Remark on the Helmholtz decomposition in domains with noncompact boundary

Let \(\varOmega \) be a domain in \(\mathbb {R}^{d+1}\) whose boundary is given as a uniform Lipschitz graph \(x_{d+1}=\eta (x)\) for \(x \in \mathbb {R}^d\) . For such a domain, it is known that the Helmholtz decomposition is not always valid in \(L^p(\varOmega )\) except for the energy space \(L^2 (\varOmega )\) . In this paper we show that the Helmholtz decomposition still holds in certain anisotropic spaces which include vector fields decaying slowly in the \(x_{d+1}\) variable. In particular, these classes include some infinite energy vector fields. For the purpose, we develop a new approach based on a factorization of divergence form elliptic operators whose coefficients are independent of one variable.     

Oblique-Incidence Characteristics of a Parallel-Aligned Nematic-Liquid-Crystal Spatial Light Modulator

We have developed optically-addressed and electrically-addressed liquid crystal spatial phase-only light modulators having no pixelized structures. We obtained a large depth of phase-only modulation and high diffraction efficiency based on the electro-optical characteristics of a parallel-aligned nematic liquid crystal. These spatial light modulators (SLM) are of the reflection type, so there would be a loss of power in the readout light from the half mirror, which was set up so as to separate the incident and reflected lights. To optimize the characteristics of a reflection type spatial phase-only light modulator, we have proposed an oblique incident optical readout setup. We have examined the effect of conditions such as the polarization direction and the incidence angle of the readout light, and the orientation of liquid crystal molecules in the SLM. High diffraction efficiency close to the theoretical maximum value was obtained by adjusting the above conditions. The simulation analysis can well explain the experimental results of phase modulation.     

Rattling in the Quadruple Perovskite CuCu3V4O12

Of particular interest is a peculiar motion of guest atoms or ions confined to nanospace in cage compounds, called rattling. While rattling provides unexplored physical properties through the guest–host interactions, it has only been observed in a very limited class of materials. Herein, we introduce an A‐site‐ordered quadruple perovskite, CuCu₃V₄O₁₂, as a new family of cage compounds. This novel AA′₃B₄O₁₂‐type perovskite has been obtained by a high‐pressure synthesis technique and structurally characterized to have cubic Im$\bar 3$ symmetry with an ionic model of Cu²⁺Cu²⁺₃V⁴⁺₄O₁₂. The thermal displacement parameter of the A‐site Cu²⁺ ion is as large as U_iso≈0.045 Ų at 300 K, indicating its large‐amplitude thermal oscillations in the oversized icosahedral cages. Remarkably, the presence of localized phonon modes associated with rattling of the A‐site Cu²⁺ ion manifests itself in the low‐temperature specific heat data. This work sheds new light on the structure–property relations in perovskites.     

Proton-coupled electron-transfer processes in photosystem II probed by highly resolved g-anisotropy of redox-active tyrosine YZ

The oxidation of a redox-active tyrosine residue Y(Z) in photosystem II (PSII) is coupled with proton transfer to a hydrogen-bonded D1-His190 residue. Because of the apparent proximity of Y(Z) to the water-oxidizing complex and its redox activity, it is believed that Y(Z) plays a significant role in water oxidation in PSII. We investigated the g-anisotropy of the tyrosine radical Y(Z)(?) to provide insight into the mechanism of Y(Z)(?) proton-coupled electron transfer in Mn-depleted PSII. The anisotropy was highly resolved by electron paramagnetic resonance spectroscopy at the W-band (94.9 GHz) using PSII single crystals. The g(X)-component along the phenolic C-O bond of Y(Z)(?) was calculated by density functional theory (DFT). It was concluded from the highly resolved g-anisotropy that Y(Z) loses a phenol proton to D1-His190 upon tyrosine oxidation, and D1-His190 redonates the same proton back to Y(Z)(?) upon reduction.     

Stabilization mechanism of clarithromycin tablets under gastric pH conditions

It has been reported that tablets of clarithromycin (CAM), a 14-membered macrolide antibiotic, are especially stable under low pH conditions such as in gastric fluid, and showed excellent antibacterial efficiency even though CAM molecules themselves are rapidly decomposed. Therefore, we aimed to clarify the stabilization mechanism of CAM tablets under low pH conditions. From the results of stability and dissolution tests, the optimal decomposition rate constant (K(dec)) and dissolution rate constant (K(dis)) at various pH values were calculated by curve-fitting to consecutive reactions. Consequently, log(K(dec)) increased as pH decreased. On the other hand, log(K(dis)) increased as pH decreased from 3.0 to 1.5, but decreased as pH decreased from 1.5 to 1.0. In addition, the disintegration time of commercially available tablets at pH 1.0 and 1.2 was found to be delayed, resulting in a decrease of K(dis). Furthermore, from powder X-ray diffraction, HPLC and elemental analysis, the delay in disintegration time might be attributable to the formation of a transparent gel, formed by the reaction between CAM molecule and hydrochloric acid under low pH conditions, on the surface of CAM tablet. On the basis of these results, this report can be considered the first case where a transparent gel prevents gastric fluid from penetrating the tablet, resulting in reduced decomposition of CAM following oral administrating.     

A probable hydrogen-bonded Meisenheimer complex: an unusually high S(N)Ar reactivity of nitroaniline derivatives with hydroxide ion in aqueous media

Observations show that nitroanilines exhibit an unusually high S(N)Ar reactivity with OH(-) in aqueous media in reactions that produce nitrophenols. S(N)Ar reaction of 4-nitroaniline (2a) in aqueous NaOH for 16 h yields 4-nitrophenol (4a) quantitatively, whereas a similar reaction of 4-nitrochlorobenzene (1a) gave 4a in 2% yield together with recovered 1a in 97%, suggesting that the leaving ability of the NH(2) group far surpasses that of Cl under these conditions. An essential feature of S(N)Ar reactions of nitroanilines is probably that the NH(2) leaving group participates in a hydrogen-bonding interaction with H(2)O. Density functional theory (DFT) calculations for a set of 4-nitroaniline, OH(-), and H(2)O suggest a possible formation of a Meisenheimer complex stabilized by hydrogen-bonding interactions and a six-membered ring structure. The results obtained here contrast with conventional S(N)Ar reactivity profiles in which nitroanilines are nearly unreactive with nucleophiles in organic solvents.     

Spectral Properties of the Linearization at the Burgers Vortex in the High Rotation Limit

We study a linearized operator of the equation for the axisymmetric Burgers vortex which gives a stationary solution to the three dimensional Navier–Stokes equations with an axisymmetric background straining flow. It is numerically known that the Burgers vortex obtains better stabilities as the circulation number (or the vortex Reynolds number) is increasing. Although the global stability of the axisymmetric Burgers vortex is already proved rigorously, mathematical understanding of this numerical observation has been lacking. In this paper we study a linearized operator that includes the circulation number as a parameter, and prove that if the operator is restricted on a suitable invariant subspace, then its spectrum moves to the left as the circulation number goes to infinity. As an application, we show that the axisymmetric Burgers vortex with a high rotation has a better stability, in the sense that the non-radially symmetric part of solutions to the associated evolution equation decays faster in time if the circulation number is sufficiently large.     

Prediction error criterion for selecting variables in a linear regression model

Several criteria, such as CV, C _p , AIC, CAIC, and MAIC, are used for selecting variables in linear regression models. It might be noted that C _p has been proposed as an estimator of the expected standardized prediction error, although the target risk function of CV might be regarded as the expected prediction error R _PE. On the other hand, the target risk function of AIC, CAIC, and MAIC is the expected log-predictive likelihood. In this paper, we propose a prediction error criterion, PE, which is an estimator of the expected prediction error R _PE. Consequently, it is also a competitor of CV. Results of this study show that PE is an unbiased estimator when the true model is contained in the full model. The property is shown without the assumption of normality. In fact, PE is demonstrated as more faithful for its risk function than CV. The prediction error criterion PE is extended to the multivariate case. Furthermore, using simulations, we examine some peculiarities of all these criteria.     

Velocity field after wave breaking

The velocity field in breaking water waves is considered in this paper. A numerical simulation describes in detail the transition from a primary overturning and consequent rebounding jets into a bore front, where the vorticity in the coherent large‐scale eddy structures devolves into turbulence. Spatial changes in the frequency spectra of the kinetic energy and the enstrophy are associated with the production, transport and dissipation of the Reynolds stress and the various wave and turbulent mixing length scales. Mean velocity fields and the wave and kinetic energy in a surf zone are evaluated. Fourier and wavelet spectral analysis is applied to study both the surface elevation and energy changes, and the distinction that must be made between spilling and plunging breakers is clarified in this paper. Copyright © 2002 John Wiley & Sons, Ltd.     

Adsorptive accumulation voltammetry of copper(II) using complex formation reaction with salicylideneamino-2-thiophenol

Summary The cathodic stripping voltammetry of copper(II) was investigated with a method, based on the adsorptive accumulation of the Cu(II)-salicylideneamino-2-thiophenol (SATP) complex on a hanging mercury drop electrode. The copper(II)-SATP complex could be accumulated on the electrode at –0.20 V in 0.01 mol/l nitric acid. The reduction peak of the copper complex was observed by scanning the potential in a negative direction in the differential pulse mode. The calibration curve for copper was linear over the range 5×10^–9–1×10^–7 mol/l. This method was applied to determine copper(II) in GSJ (Geological Survey of Japan) standard rock reference materials.