The reaction of perfluorobicyclic ethers and perfluorospiro-ethers with anhydrous aluminum chloride

Perfluorobicyclic ethers and perfluorospiroethers, all containing an oxolane skeleton, were treated with AlCl₃ in a heterogeneous manner to give the corresponding α,α,α′-trichlorinated and α,α-dichlorinated products, respectively. From perfluoroacetal compounds, for example, perfluoro(8-methoxy-7-oxabicyclo- [4.3.0]nonane), mono- and di-chlorinated products, i.e. perfluoro- (8-chloro-8-methoxy-7-oxabicyclo[4.3.0]nonane) and perfluoro- (8,8-dichloro-7-oxabicyclo[4.3.0]nonane) were obtained in good yields. The action of fuming sulfuric acid on these polychlorinated products led to the formation of the corresponding lactones. Perfluoro(6-chloro-7-oxa-8-oxobicyclo[4.3.0]nonane) was treated with (CH₃)₂NLi to give N,N-dimethylundecafluoro-2-oxocyclohexyl- acetamide.     

Chemical role of amines in the colloidal synthesis of CdSe quantum dots and their luminescence properties

The role of organic amines in the colloidal synthesis of CdSe quantum dots (QDs) has been studied. CdSe QDs were synthesized from the source solutions containing 5 vol% of amines having various alkyl chain lengths, stereochemical sizes and electron donation abilities. The role of the additional amines was evaluated on the basis of the photoluminescence (PL) properties such as PL wavelength and intensity of the obtained CdSe QDs. The observed PL spectra were explained by the fact that the amines behaved as capping ligands on the surface of the QDs in the product colloidal solution and complex ligands for cadmium in the source solutions. It was shown that the particle size was controlled by the diffusion process depending on the mass and stereochemical shape of the amines, and the luminescence intensity increased with the increasing electron donation ability and capping density of the amines.     

Initial boundary value problems for a quantum hydrodynamic model of semiconductors: Asymptotic behaviors and classical limits

The present paper proves the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for a quantum hydrodynamic model of semiconductors over a one-dimensional bounded domain. We also discuss on a singular limit from this model to a classical hydrodynamic model without quantum effects. Precisely, we prove that a solution for the quantum model converges to that for the hydrodynamic model as the Planck constant tends to zero. Here we adopt a non-linear boundary condition which means quantum effect vanishes on the boundary. In the previous researches, the existence and the asymptotic stability of a stationary solution are proved under the assumption that a doping profile is flat, which makes the stationary solution also flat. However, the typical doping profile in actual devices does not satisfy this assumption. Thus, we prove the above theorems without this flatness assumption. Firstly, the existence of the stationary solution is proved by the Leray-Schauder fixed-point theorem. Secondly, we show the asymptotic stability theorem by using an elementary energy method, where the equation for an energy form plays an essential role. Finally, the classical limit is considered by using the energy method again.     

Computation of Weng's rank 2 zeta function over an algebraic number field

In this paper, we study the zeta function, named non-abelian zeta function, defined by Lin Weng. We can represent Weng's rank r zeta function of an algebraic number field F as the integration of the Eisenstein series over the moduli space of the semi-stable OF-lattices with rank r. For r=2, in the case of F=Q, Weng proved that it can be written by the Riemann zeta function, and Lagarias and Suzuki proved that it satisfies the Riemann hypothesis. These results were generalized by the author to imaginary quadratic fields and by Lin Weng to general number fields. This paper presents proofs of both these results. It derives a formula (first found by Weng) for Weng's rank 2 zeta functions for general number fields, and then proves the Riemann hypothesis holds for such zeta functions.     

Hyperbolicity, heterodimensional cycles and Lyapunov exponents for partially hyperbolic dynamics

We prove a dichotomy of C² partially hyperbolic sets with one-dimensional center direction admitting no zero Lyapunov exponents, either hyperbolicity over the supports of ergodic measures or approximation by a heterodimensional cycle. This provides a partial result to the C¹ Palis Conjecture that claims a dichotomy, hyperbolicity or homoclinic bifurcations in a dense subset of the space of C¹ diffeomorphisms. Moreover, a theorem of Ma?é applied in the proof is modified to have an additional property concerning the Hausdorff distance between a periodic orbit and the support of a hyperbolic ergodic measure.     

Microfabrication of gold dots in SiO2/TiO2 glass films by two-photon absorption

Photogeneration of Au nanoparticles in SiO₂/TiO₂ glass films was carried out by two-photon absorption with a femtosecond pulse laser. Exquisite microdot-arrays of Au with micrometer spatial resolution were achieved by scanning of the focused laser beam. These structures were constructed in SiO₂/TiO₂ glass films by a sol–gel method. The sol–gel method demonstrated that Au dots microarray are fabricated at any position by two-photon absorption in the glass. The results show the utility of a two-photon absorption technique in the fabrication of complicated patterns with metal particles.     

High temperature superconductor micro SQUID magnetometer for molecular-based magnets

We have developed a high temperature superconductor (HTS) micro SQUID magnetometer for molecular-based magnets. By employing the dipole approximation, we verified the flux value of 40Φ₀ from the saturation magnetic moment of the ferrimagnetic microcrystal of [Mn₂(H₂O)₂(CH₃COO)][W(CN)₈] · 2H₂O (15 × 15 × 13 μm). Considering the relative arrangement of the sample and the SQUID loop, including the influence of the film and grease, the calculated the flux values were Φ = 71Φ₀ and 31Φ₀ at distances of 20 and 30 μm between the sample bottom face and the SQUID plane, respectively. Thus, the experimentally obtained flux value is reasonable.