The Hopf invariant of a Haefliger knot

We show that for any given differentiable embedding of the three-sphere in six-space there exists a Seifert surface (in six-space) with arbitrarily prescribed signature. This implies, according to our previous paper, that given such a (6,3)-knot endowed with normal one-field, we can construct a Seifert surface so that the outward normal field along its boundary coincides with the given normal one-field. This aspect enables us to understand the resemblance between Ekholm–Szűcs’ formula for the Smale invariant and a formula in our previous paper for differentiable (6,3)-knots. As a consequence, we show that an immersion of the three-sphere in five-space can be regularly homotoped to the projection of an embedding in six-space if and only if its Smale invariant is even. We also correct a sign error in our previous paper: “A geometric formula for Haefliger knots” [Topology 43: 1425–1447 2004].      

Structural, optical, and electronic properties of a series of 3,4-propylenedioxythiophene oligomers in neutral and various oxidation States

A series of 3,4-propylenedioxythiophene (ProDOT) oligomers (nP(Hex)) with dihexyl side chains and methylthio end-capping units was synthesized as a model of poly(3,4-alkylenedioxythiophene)s. The slope of the linear relationship between the energy of the absorption maxima of nP(Hex) in the neutral states and the reciprocal of the number of monomer units (1/n) was found to be comparable to that of 3,4-ethylenedioxythiophene (EDOT) oligomers, suggesting that both the ProDOT and the EDOT oligomers have a similar effective conjugation. In cyclic voltammetry measurements, both the first and second oxidation waves and the third and fourth waves were shown to merge into one peak with increasing chain length. The stepwise chemical oxidations of nP(Hex) with SbCl(5) in CH(2)Cl(2) at room temperature gave their stable cationic species in various oxidation states, and it was found that only the radical cations (polarons) have an obvious absorption band in the visible region. Interestingly, when the absorption spectra of tetramer radical cation 4P(Hex)(+·) were measured at low temperatures, reversible disproportionation into dication 4P(Hex)(2+) and neutral species 4P(Hex) was observed in addition to π-dimer formation. Furthermore, the radical cations of the longer oligomers showed only the disproportionation reaction. From the comparisons of the results of experiments and the theoretical calculations of the dications, 6P(Hex)(2+) was found to have a closed-shell nature, and only a weak singlet biradical character appeared even in longer oligomers 10P(Hex)(2+) and 12P(Hex)(2+). Overall, the electron-donating dioxy substituents are considered to stabilize high p-doping levels with closed-shell dication (bipolaron) structures in poly(3,4-alkylenedioxythiophene)s, which enables the transparency properties of the polymers.     

Multiscale evaluation method of the drag effect on shallow water flow through coastal forests based on 3D numerical simulations

This study presents a method for determining the drag parameter in the 2D shallow water (SW) equation for flows through a coastal forest by conducting a series of 3D numerical simulations (3D NSs). Following the theory of multiscale modeling, an evaluation method procedure is proposed. We first prepare a local test domain that contains a sufficient number of trees to constitute part of a coastal forest. Then, 3D NSs are conducted in this test domain with various inflow conditions. Based on the corresponding results, the momentum losses over the test domain are converted into the drag parameter of the global SW equation. A response surface of the drag parameter is constructed as a function of the flow conditions. The stabilized finite element method is employed for both the local and the global NSs, and the phase-field method is utilized to represent 3D free surfaces. Comparisons between the 2D SW calculation results and the 3D NS results are also performed to verify the validity of the proposed method.     

Femtosecond laser microprocessing with three-dimensionally isotropic spatial resolution using crossed-beam irradiation

We describe the use of a crossed-beam irradiation system in three-dimensional femtosecond laser microprocessing to obtain three-dimensionally isotropic spatial resolution. In the crossed-beam geometry, two orthogonal objective lenses are arranged to share a common focal point. The synthesized focal spot produces an isotropic illumination volume. We demonstrate that microfluidic channels with substantially circular cross-sectional shapes can be directly fabricated inside glass by using the crossed-beam irradiation system.     

Synthesis of non-stoichiometric (LaO)CuS thin films by pulse laser deposition

We have attempted to control the photoluminescence spectrum of transparent p-type semiconductor (LaO)CuS to check possibilities of phosphor application using non-stoichiometric thin films prepared by pulse laser deposition method. Two kinds of samples are examined, one is the samples that contain the excess S and the other is the excess Cu. All samples are a single phase without impurities, regardless of heavily doping. Lattice constants for all samples don’t depend on the concentration of excess atoms. Perhaps, this is due to the nature of the layered materials. Introduction of excess atoms leads to change the photoluminescence spectra. The excess S and Cu have much effect on the red and the blue luminescence bands, respectively. We have succeeded in the tuning luminescence band of photoluminescence spectra.     

Computerized Simulation and Chromatic Adaptation Experiments Based on a Model of Aged Human Lens

Color appearance seen by old people does not significantly differ from that seen by young subjects even though their ocular lens has become more yellow with age. We calculated the age-related change of lights reflected from Munsell color chips onto the retina, and derived results that show that the chromaticity values of all the color chips shifted to the yellow region of the xy-chromaticity diagram. However, a replot on the CIELAB diagram and the estimation by means of the von Kries adaptation model suggests that old people may compensate their color vision using a general chromatic adaptation process. To test this hypothesis, we conducted two experiments: a chromatic adaptation experiment and a color matching experiment to simulate D65-lights as seen by older people but using young subjects. The results indicate that chromatic adaptation does not provide a complete explanation for color compensation by older people, suggesting that an age-related change of the yellow-blue opponent color mechanism may contribute to this compensation.     

A new heptacoordinated organogermanium compound; trichlorogermyl[tris(2-methoxyphenyl)]methane

A new hypercoordinated organogermanium compound, trichlorogermyl[tris(2-methoxyphenyl)]methane (4) was prepared, and its tricapped tetrahedral structure was confirmed by X-ray crystallographic analysis. All interatomic oxygen?germanium distances are shorter than the sum of van der Waals radii of O and Ge (3.62 Å).     

Ferrocene-modified bis(spiropyridopyran)s as synthetic signaling receptors for guanine-guanine dinucleoside derivatives

A ferrocene-linked bis(spiropyridopyran) was designed and synthesized, that recognized guanine-guanine dinucleoside derivatives via complementary hydrogen bonds in CH2Cl2, resulting in the isomerization of the colorless spiropyridopyran as self-indicating receptors.