End-point maximal regularity and its application to two-dimensional Keller–Segel system

We prove the maximal L ^ρ regularity of the Cauchy problem of the heat equation in the Besov space [(B)\dot]_1,r⁰(\mathbbRⁿ){\dot{B}_{1,\rho}^0(\mathbb{R}^n)}, 1 < ρ ≤ ∞, which is not UMD space. And as its application, we establish the time local well-posedness of the solution of two dimensional nonlinear parabolic system with the Poisson equation in [(B)\dot]_1,2⁰(\mathbbR²){\dot{B}_{1,2}^0(\mathbb{R}^2)} , where the equation is considered in the space invariant by a scaling and particularly the natural free energy is well defined from the initial time. The small data global existence is also obtained in the same class.     

Interpolation inequality of logarithmic type in abstract Besov spaces and an application to semilinear evolution equations

An abstract version of Besov spaces is introduced by using the resolvent of nonnegative operators. Interpolation inequalities with respect to abstract Besov spaces and generalized Lorentz spaces are obtained. These inequalities provide a generalization of Sobolev inequalities of logarithmic type. Uniqueness problems to abstract semilinear evolution equations are also discussed (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ellagitannin Digestion in Moth Larvae and a New Dimeric Ellagitannin from the Leaves of Platycarya strobilacea

Ellagitannins (ETs) are plant polyphenols with various health benefits. Recent studies have indicated that the biological activities of ETs are attributable to their degradation products, including ellagic acid and its gut microflora metabolites, such as urolithins. Insect tea produced in the Guangxi region, China, is made from the frass of moth larvae that feed on the ET-rich leaves of Platycarya strobilacea. Chromatographic separation of the Guangxi insect tea showed that the major phenolic constituents are ellagic acid, brevifolin carboxylic acid, gallic acid, brevifolin, and polymeric polyphenols. Chemical investigation of the feed of the larvae, the fresh leaves of P. strobilacea, showed that the major polyphenols are ETs including pedunculagin, casuarictin, strictinin, and a new ET named platycaryanin E. The new ET was confirmed as a dimer of strictinin having a tergalloyl group. The insect tea and the leaves of P. strobilacea contained polymeric polyphenols, both of which were shown to be composed of ETs and proanthocyanidins by acid hydrolysis and thiol degradation. This study clarified that Guangxi insect tea contains ET metabolites produced in the digestive tract of moth larvae, and the metabolites probably have higher bioavailabilities than the original large-molecular ETs of the leaves of P. strobilacea.     

Multispectral hyperbolic incoherent holography

This paper presents a new method of multispectral hyperbolic incoherent holography in which a hyperbolic volume interferogram was directly measured by an appropriate designed interferometer. This method enables to obtain a set of spectral components of three-dimensional images and continuous spectra for spatially incoherent, polychromatic objects. We introduced a calibration method of a phase aberration of the interferometer. The spectral resolution and spatial resolutions are investigated based on analytical solution of impulse response function of hyperbolic holography. From experimental results and theoretical predictions, the validity of the calibration method was confirmed. Experimental results agree with the theoretical ones. Consequently, the retrieved images obtained by the method are shown to demonstrate the performance of the method.     

The Electronic State of Hydrogen in the α Phase of the Hydrogen‐Storage Material PdH(D)x: Does a Chemical Bond Between Palladium and Hydrogen Exist?

The palladium–hydrogen system is one of the most famous hydrogen‐storage systems. Although there has been much research on β‐phase PdH(D)_x, we comprehensively investigated the nature of the interaction between Pd and H(D) in α‐phase PdH(D)_x (x<0.03 at 303 K), and revealed the existence of Pd?H(D) chemical bond for the first time, by various in situ experimental techniques and first‐principles theoretical calculations. The lattice expansion, magnetic susceptibility, and electrical resistivity all provide evidence. In situ solid‐state ¹H and ²H NMR spectroscopy and first‐principles theoretical calculations revealed that a Pd?H(D) chemical bond exists in the α phase, but the bonding character of the Pd?H(D) bond in the α phase is quite different from that in the β phase; the nature of the Pd?H(D) bond in the α phase is a localized covalent bond whereas that in the β phase is a metallic bond.     

Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions

An interaction equation of the capillary-gravity wave is considered. We show that the Cauchy problem of the coupled Schrödinger-KdV equation,

is locally well-posed for weak initial data . We apply the analogous method for estimating the nonlinear coupling terms developed by Bourgain and refined by Kenig, Ponce, and Vega.

     

Two dimensional elliptic equation with critical nonlinear growth

We study the asymptotic behavior of solutions to a semilinear elliptic equation associated with the critical nonlinear growth in two dimensions.

where is a unit disk in and denotes a positive parameter. We show that for a radially symmetric solution of (1.1) satisfies

Moreover, by using the Pohozaev identity to the rescaled equation, we show that for any finite energy radially symmetric solutions to (1.1), there is a rescaled asymptotics such as

locally uniformly in . We also show some extensions of the above results for general two dimensional domains.

     

Transmission electron microscopy study of an AlN nucleation layer for the growth of GaN on a 7-degree off-oriented (0 0 1) Si substrate by metalorganic vapor phase epitaxy

We have investigated the morphology of the high-temperature-grown AlN nucleation layer and its role in the early stage of GaN growth, by means of transmission electron microscopy. The nitride was selectively grown on a 7-degree off-oriented (0 0 1) patterned Si substrate by metalorganic vapor phase epitaxy. AlN was deposited on the inclined unmasked (1 1 1) facet in the form of islands. The size of the islands varied along the slope, which is attributable to the diffusion of the growth species in the vapor phase. The GaN nucleation occurred at the region where rounded AlN islands formed densely. The threading dislocations were observed to generate in the GaN nucleated region.