Class number parity for cyclotomic fields

We give a simple criterion for the parity of the class number of the cyclotomic field.

     

Thermal decomposition of poly(sec-amyl methacrylate)

The thermal decomposition of poly(sec-amyl methacrylate) is studied by simultaneous thermogravimetry–gas chromatography–mass spectrometry and by pyrolysis–gas chromatography. The TG curve has four distinct breaks and a plateau. Results of the identification of the evolved gas at the individual breaks by GC–MS techniques lead to the conclusion that these breaks correspond to the individual processes in the decomposition mechanism like that of poly(tert-butyl methacrylate): the first break, the depolymerization initiated at the unsaturated chain ends; the second break, the depolymerization initiated at the saturated chain ends; the third break, the ester decomposition; the plateau, the inhibition of decomposition by the formation of poly(methacrylic anhydride); the fourth break, the decomposition of poly(methacrylic anhydride). The extent of ester decomposition is related to the substituent constants based on Hammett equation. The ester decomposition product is separated into three pentene isomers by pyrolysis–gas chromatography: trans-2-pentene, cis-2-pentene, and 1-pentene. As raising decomposition temperature, the composition ratio of trans-2-pentene decreases and becomes constant above 620 K, and the composition ratios of cis-2-pentene and 1-pentene increase and also become constant above 620 K. These results are accounted for by mobility of atoms included in the substituent at forming a ring transition state.     

Photoconductivity of poly(N-acryloylcarbazole)

The photoconductivity of poly(N-acryloylcarbazole) (PACz), with the pendant carbazolyl group only a short distance from the skeletal chain of the polymer but separated from it by a carbonyl group, is investigated and compared with that of poly(N-vinylcarbazole) (PVCz). There is no significant difference between PACz and PVCz in the temperature, light intensity, and spectral dependences of the photocurrent. The photoconductivity of PACz, however, is much inferior to that of PVCz and even to that of poly(N-carbazolylethylvinylether), a representative vinyl polymer with pendant carbazolyl groups far from the skeletal chain. The poor photoconductivity of PACz is discussed in relation to the intensity of the electronic interaction between neighboring carbazolyl groups in the polymer chain and to singlet exciton migration. It is attributed mainly to an extremely low efficiency of extrinsic carrier generation via a singlet exciton, which is due to the poor electron-donating character and the extremely short lifetime of a singlet exciton in the presence of the carbonyl group.     

Specificity and biomineralization activities of Ti-binding peptide-1 (TBP-1)

Numerous peptide aptamers that recognize inorganic materials have been isolated using in vitro peptide evolution systems. However, it remains unknown how peptides interact with inorganic materials or how specific those interactions are. We, therefore, assessed the target specificities of the peptide aptamer TBP-1 (RKLPDAPGMHTW) by monitoring its ability to bind 10 different metals. We found that phages displaying TBP-1 bound to Ti, Si, and Ag surfaces but not to Au, Cr, Pt, Sn, Zn, Cu, or Fe. As previously seen with Ti, binding to Si and Ag was diminished by R1A, P4A, or D5A mutation, suggesting that the same molecular mechanism underlies TBP-1 binding to all three materials. We also observed that a synthetic TBP-1 peptide mediated mineralization of both silica and Ag. It, thus, appears that although the overall chemical characteristics of Ti, Si, and Ag surfaces are dissimilar, they share a common subnanometric structure that is recognized by TBP-1.     

Extensive quinoidal oligothiophenes with dicyanomethylene groups at terminal positions as highly amphoteric redox molecules

A series of highly extensive quinoidal oligothiophenes carrying a dicyanomethylene group at both terminal positions is synthesized. As the quinoidal structures extend, they have highly amphoteric abilities and show strong electronic absorptions in the visible to near-infrared region. The higher homologues, quinquethiophene and sexithiophene, exist as equilibrium mixtures with the biradical species.     

Fluorescence enhancement by hydroperoxides based on a change in the intramolecular charge transfer character of benzofurazan

Strong fluorescence signals were observed after the reaction of novel reagents with hydroperoxides.     

Synthesis and Some Properties of Low Melting Ferroelectric Liquid Crystals of Benzylidene Anilines

A series of chiral benzylidene-aniline compounds, 4-alkoxybenzylidene 4′-(2-methylbutyloxycarbonyl)anilines, have been synthesized and their mesomorphic properties are examined. They showed a monotropic chiral smectic C phase in conjunction with enantiotropic smectic A phase, and their chiral smectic C—smectic A phase transition temperatures are around room temperatures. Their spontaneous polarization values are moderately higher than those of DOBAMBC “4-decyloxybenzylidene 4′-amino-(2-methylbutyl)cinnamate”.     

Recurrent traveling waves in a two-dimensional saw-toothed cylinder and their average speed

We study a curvature-dependent motion of plane curves in a two-dimensional infinite cylinder with spatially undulating boundary. The law of motion is given by V=κ+A$V=\kappa +A$, where V is the normal velocity of the curve, κ is the curvature, and A is a positive constant. The boundary undulation is assumed to be almost periodic, or, more generally, recurrent in a certain sense. We first introduce the definition of recurrent traveling waves and establish a necessary and sufficient condition for the existence of such traveling waves. We then show that the traveling wave is asymptotically stable if it exists. Next we show that a regular traveling wave has a well-defined average speed if the boundary shape is strictly ergodic. Finally we study what we call “virtual pinning”, which means that the traveling wave propagates over the entire cylinder with zero average speed. Such a peculiar situation can occur only in non-periodic environments and never occurs if the boundary undulation is periodic.