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.     

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.     

Probing for electrical inclusions with complex spherical waves

Let a physical body Ω in ?² or ?³ be given. Assume that the electric conductivity distribution inside Ω consists of conductive inclusions in a known smooth background. Further, assume that a subset Γ ? ?Ω is available for boundary measurements. It is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on Γ. More precisely: given a ball B with center outside the convex hull of Ω and satisfying (B? ∩ ?Ω) ? Γ, boundary measurements on Γ with explicitly given Dirichlet data are enough to determine whether B intersects the inclusion. An approximate detection algorithm is introduced based on the theory. Numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion‐free domain near Γ and is robust against measurement noise. © 2007 Wiley Periodicals, Inc.     

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.     

Crystallographic report: Bis{µ‐[O‐cyclopentyl(4‐methoxyphenyl)dithiophosphonato]1κ:S,2κ:S‐[O‐cyclopentyl(4‐methoxyphenyl)dithiophosphonato]‐1κ2S,S′}dicadmium(II)

The centrosymmetric title compound, [Cd₂{CH₃OC₆H₄P(OC₅H₉)S₂}₄], features an eight‐membered [? Cd? S? P? S? ]₂ ring owing to the presence of bridging dithiolate ligands. Tetrahedral coordination geometries for cadmium are completed by chelating ligands. Copyright © 2004 John Wiley & Sons, Ltd.     

Pfaffian systems and Radon transforms on affine Grassmann manifolds

Mathematische Annalen -     

Electronic effect on the regioselectivity in the ring opening of para-substituted phenyloxiranes by acetylides

The electronic effect on the regioselectivity in the alkynylation of phenyloxiranes was investigated using three kinds of metal acetylides. BF₃ mediated lithium acetylide provided either the α- or β-alkynylated products by controlling the effect of the para-substituents of the phenyloxiranes. LiClO₄ mediated lithium acetylide and titanium acetylide, on the other hand, afforded predominantly the β- and α-products, respectively.