On Exponential Sums Involving the Ideal Counting Function in Quadratic Number Fields

 Let χ be a Dirichlet character modulo k > 1, and F _χ(n) the arithmetical function which is generated by the product of the Riemann zeta-function and the Dirichlet L-function corresponding to χ in . In this paper we study the asymptotic behaviour of the exponential sums involving the arithmetical function F _χ(n). In particular, we study summation formulas for these exponential sums and mean square formulas for the error term. Received April 17, 2001; in revised form April 2, 2002     

Morphology of ABC triblock copolymer/homopolymer blend systems

Morphological variations of ABC triblock copolymers through the blending of B or A/C homopolymers, all with short chain lengths, were studied experimentally. The samples were symmetric ISP triblock copolymers, where I, S, and P denote polyisoprene, polystyrene, and poly(2‐vinylpyridine), and component homopolymers. Microphase‐separated structures of the solvent‐cast films were observed with transmission electron microscopy and small‐angle X‐ray scattering. For an ISP/S system, the lattice constant of the tricontinuous gyroid structure (G‐structure) increased with an increase in the volume fraction of S (?_s) if the amount of added homopolymer was small, but it reached a certain limit, reflecting the fact that the midblock chain had a limit for chain stretching. For I/ISP/P blends, on the contrary, the lattice constant of the G‐structure continued increasing with decreasing ?_s. This result shows that the I and P domains did not have a limit for chain stretching because the two end blocks had free ends. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1135–1141, 2002     

Vacuum fusion determination of oxygen in gadolinium,terbium metal and iron-terbium alloy

The extraction conditions for the accurate determination of oxygen in gadolinium, terbium and iron-terbium alloy using vacuum fusion analysis were studied. The influence of the gettering effect, the analyzing temperature and the weight ratio of the bath metal to the sample were investigated. Oxygen values of gadolinium and terbium were measured by the graphite crucible, the graphite capsule, the tin bath, the iron-tin bath and the platinum-tin bath techniques in the temperature range of 1500–2100 °C using vacuum fusion analysis. These oxygen values were compared with those obtained by inert gas fusion analysis. In inert gas fusion analysis, the samples were analyzed with iron and tin in a tin capsule, and the samples with platinum in a tin capsule were analyzed in a graphite capsule enclosing with carbon powder. Oxygen values of both metal samples in the graphite capsule at 2000 °C, with an iron-tin bath at 1850 °C and a platinum-tin bath at 2000 °C in vacuum fusion analysis, were respectively in good agreement within their errors; the oxygen values of gadolinium were also in good agreement with that from inert gas fusion analysis in the iron-tin bath, but those of terbium were not in agreement. This agreement for gadolinium guarantees the reliability of the conditions for the accurate determination, and the difference of oxygen values for terbium suggests a need for further consideration on the conditions of the inert gas fusion analysis.     

Critical brush density for the transition between carpet-only and carpet/brush double-layered structures

The critical brush density, where transition from carpet-only structure to carpet/brush double-layered structure occurs, was estimated for a weakly ionic amphiphilic diblock copolymer, (diethylsilacyclobutane)34-b-(methacrylic acid)50, monolayer on water by an in situ X-ray reflectivity technique. The brush density in the monolayer was controlled from 0.11 to 0.60 brush chain/nm2 by changing surface pressure and mixing a poly(diethylsilacyclobutane) homopolymer separately synthesized. Only a carpet layer was formed at a low brush density condition, but a carpet and brush double layer was found for a higher brush density of more than 0.48/nm2. This brush density, which is fairly high, would be valuable for discussing the polyelectrolyte brush nanostructure.     

Significant reduction of on-site Coulomb energy U due to short-range correlation in an organic Mott insulator.

By carrying out a first-principles T-matrix calculation on multiple scatterings between electrons, we show that the intramolecular electron-electron interaction energy U, of a Mott insulator of the organic radical 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA) is significantly reduced from the naive expectation value of the Coulomb interaction (7.3 eV and 5.3 eV, respectively, for the bare and screened Coulomb interactions) to 2.9 eV due to the short-range correlation. This result together with the intermolecular interaction energy D=1.3 eV explains the experimental optical gap (1.5 eV). The associated two-particle wavefunction clearly shows the Coulomb hole indicating that two electrons with antiparallel spins cannot approach because of the Coulomb repulsion. We also discuss the energetics and magnetics of this system.     

Direct EPR observations of both oxidized and reduced porphyrin dimers in the lowest excited states: a novel analysis of a homobiradical with a strong antiferromagnetic interaction

The oxidized and reduced forms of bis(tetra-tert-butyltetraazaporphinato)lutetium (III) (Lu(TAP)2) have been examined by time-resolved EPR (TREPR) spectroscopy, showing both the first EPR investigation of a homobiradical with a strong antiferromagnetic interaction and usefulness of TREPR for investigating excited-state properties of different oxidation states.     

MODELS FOR THE CHROMOPHORE STRUCTURE OF THE PHOTOTRANSFORMATION INTERMEDIATES OF PEA PHYTOCHROME IN VITRO

Abstract— The changes in the chromophore structure of pea phytochrome during phototransformation in vitro from the red-light-absorbing form (P_r) to the far-red-light-absorbing form (P_fr), and from P_fr to P_r, were analysed in terms of wavelength and oscillator strength of absorption, using the zero-differential overlap approximation of the molecular orbital theory for electrons. The effect of a point-charge and a point-dipole on the optical absorption of phytochromobilin intermediates were examined using the stationary perturbation theory for degenerate states. The results indicate that the cis-trans photoisomerization of the pyrrole ring D, if any, occurred within 10 μs after a laser-flash excitation of the phytochrome, and that the conformations of phytochromobilin and the protein moiety of phytochrome were not significantly changed during the period of examination of phototransformation in either direction.