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.     

Constructive and Destructive Two-Pulse Excitation Investigated with a White-Light Michelson Interferometer

Linear propagation of two pulses through methanol solution of aluminum phthalocyanine chloride is investigated using a modified white-light Michelson interferometer. The observed coherence time of the white light is 6 fs, and the separation between the two-excitation pulses is set to about 10 fs. The excitation is dependent on the phase-relation between the two pulses. We have observed an enhancement of the excitation when the two pulses are in-phase and strong suppression of the excitation when the two pulses are out of phase by π.     

Structure of cypridina biluciferyl,a dimer of cypridina luciferyl radical having bioluminescent activity

Structure of $\text{Cypridina}$ biluciferyl (luciferyl radical dimer), which is produced by chemical oxidation of $\text{C}$. luciferin with such as ferricyanide, was determined to be the symmetric 5,5′-dimer of $\text{C}$. luciferin. It gives light in the presence of $\text{C}$. luciferase, although the bioluminescent rate is very low. We suggest that the biluciferyl is an intermediate in the oxidation of the luciferin to $\text{C}$. luciferinol.     

Application of gas chromatograph-mass spectrometer-computer system to evaluation of 14C-labelled compounds

Usefulness of gas chromatograph-mass spectrometer-computer system (GC-MS-CPU) not only for measurement of specific activities of 14C-labelled compounds in a mixture but also for evaluation of 14C-labelled compounds in terms of examining their purities and elucidating chemical structures of the impurities was proved. A sample of methyl 2-(p-chlorophenyl-14Cn)-3-methylbutylate (III) synthesized from p-chlorophenyl-14Cn-acetonitrile (VI) was analyzed by GC-MS-CPU, and it was found that the labelled compound was contaminated with a small amount of the corresponding m-isomer (IV) having a very high specific activity. Further examination suggested that the contaminating m-isomer (IV) originated from m-chlorophenyl-14Cn-acetonitrile (IX) which had already contaminated in the starting material (VI), and also that cyanomethylation of p-dichlorobenzene-14Cn (VIII) by benzene-type reaction resulted in producing a mixture of p- and m-chlorophenyl-14Cn-acetonitriles (VI, IX).     

Solvent-Vapor-Induced Reversible Single-Crystal-to-Single-Crystal Transformation of a Triphosphaazatriangulene-Based Metal–Organic Framework

A triphosphaazatriangulene (H₃L) was synthesized through an intramolecular triple phospha-Friedel–Crafts reaction. The H₃L triangulene contains three phosphinate groups and an extended π-conjugated framework, which enables the stimuli-responsive reversible transformation of [Cu(HL)(DMSO)⋅(MeOH)]_n, a 3D-MOF that exhibits reversible sorption characteristics, into (H₃L⋅0.5 [Cu₂(OH)₄⋅6 H₂O] ⋅4 H₂O), a 1D-columnar assembled proton-conducting material. The hydrophilic nature of the latter resulted in a proton conductivity of 5.5×10⁻³ S cm⁻¹ at 95 % relative humidity and 60 °C.     

Three-directional spectral dispersion for smoothing of a laser irradiance profile

In inertial confinement fusion research, uniform laser irradiation on a fusion target is a key issue. We propose a new method of beam smoothing in which we use three-directional spectral dispersion to reduce the coherent speckle that is unavoidable in the usual two-directional spectral-dispersion scheme. We have used this smoothing technique in a Nd:glass laser system and have demonstrated that the coherent speckle is reduced by a factor of 2.9 from that in two-directional spectral dispersion.     

Enantioselective Addition of Allylic Trimethoxysilanes to Aldehydes Catalyzed by p-Tol-BINAP small middle dotAgF

Catalytic asymmetric allylation of aldehydes with allylic trimethoxysilanes was achieved with the p-Tol-BINAP small middle dotAgF complex as catalyst [Eq. (a); p-Tol-BINAP=2,2'-bis(di-p-tolylphosphanyl)-1,1'-binaphthyl)]. High anti and enantioselectivities were obtained in the reaction with crotyltrimethoxysilane, irrespective of the configuration at the double bond.     

The optical properties and laser characteristics of Cr and Nd co-doped Y3Al5O12 ceramics

We have fabricated Cr³⁺ and Nd³⁺ co-doped YAG (Cr;Nd:YAG) ceramics, and investigated their optical properties and laser characteristics. The Cr;Nd:YAG has two broad absorption bands at around 440 nm (⁴A₂→⁴T₁) and 600 nm (⁴A₂→⁴T₂) respectively, caused by Cr³⁺ ions. In the case of pumping at 440 nm, the maximum effective lifetime of the Cr;Nd:YAG was 737 μs with a 0.1 at% Cr³⁺ and 1.0 at% Nd³⁺ co-doped YAG sample. Cr³⁺ ions take a role of an effective sensitizer to convert the UV light of flashlamp. For single-shot laser operation, a 10.4 J output energy at 1064 nm was obtained with 0.1 at% Cr³⁺ and 1.0 at% Nd³⁺ co-doped YAG ceramic rod with a laser efficiency of 4.9%. The laser efficiency was found to be more than twice that of a 1.0 at % Nd³⁺:YAG ceramic rod.