Real-linear isometries between function algebras

Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → {z ∈ ℂ: |z| = 1}, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and T( f ) = k[`(fof)]T\left( f \right) = \kappa \overline {fo\phi } on ChB \ K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily uniformly closed) function algebras.     

Tomographic implementation of astronomical speckle imaging from bispectra

A bispectral method for astronomical speckle imaging utilizes an average speckle bispectrum of an object to derive its Fourier phase. There has been, however, a problem in conventional bispectral algorithm owing to difficulty in processing bispectral data in a four-dimensional (4D) space. In this paper, we propose an implementation to overcome this problem, where a one-dimensional (1D) object projection is reconstructed from a two-dimensional (2D) average bispectrum of speckle projections, and object projections so obtained at various angles are then tomographically combined into a 2D object image. In this tomographic approach, processes are separable into those for individual projection angles, implying that bispectral data required to be stored at a time are from 4D to 2D and computation time can be substantially reduced by parallelizing angle-by-angle processes. We have performed experiments using simulated and observed data, and have demonstrated the feasibility of the present approach with an achievable accuracy comparable to that of a conventional approach.     

White light emission of Mn-doped SnO-ZnO-P2O5 glass containing no rare earth cation

The authors have demonstrated white light emission of rare earth (RE)-free Mn-doped SnO-ZnO-P(2)O(5) glass. The RE-free glass shows white light emission with a high value of quantum efficiency (QE) comparable to conventional crystalline phosphor. It is notable that the high QE value is attained for RE-free transparent glass, and the broad emission can be continuously tuned by both the amount of activator and the composition of the glass. Since this glass possesses low-melting property, we emphasize that the glass phosphor will lead to the development of a novel inorganic white-light-emitting device in combination with a solid state UV light-emitting source.     

Formation mechanism of element distribution in glass under femtosecond laser irradiation

We report on the formation mechanism of element distribution in glass under high-repetition-rate femtosecond laser irradiation. We simultaneously focused two beams of femtosecond laser pulses inside a glass and confirmed the formation of characteristically shaped element distributions. The results of the numerical simulation in which we considered concentration- and temperature-gradient-driven diffusions were in excellent qualitative agreement with the experimental results, indicating that the main driving force is the sharp temperature gradient. Since the composition of a glass affects its refractive index, absorption, and luminescence property, the results in this study provide a framework to fabricate a functional optical device such as optical circuits with a high-repetition-rate femtosecond laser.     

Comparison of reactivity on step and terrace sites of Pd (3 3 2) surface for the dissociative adsorption of hydrogen: A quantum chemical molecular dynamics study

The notion of “active sites” is fundamental to heterogeneous catalysis. However, the exact nature of the active sites, and hence the mechanism by which they act, are still largely a matter of speculation. In this study, we have presented a systematic quantum chemical molecular dynamics (QCMD) calculations for the interaction of hydrogen on different step and terrace sites of the Pd (3 3 2) surface. Finally the dissociative adsorption of hydrogen on step and terrace as well as the influence of surface hydrogen vacancy for the dissociative adsorption of hydrogen has been investigated through QCMD. This is a state-of-the-art method for calculating the interaction of atoms and molecules with metal surfaces. It is found that fully hydrogen covered (saturated) step sites can dissociate hydrogen moderately and that a monovacancy surface is suitable for significant dissociative adsorption of hydrogen. However in terrace site of the surface we have found that dissociation of hydrogen takes place only on Pd sites where the metal atom is not bound to any pre-adsorbed hydrogen atoms. Furthermore, from the molecular dynamics and electronic structure calculations, we identify a number of consequences for the interpretation and modeling of diffusion experiments demonstrating the coverage and directional dependence of atomic hydrogen diffusion on stepped palladium surface.     

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.     

Laser-induced fluorescence and infrared spectroscopic studies on the specific solvation of tris(1-(2-thienyl)-4,4,4-trifluoro-1,3-butanedionato)europium(III) in an ionic liquid

The extraction constant and the two-phase stability constant (K_D,Mβ₃) of tris(2-thenoyltrifluoroacetonato)europium(III) between 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C₄mim][Tf₂N]) as an ionic liquid and an aqueous phase were determined by considering the extraction equilibria including anionic tetrakis(2-thenoyltrifluoroacetonato)europate(III). Specific solute-solvent interactions between the neutral Eu(III) chelate and [C₄mim][Tf₂N] molecules were revealed from the relationships between the distribution constant of the enol form of 2-thenoyltrifluoroacetone (Htta) as a proton chelate and the distribution constant (K_D,M) of the neutral Eu(III) chelate because the [C₄mim][Tf₂N] system gave the high K_D,Mβ₃ value compared with those in conventional molecular solvents such as benzene and 1,2-dichloroethane. The coordination environment of Eu³⁺ in the neutral Eu(III) chelate in [C₄mim][Tf₂N] was investigated by time-resolved laser-induced fluorescence spectroscopy and infrared absorption spectroscopy. Both methods consistently indicated that not only the Eu(III) chelate extracted but also Eu(tta)₃(H₂O)₃ synthesized as a solid crystal were almost completely dehydrated in [C₄mim][Tf₂N] saturated with water. Consequently, the higher K_D,M or extractability of the neutral Eu(III) chelate in the [C₄mim][Tf₂N] system can be ascribed to the dehydration of the Eu(III) chelate, which is caused by the specific solvation with [C₄mim][Tf₂N] molecules.     

Ion chromatography of nitrite at the ppb level with photometric measurement of iodine formed by post-column reaction of nitrite with iodide

The difficulty in ion-chromatographic determination of nitrite in aqueous solutions containing a high concentration of chloride arises mainly from incomplete resolution of the peaks for these anions on the separation column whose efficiency is not high. A photometric measurement of iodine formed by a reaction of nitrite with iodide has been found to make it possible to determine, chromatographically, trace amounts of nitrite without any interference from chloride; chloride does not oxidize iodide to produce iodine. The proposed method was based on the separation of nitrite from matrix anions on a silica-based anion-exchange column with a 1.5·10⁻³ M phthalate eluent (pH 5.0), followed by photometric measurement of the iodine (as triiodide) formed via a post-column reaction of the separated nitrite with iodide. The optimal conditions for the post-column reaction were established by varying the concentrations of iodide, copper(II) and nitric acid in a post-column-reaction solution and the length of a reaction tube. A calibration graph for nitrite, plotted as peak heights versus concentrations, was linear up to 1.50·10⁻⁵ M (690 ppb). The detection limit, defined at S/N=3, was 1.00·10⁻⁷ M (4.60 ppb) nitrite. The presence of chloride ions up to 0.01 M did not give any interference to the determination of nitrite. This method was successfully applied to the determination of nitrite in lake water, river water, sewage works water and snow samples without any pretreatment.