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.     

Almost automorphic solutions for abstract functional differential equations

For abstract linear functional differential equations with an almost automorphic forcing term, we establish a result on the existence of almost automorphic solutions, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations.     

Pfaffian systems and Radon transforms on affine Grassmann manifolds

Mathematische Annalen -     

Ethylene polymerization by chromium complexes with phosphorous‐bridged bisphenoxy ligand

Chromium catalysts combined with phosphorous‐bridged bisphenoxy ligands were found to be highly active for ethylene polymerization. The most efficient catalyst precursor among them, generated by combining bis[3‐tert‐butyl‐5‐methyl‐2‐hydroxyphenyl](phenyl)phosphine hydrochloride ( 1a ) and CrCl₃(THF)₃, was characterized. X‐ray analysis of (3‐tert‐butyl‐5‐methyl‐2‐phenoxy)(3‐tert‐butyl‐5‐methyl‐ 2‐hydroxyphenyl)(phenyl)phosphine bis(tetrahydrofuran)chromium dichloride ( 6 ), obtained by the reaction of 1a and CrCl₃(THF)₃ in the presence of NaH, revealed a unique structure in which one phenol moiety of the bisphenol did not coordinate to the chromium center. Complex 6 showed higher activities than those observed in the in situ catalyst system. Polyethylene of various molecular weights was obtained with differing activators. The highest activity (113.5 kg mmol (cat)^?1 h^?1) was observed when TIBA/TB was used as a cocatalyst. A medium molecular weight polymer with narrow molecular weight distribution (M_w = 128,700, M_w/M_n = 1.8) was obtained using a 6 ‐TIBA/B(C₆F₅)₃ system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3668–3676, 2007     

Hydration Structure Around the Carboxyl Group Studied by Neutron Diffraction with 12C/13C and H/D Isotopic Substitution Methods

Time-of-Flight (TOF) neutron diffraction measurements have been carried out on aqueous 8 mol% sodium acetate solutions in D₂O. Scattering cross sections that were observed for sample solutions involving ¹²C/¹³C and H/D isotopically substituted acetate ions were used to derive the first-order difference functions, Δ_H(Q) and Δ_C(Q), and corresponding distribution functions, G _H(r;r) and G _C(r;r), which describe the environmental structure around the methyl and the carboxyl groups within the acetate ion, respectively. Structural parameters concerning the first hydration shell of the carboxyl group within the acetate ion were obtained through the least squares fit to the observed intermolecular difference function, Δ_C ^inter(Q). The nearest neighbor C _O...D _W1 (C_O: carboxyl carbon atom, D_W1: water deuterium atom) distance, r(C _O...D _W1 ), and the angle, ∠ C _O ...D _W1 -O _W (O _W : water oxygen atom), were determined to be 2.63(1) Å and 120(1)°, respectively. The coordination number, n(C _O ...D _W1 ), was obtained to be 4.0(1). These results are consistent with the hydration structure in which water molecules in the first hydration shell of the carboxyl group are hydrogen-bonded with oxygen atoms of the carboxyl group.