a temperature change was theoretically simulated by considering the kinetics of gas molecules on the semiconductor surface.     

Mechanism of alternating copolymerization of 4-hydroxy-4′-vinylbiphenyl with α-chloromaleic anhydride

The copolymerization of 4-hydroxy-4′-vinylbiphenyl (HVB) with α-chloromaleic anhydride (CMAn) was investigated in THF, 1,4-dioxane, and acetonitrile. The formation of the 1:1 charge transfer complex between HVB and CMAn was confirmed spectroscopically, and the corresponding equilibrium constant (K_eq) was determined as follows: K_eq = 0.19, 0.11, and 0.058 mol/L in THF, 1,4-dioxane, and CH₃CN, respectively. The copolymer composition is affected by the solvent, i.e., the content of HVB in the copolymer obtained in THF or 1,4-dioxane is lower than 50 mol % whereas the copolymer obtained in CH₃CN has excess of HVB units. The maximum rate of copolymerization was observed at a 1:1 initial comonomer mole ratio, irrespective of the solvent polarity. Plots of R_p/[HVB] vs. [HVB] gave a straight line with a slope and an intercept for the copolymerization in THF whereas a straight line in CH₃CN has no slope. On the basis of these results and ¹³C-NMR spectra of the copolymers, the mechanism of the predominant formation of alternating copolymers is discussed.     

Development of a bienzyme reactor sensor system for the determination of ornithine

A bienzyme reactor sensor system with amperometric detection was developed for the determination of ornithine. The system based on the immobilized enzymes (ornithine carbamyl transferase and pyruvate oxidase) consisted of a buffer tank, a peristaltic pump, an enzyme reactor, an oxygen electrode and a recorder. Then, 0.1 M MOPS buffer, containing pyruvic acid (0.5 mM) and carbamyl phosphate (0.5 mM), was continuously transferred into the system at 35 °C. Phosphate ion was formed enzymatically by transformation of ornithine in the presence of carbamyl phosphate. Pyruvate oxidase is activated by the presence of phosphate. Therefore, ornithine was determined from the oxygen consumed upon oxidation of pyruvic acid catalyzed by pyruvate oxidase in the presence of phosphate ion. The limit of detection was 0.05 mM and the response was linear to 3 mM (R²=0.9905). The variation coefficients were 4.9 (n=15) and 3.9% (n=15) for 1.1 and 3.0 mM standard ornithine, respectively. Good comparative results (R²=0.9238) were observed between ornithine contents in prawn muscle determined by the proposed system and by the HPLC. One assay was completed within 4 min. The immobilized enzymes were stable for 2 months at 4 °C and more than 150 samples could be continually determined using this enzyme reactor.     

Discovery of Hexagonal Structured Pd–B Nanocrystals

We report on hexagonal close-packed (hcp) palladium (Pd)–boron (B) nanocrystals (NCs) by heavy B doping into face-centered cubic (fcc) Pd NCs. Scanning transmission electron microscopy–electron energy loss spectroscopy and synchrotron powder X-ray diffraction measurements demonstrated that the B atoms are homogeneously distributed inside the hcp Pd lattice. The large paramagnetic susceptibility of Pd is significantly suppressed in Pd–B NCs in good agreement with the reduction of density of states at Fermi energy suggested by X-ray absorption near-edge structure and theoretical calculations.     

Reaction of 2-propargylphenylcarbamates with diphenyliodonium salts via Meyer-Schuster rearrangement

The syntheses of 2,3-dihydro-4-quinolones from 2-propargylphenylcarbamates by one-pot tandem process that involves Meyer-Schuster rearrangement or arylative Meyer-Schuster rearrangement/Michael addition of carbamate nitrogen to the resulting vinyl ketones have been developed. Phenylcarbamates tethering tertiary propargyl alcohols underwent arylative Meyer-Schuster rearrangement/Friedel-Crafts alkylation to produce 2,3-dihydroindenones.