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.     

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 -     

Determination of elemental composition of airborne dust and dust suspended in rain

To clarify the magnitude of wash-out effect of rain on the elemental composition of airborne dust and the possible origin of the dust, the dust samples were collected with a high-volume air sampler at the JAERI-Tokai. The dust suspended in rain was also collected from rain by filtration. Up to 20 elements in both types of the dust were determined by instrumental neutron activation analysis. It was found that the elements determined could be classified into 3 groups from the elemental composition and the elemental correlation in both types of the dust samples.     

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.     

Prompt gamma-ray analysis using cold and thermal guided neutron beams

The extraction behavior of uranium(VI), plutonium(IV) and some fission products like zirconium(IV), ruthenium(III) and europium(III) from 3.5M nitric acid with -irradiated organic phase pre-equilibratedn-dodecane solutions of dihexyl derivatives of hexanamide (DHHA), octanamide (DHOA) and decanamide (DHDA) has been investigated as a function of absorbed dose upto 184·10⁴ Gy. The results indicate that the extraction of uranium(VI) decreases gradually with dose upto 72·10⁴ Gy and becomes almost constant thereafter, while, the extraction of plutonium(IV) decreases upto a dose of 20·10⁴ Gy and then increases rapidly up to a dose of 82·10⁴ Gy indicating synergistic effects of radiolytic products formed at higher doses. Extraction of zirconium(IV) increases gradually upto a dose of 72·10⁴ Gy. Europium(III) does not get extracted with any of these amides in the entire dose range (0–184·10⁴ Gy) studied, however, ruthenium shows insignificant increase in extraction with dose. The decrease inD values noticed in the case of plutonium and zirconium after the dose of 72·10⁴ Gy which was attributed to the third phase formation and emulsification. Infrared studies confirm the final products of radiolysis as the respective amines and carboxylic acids. The degraded amide contents have been estimated by quantitative IR spectrophotometric technique. Extraction data obtained for uranium(VI) and plutonium(IV) with TBP/n-dodecane system have also been compared under similar experimental conditions.