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.     

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.     

Indirect measurement of secondary-particle distributions by an Au activation method at the KEK neutrino target station

Gold activation detectors were placed at nine positions on the inner wall of the KEK neutrino target station, and were exposed to secondary particles during approximately one month of machine operation. After exposure, the production rates of 19 spallation nuclides, which were produced in the Au activation detectors by nuclear reactions with different threshold energies, were determined by γ-ray spectrometry. Thus, it was indicated that the Au activation detector is a novel tool for obtaining the distribution of various secondary particles with high intensity and high energy.     

Synthesis and thermal properties of disiloxane-arylene polymers by dehydrocoupling polymerization of bis(dimethylsilyl)arylene with water

Disiloxane-arylene polymers having phenylene, biphenylene, and fluorenylene groups as arylene units were synthesized by dehydrocoupling polymerization of corresponding bis(silane) derivatives with water. The reactivity of Si-H was not affected by the structure of aromatic groups in the reaction. The polymers containing biphenylene and fluorenylene units are amorphous and show higher glass transition temperatures than the polymer from 1,4-bis(dimethylsilyl)benzene.     

Palladium-catalyzed synthesis of indoles from 2-nitrostyrenes

In the presence of palladium salts, oxidation of 2-nitrostyrenes 1 with nitrous acid alkyl esters 2 resulted in the formation of 2-nitrophenylacetaldehyde dialkyl acetals 3. Reductive cyclization of the acetals 3 with iron powder in acetic acid afforded indoles 5 in good yield.     

Mechanical fabrication of metal nano-contacts showing conductance quantization under electrochemical potential control

We have mechanically fabricated Ni and Cu nano-constrictions in solution to study their quantized conductance behavior under electrochemical potential control. Conductance quantization was observed at both metals in solution at room temperature for the first time. The conductance of Cu nano-constriction was quantized in units of G₀(=2e²/h). A sharp 1G₀ peak was observed in the conductance histogram. For Ni, a rather broad peak at 1–1.5G₀ was observed in the histogram. The conductance quantization behavior was discussed by comparing previously documented results of nano-constrictions fabricated in air or ultra-high vacuum conditions, with those fabricated in solution.     

Copper‐Catalyzed Stereoselective Aminoboration of Bicyclic Alkenes

A copper‐catalyzed aminoboration of bicyclic alkenes, including oxa‐ and azabenzonorbornadienes, has been developed. With this method, amine and boron moieties are simultaneously introduced at an olefin with exo selectivity. Subsequent stereospecific transformations of the boryl group can provide oxygen‐ and nitrogen‐rich cyclic molecules with motifs that may be found in natural products or pharmaceutically active compounds. Moreover, a catalytic asymmetric variant of this transformation was realized by using a copper complex with a chiral bisphosphine ligand, namely (R,R)‐Ph‐BPE.