Mini-Maximizers for Reaction-Diffusion Systems with Skew-Gradient Structure

A reaction-diffusion system with skew-gradient structure is a sort of activator-inhibitor system that consists of two gradient systems coupled in a skew-symmetric way. Any steady state of such a system corresponds to a critical point of some functional. The aim of this paper is to study the relation between a stability property as a steady state of the reaction-diffusion system and a mini-maximizing property as a critical point of the functional. It is shown that a steady state of the skew-gradient system is stable regardless of time constants if and only if it is a mini-maximizer of the functional. It is also shown that the mini-maximizing property is closely related with the diffusion-induced instability. Moreover, by using the property that any mini-maximizer on a convex domain is spatially homogeneous, quite a general instability criterion is obtained for some activator-inhibitor systems. These results are applied to the diffusive FitzHugh-Nagumo system and the Gierer-Meinhardt system.     

Homogeneous two-manifolds with an invariant two-form

We study a 2-dimensional manifold that admits a homogeneous action of a 3-dimensional Lie group G, and has a 2-form invariant under G. We show that such a manifold can be realized as a surface in the affine 3-space, and list such realizations.      

Hyers–Ulam stability of linear differential operator with constant coefficients

Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electron transport membrane: Preparation of polypeptide membrane with spacers between the polymer matrix and viologen moiety and their application to an electron transfer reaction

Polypeptide membranes with several lengths of spacers [? (CH₂)_n? ; n = 3, 6, 12] between the polymer matrix and viologen moiety as a functional group were prepared. Reduction of K₃Fe(CN)₆ with Na₂S₂O₄ across the obtained membrane in aqueous media were carried out and reduction rate of K₃Fe(CN)₆ across the membrane of n = 6 was faster than that of n = 3. However, the reduction of the membrane (n = 12) did not proceed chemically and electrochemically at all.     

Conductive diamond hollow fiber membranes

Boron-doped diamond hollow fiber membrane (BDD–HFM) was fabricated as a novel type of porous conductive diamond. BDD–HFM was obtained by deposition of BDD polycrystalline film onto a quartz filter substrate consisting of quartz fibers, followed by etching of the substrate in HF/HNO₃ aqueous solution. Cross-sectional scanning electron microscope (SEM) observation showed the inner diameter and wall thickness of the BDD hollow fibers were in the range of 0.4–2 and 0.2–2 μm, respectively. The BDD–HFM electrode exhibited a relatively large double-layer capacitance (ca. 13 F g⁻¹) in 0.1 M H₂SO₄. Electrochemical AC impedance properties were simulated using an equivalent circuit model containing a transmission line model, which indicated characteristics of a porous electrode material.     

The response of a spherical tissue-equivalent proportional counter to different heavy ions having similar velocities

A tissue-equivalent proportional counter (TEPC) has been used as a dosimeter in mixed radiation fields. Since it does not measure LET directly, the response function must be characterized in order to estimate quality factor and thus equivalent dose for the incident radiation. The objectives of this study were to measure the response of a spherical TEPC for different high-energy heavy ions (HZE) having similar velocity and to determine how quality factors can be determined. Data were obtained at the HIMAC heavy ion accelerator for ⁴He and ¹²C at (β=0.59) and ¹²C, ¹⁶O, ²⁸Si and ⁵⁶Fe at (β=0.70). A particle spectrometer recorded the charge and position of each incident beam particle. Events with low energy deposition were observed for particles that passed through the wall of the TEPC but not through the sensitive volume. The frequency averaged lineal energy, , was always less than the LET of the incident particles. The dose averaged lineal energy, , was approximately equal to LET for particles with LET greater than 10 keV/μm, whereas was larger than LET for the lighter particles with lower LET. Part of this effect is due to detector resolution and energy straggling that increases the variance of the response function. Although the TEPC is not a LET spectrometer, it can provide real time measurements of dose and provide estimates of quality factors for HZE particles using averaged values of lineal energy.     

Formation of metallic Ni nanoparticles on titania surfaces by chemical vapor reductive deposition method

Metallic Ni nanoparticles were successfully prepared on the surface of titania thin film substrate by a novel method, named as chemical vapor reductive deposition (CVRD) method. The growth of the nanoparticles was based on the specific adsorption and heterogeneous nucleation on the surface of substrate, not via vapor-phase formation and subsequent sedimentation. The nanoparticle size was found to be well controllable between 10 and 30 nm by the preparation time and vapor pressure of metal complex precursor. ESCA and electron diffraction results clearly demonstrated Ni nanoparticles as metallic. Titania thin film with metallic Ni nanoparticles on its surface showed high efficiency in their photocatalysis of hydrogen evolution from decomposition of ethanol.     

Dielectric properties of ferroelectric/DMS heterointerface using YMnO3 and Ce doped Si

Bottom gate type Al/Si:8.2 at%Ce/YMnO₃/Pt capacitor was fabricated. Although it was polycrystalline, we successfully obtained Si:8.2 at%Ce film on ferroelectric YMnO₃. The dielectric properties of the capacitor were carefully investigated. Although the capacitance shows frequency dispersion, the capacitor exhibits a ferroelectric type C-V hysteresis loop. From the PUND and P-V measurements, ferroelectric polarization was distinguished from the another polarization, Based on these dielectric measurements, effect of polarization induced by the ferroelectric YMnO₃ on the carrier modulation in the diluted magnetic semiconductor, Ce doped Si film was discussed.