On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Reaction of C3 and C4 ketoses with alkenals and alkenones in water

Treatment of 1,3-dihydroxyacetone and acrolein with aqueous KOH gave a tetrahydrofuran derivative, 1,4-dihydroxy-3,7-dioxabicyclo[3.3.0]octane, in 80% yield. Similarly, 6-alkyl substituted 1,4-dihydroxy-3,7-dioxabicyclo[3.3.0]octanes were obtained by reaction of 1,3-dihydroxyacetone with various α,β-unsaturated aldehydes. In the cases of long chain alkenals, the reaction was effectively accelerated in the presence of organic co-solvent. On the other hand, the corresponding tricyclic products were synthesized by reaction of 1,3-dihydroxyacetone with cyclic enones, such as 2-cyclopentenone and 2-cyclohexenone. This method was successfully applied to the reaction of a tetrulose in the absence of any protecting groups.     

Facilitated sulfate transfer across the nitrobenzene-water interface as mediated by hydrogen-bonding ionophores.

Facilitated SO4(2-) transfers by hydrogen bond-forming ionophores are investigated across the nitrobenzene (NB)-water interface by using polarography with a dropping electrolyte electrode. Bis-thiourea 1, alpha,alpha'-bis(N'-p-nitrophenylthioureylene)-m-xylene, is found to significantly facilitate the transfer of the highly hydrophilic SO4(2-) whereas its counterpart, N-(p-nitrophenyl)-N'-propylthiourea (ionophore 2), cannot. In contrast to the predominant formation of a 1:1 complex with SO4(2-) in the bulk NB phase, the SO4(2-) transfer assisted by 1 is indeed based on the formation of a 1:2 complex between SO4(2-) and ionophore, even under the condition of [SO4(2-)]aq > [1]org. Such an exclusive formation of the 1:2 (SO4(2-) to ionophore) complex at the NB-water interface is not observed with structurally similar bis-thiourea 3, alpha,alpha'-bis(N'-phenylthioureylene)-m-xylene, where p-nitrophenyl moietes of bis-thiourea 1 are simply replaced by phenyl groups. The facilitated transfer of SO4(2-) with bis-thiourea 1 is further compared to that of HPO4(2-) and H2PO4- across the NB-water interface, which was previously shown to be assisted by 1 through the formation of the 1:1 and 2:1 (anion to ionophore) complexes, respectively. On the basis of these examinations, unique binding behaviors of hydrogen bond-forming ionophores at the NB-water interface are discussed, with a view towards development of ionophore-based anion-selective chemical sensors.     

InGaAs/InAlAs Five Layer Asymmetric Coupled Quantum Well (FACQW) for Ultra-Wideband Ultrafast Optical Modulators

An InGaAs/InAlAs five-layer asymmetric coupled quantum well (FACQW) is expected to show very large electrorefractive index change. n in a wideband transparency region. Band structures of the FACQW are analyzed with Luttinger-Kohn Hamiltonian. The electrorefractive characteristics of the FACQW are discussed.     

Development of Non-Halogen Flame Retardant Optical Fiber and Optical Fiber Cord

A non-halogen highly flame-retardant 0.9mm optical fiber and 2.0mm simplex optical cord, which are harmonized with the ecosystem, have been developed. The characteristics of them are presented in this paper.     

Hetergeneous-nucleation synthesis of monodisperse ε-cobalt nanoparticles using palladium seeds

Monodisperse bimetallic Pd–Co nanoparticles were prepared via a thermal decomposition of cobalt carbonyl using palladium seeds at the Pd/Co molar ratios 0.5%, 1%, and 5%. The heterogeneously nucleated nanoparticles without any size-selective precipitation are sufficiently uniform to self-assemble into ordered arrays. The as-synthesized nanoparticles are each a single crystal with a complex cubic structure called ε-Co. The presence of Pd seeds seems to improve the stability of Co nanoparticles against oxidation based on the results from time-dependent magnetization measurement.     

Pfaffian systems and Radon transforms on affine Grassmann manifolds

Mathematische Annalen -     

Mass spectrometric analysis of low molecular mass polyesters by laser desorption/ionization on porous silicon

A low molecular mass polyester was analyzed by desorption/ionization on porous silicon (DIOS) mass spectrometry. The results were compared with those of matrix-assisted laser desorption ionization (MALDI) mass spectrometry using matrixes of alpha-cyano-4-hydroxycinnamic acid (CHCA) and 10,15,20-tetrakis(pentafluorophenyl)porphyrin (F20TPP). The CHCA matrix was not suitable for characterization of low molecular mass components of the polyester because the matrix-related ions interfered with the component ions. On the other hand, the F20TPP matrix showed no interference because no matrix-related ions appeared below m/z 822. However, the solvent selection for determining optimal conditions of sample preparation was limited, because F20TPP does not dissolve readily in any of the available organic solvents. In the DIOS spectra, the polymer ions were observed at high sensitivity without a contaminating ion. No matrix is needed for DIOS spectra of low molecular mass polyesters, facilitating sample preparation and selectivity of a precursor ion in post-source decay measurements.