Interaction cohomology of forward or backward self-similar systems

We investigate the dynamics of forward or backward self-similar systems (iterated function systems) and the topological structure of their invariant sets. We define a new cohomology theory (interaction cohomology) for forward or backward self-similar systems. We show that under certain conditions, the space of connected components of the invariant set is isomorphic to the inverse limit of the spaces of connected components of the realizations of the nerves of finite coverings U of the invariant set, where each U consists of (backward) images of the invariant set under elements of finite word length. We give a criterion for the invariant set to be connected. Moreover, we give a sufficient condition for the first cohomology group to have infinite rank. As an application, we obtain many results on the dynamics of semigroups of polynomials. Moreover, we define postunbranched systems and we investigate the interaction cohomology groups of such systems. Many examples are given.     

Rank of 3-tensors with 2 slices and Kronecker canonical forms

Tensor type data are becoming important recently in various application fields. We determine the rank of a 3-tensor with 2 slices in comparison with its Kronecker canonical form over the complex and real number field.     

Stability of certain minimal submanifolds in compact symmetric spaces of rank two

In [T. Kimura, M.S. Tanaka, Totally geodesic submanifold in compact symmetric spaces of rank two, Tokyo J. Math., in press], the authors obtained the global classification of the maximal totally geodesic submanifolds in compact connected irreducible symmetric spaces of rank two. In this paper, we determine their stability as minimal submanifolds in compact symmetric spaces of rank two.     

An interaction site model integral equation study of molecular fluids explicitly considering the molecular orientation

We implemented an interaction site model integral equation for rigid molecules based on a density-functional theory where the molecular orientation is explicitly considered. In this implementation of the integral equation, multiple integral of the degree of freedom of the molecular orientation is performed using efficient quadrature methods, so that the site-site pair correlation functions are evaluated exactly in the limit of low density. We apply this method to Cl(2), HCl, and H(2)O molecular fluids that have been investigated by several integral equation studies using various models. The site-site pair correlation functions obtained from the integral equation are in good agreement with the one from a simulation of these molecules. Rotational invariant coefficients, which characterize the microscopic structure of molecular fluids, are determined from the integral equation and the simulation in order to investigate the accuracy of the integral equation.     

Generalized characteristic interface conditions for high-order multi-block computation

In practical fluid computation with structured grids around complex geometries, singular points with metric discontinuity can frequently be found. Generally, the grid singularities may cause numerical oscillations when some high-order finite difference scheme is applied. Recently, an excellent theory has been proposed which solves the above singular problem by block decomposition along the singular surface and by imposition of the characteristic interface conditions (CIC) on the block interface. However, the original theory has constraints on the mathematical treatment of the block interface, and therefore prevents numerical flexibility from a practical point of view. In this article, in order to extend the functions of the original CIC, we propose the generalized characteristic interface conditions (GCIC). Proper numerical test analysis is conducted to validate the performance of the GCIC, and as a practical application, multi-block computation is performed with the GCIC applied to complex geometry.     

Fabrication of freestanding m-plane GaN wafer by using the HVPE technique on an aluminum carbide buffer layer on an m-plane sapphire substrate

A freestanding m-plane GaN wafer is fabricated by using the hydride vapor-phase epitaxy (HVPE) technique on an aluminum carbide buffer layer on an m-plane sapphire substrate. X-ray pole-figure measurements show a clear m-plane orientation of the GaN surface. The full-width at half-maximum (FWHM) of GaN (1 1¯ 0 0) X-ray rocking curve (XRC) with the scattering vector along the [1 1 2¯ 0] direction is approximately 800 arcsec; this indicates good crystallinity. On the other hand, the FWHM for the case in which the scattering vector is oriented along the [0 0 0 1] direction is broad; this suggests the influence of structural defects along this direction. In fact, basal plane stacking faults (BSF) with a density of approximately 3×10⁵ cm⁻¹ is observed by transmission electron microscopy (TEM). The preparation of a 45-mm-diameter m-plane GaN wafer due to spontaneous separation of the GaN layer from the sapphire substrate is demonstrated.     

A narrow process window for the preparation of polytypes of microcrystalline silicon carbide thin films by hot-wire CVD method

Effects of deposition conditions on the structure of microcrystalline silicon carbide (μc-SiC) films prepared by hot-wire chemical vapor deposition (hot-wire CVD) method have been investigated. It is found from X-ray diffraction patterns of the film that a diffraction peak from crystallites from hexagonal polytypes of SiC is observed in addition to those of 3 C-SiC crystallites. This result is obtained in the film under a narrow deposition conditions of SiH₃CH₃ gas pressure of 8 Pa, the H₂ gas pressure of 80–300 Pa and the total gas pressure of 40–300 Pa under fixed substrate and filament temperatures employed in this study. Furthermore, the grain size of hexagonal crystallites (about 20 nm) on c-Si substrates becomes larger than that of 3 C-SiC crystallites (about 10 nm) for the films deposited under the total gas pressure of 36–88 Pa. The fact that microcrystalline hexagonal SiC can be deposited under limited deposition conditions could be interpreted in the context of a result for c-SiC polytypes prepared by thermal CVD method.     

A dimethoxytriazine type glycosyl donor enables a facile chemo-enzymatic route toward α-linked N-acetylglucosaminyl-galactose disaccharide unit from gastric mucin

An efficient chemo-enzymatic process for construction of the α-linked disaccharide unit (GlcNAcα1-4Gal) found in gastric mucin has been developed. The process consists of a one-step preparation of a novel triazine type glycosyl donor in water and the subsequent transglycosylation to a galactose derivative catalysed by α-N-acetylglucosaminidase.     

On Downing-Kirk's theorem

In this paper, using the notion of τ-distance, we prove a generalization of Downing-Kirk's theorem.     

Identification of aluminum species in an aluminum-accumulating plant, hydrangea (Hydrangea macrophylla), by electrospray ionization mass spectrometry.

The use of electrospray ionization mass spectrometry (ESI-MS) in negative ion mode was investigated as a direct probe for identifying Al species in Al-accumulating hydrangea (Hydrangea macrophylla) samples. Cell sap solutions of hydrangea leaves were purified using Sephadex G-10 liquid chromatography and each fraction was analyzed using ESI-MS and ESI-MS/MS to identify Al species. In hydrangea leaves, a 1:1 Al-citrate complex was found as [AlH(-1)cit](-) (m/z 215), where H(3)cit denotes citric acid. This result is consistent with that of Ma et al. who used (27)Al-NMR.