On Shintani’s ray class invariant for totally real number fields

We introduce a ray class invariant ${X(\mathfrak{C})}$ for a totally real field, following Shintani’s work in the real quadratic case. We prove a factorization formula ${X(\mathfrak{C})=X_1(\mathfrak{C})\cdots X_n(\mathfrak{C})}$ where each ${X_i(\mathfrak{C})}$ corresponds to a real place. Although this factorization depends a priori on some choices (especially on a cone decomposition), we can show that it is actually independent of these choices. Finally, we describe the behavior of ${X_i(\mathfrak{C})}$ when the signature of ${\mathfrak{C}}$ at a real place is changed. This last result is also interpreted in terms of the derivatives L′(0, χ) of the L-functions and certain Stark units.     

Designing cyclophane-based molecular wire sensors

We propose a model molecular wire sensor that can detect zerovalent chromium by a strong increase in conductance when included in a metal-molecule-metal junction. An essential part of the sensor is a paracyclophane unit that binds to the metal atom. The nature and the energies of the molecular orbitals change drastically after the complex is formed, resulting in a 10- to 12-fold increase in conductance.     

Two convergent routes to the left-wing fragment of ciguatoxin CTX3C using O,S-acetals as key intermediates

Ciguatoxins, principal causative toxins of ciguatera seafood poisoning, are large ladderlike polycyclic ethers. Here, we report two convergent routes to synthesis of the multiolefinic left half of ciguatoxins based on a newly developed acyl radical strategy. Remarkably, only 13 steps from the monocyclic E-ring were required to construct the left wing. [reaction: see text]     

Structural phase transitions at clean and metal-covered Si(111) surfaces investigated by RHEED spot analysis

Structural phase transitions between various kinds of superlattice structures formed on a Si(111) surface have been investigated by spot analysis of reflection high-energy electron diffraction (RHEED). Reversible transitions induced by temperature changes and irreversible ones induced by metal depositions were observed. Detailed discussions on the dynamics of the phase transitions are made by quantitative analyses of integrated spot intensity and profile. For a phase transition of 7′7  1′1 structures on a clean Si(111) surface, a hysteresis with temperature difference of 5°C. between in heating and cooling processes was found in the spot intensity change, indicating a first-order transition. Hysteresis was hardly recognized, on the other hand, for transitions of Au-induced superstructures (5×2-Au or ×-Au)  1×1-Au. The spot profiles were found to be broadened during the transition of Si(111)-×-Au  1×1-Au, which was a signature of a continuous transition, while the profiles remained unchanged during the transitions of the 7×7  1×1 and 5×2-Au  1×1-Au phases. Structural conversions induced by In adsorption on the Si(111) surface kept at constant temperatures were also analyzed. The conversions at room temperature were totally dependent on the initial substrate surface structures; the 7×7 surface did not show any structural conversion with In adsorption, while the ×-In surface successively converted to a 2×2 and a × phase with coverage increase. The structural transitions at elevated temperatures were sensitively dependent on the temperatures. Sequences of transitions among the 7×7, 4×1, ×, 1×, and ×4 were quantitatively revealed as changes in RHEED spot intensity.     

Mechanism of reversible photo-induced magnetization in prussian blue analogues

Photo-induced magnetic phase transitions observed in Co—Fe Prussian blue analogues are discussed from a theoretical point of view. In this material a magnetization is induced by visible light, and the induced magnetization can be completely diminished not only by thermal annealing but also by irradiation of infra red light. After a brief survey of relevant experiments, we present an overview of our theoretical approaches to clarify the underlying mechanism of this interesting phenomenon. The ligand field at the Co site is shown to be the most relevant variable controlling spin states. The presence of Fe vacancies and the resultant ligand substitution by water molecules turns to be an essential prerequisite for the photoinduced magnetization.     

Sonochemical immobilization of noble metal nanoparticles on the surface of maghemite: mechanism and morphological control of the products

Aqueous sample solutions containing noble metal ions (HAuCl₄, Na₂PdCl₄, H₂PtCl₆), polyethyleneglycol monostearate, and magnetic maghemite nanoparticles were irradiated with high power ultrasound. Analyses of the products showed that noble metal ions were reduced by the effects of ultrasound, and the formed noble metal nanoparticles were uniformly immobilized on the surface of the maghemite. The present “one pot process” significantly simplifies the immobilization of noble metal nanoparticles on the surface of supports, compared with the conventional impregnation method. The average diameter of immobilized Au was 7–13 nm, and the diameters of Pd and Pt were several nm. The diameters depended upon the concentration of polyethyleneglycol monostearate and the concentration of noble metal ions, but not upon the maghemite concentration, indicating the possibility of the morphological controls of the products by adjusting these preparation conditions. The measurements of the average diameters and the numbers of immobilized Au nanoparticles obtained under various conditions suggest that the nucleation of Au does not occur on the surface of maghemite, but it might occur in the homogeneous bulk solution.     

Control of the Dynamic Motion of a Gel Actuator Driven by the Belousov‐Zhabotinsky Reaction

A novel self‐oscillating gel actuator with gradient structure, which generates a pendulum motion by fixing one edge of the gel without external stimuli was achieved. The gel was synthesized by copolymerizing the ruthenium catalyst for the Belousov‐Zhabotinsky reaction with N‐isopropylacrylamide and 2‐acrylamido‐2‐methylpropane sulfonic acid. Furthermore, we clarified that the period and amplitude for the self‐oscillating behavior of the gel actuator are controllable by changing the composition, temperature, and size of the gel. The maximum amplitude of the novel gel actuator is about a 100 times larger than that of the conventional self‐oscillating gel system.

     

Lipase‐Catalyzed Dynamic Kinetic Resolution of C1‐ and C2‐Symmetric Racemic Axially Chiral 2,2′‐Dihydroxy‐1,1′‐biaryls

We have discovered that the racemization of configurationally stable, axially chiral 2,2′‐dihydroxy‐1,1′‐biaryls proceeds with a catalytic amount of a cyclopentadienylruthenium(II) complex at 35–50 °C. Combining this racemization procedure with lipase‐catalyzed kinetic resolution led to the first lipase/metal‐integrated dynamic kinetic resolution of racemic axially chiral biaryl compounds. The method was applied to the synthesis of various enantio‐enriched C₁‐ and C₂‐symmetric biaryl diols in yields of up to 98 % and enantiomeric excesses of up to 98 %, which paves the way for new developments in the field of asymmetric synthesis.     

Sobolev type theorems for an operator with singularity

Spaces of Sobolev type are discussed, which are defined by the operator with singularity: , where and . This operator appears in a one-dimensional harmonic oscillator governed by Wigner's commutation relations. Smoothness of and continuity of () are studied where is in each space of Sobolev type, and results similar to Sobolev's lemma are obtained. The proofs are carried out based on a generalization of the Fourier transform. The results are applied to the Schrödinger equation.

     

Photophysical property and photostability of J-aggregate thin films of thiacyanine dyes prepared by the spin-coating method

By use of electrostatic interactions of dye molecules and poly(diallyldimethylammonium chloride) (PDDA), the spin-coating technique has been successfully applied to the preparation of stable J-aggregate thin films of thiacarbocyanine dyes on a polycarbonate or quartz plate. The J-aggregate thin films were prepared by the spin-coating of PDDA aqueous solution on dye thin films prepared on a substrate by the spin-coating of 2,2,3,3-tetrafluoro-1-propanol solution of dyes. Photophysical properties of the dye thin films and J-aggregate thin films were studied by measuring the fluorescence spectra, quantum yields, and lifetimes. Coherent size of the J-aggregates was estimated to be 3-12 by means of the absorption bandwidth (full width at half maximum) or radiative lifetime. Photostability of the J-aggregate thin films was also studied in terms of photodegradation efficiency under argon and oxygen in comparison with the dye thin films, and J-aggregate thin films were found to be more stable than the corresponding dye thin films.