High-dimensional asymptotic expansions for the distributions of canonical correlations

This paper examines asymptotic distributions of the canonical correlations between and with q≤p, based on a sample of size of N=n+1. The asymptotic distributions of the canonical correlations have been studied extensively when the dimensions q and p are fixed and the sample size N tends toward infinity. However, these approximations worsen when q or p is large in comparison to N. To overcome this weakness, this paper first derives asymptotic distributions of the canonical correlations under a high-dimensional framework such that q is fixed, m=n−p→∞ and c=p/n→c₀∈[0,1), assuming that and have a joint (q+p)-variate normal distribution. An extended Fisher’s z-transformation is proposed. Then, the asymptotic distributions are improved further by deriving their asymptotic expansions. Numerical simulations revealed that our approximations are more accurate than the classical approximations for a large range of p,q, and n and the population canonical correlations.     

On weighted-norm estimates for nonstationary incompressible Navier-Stokes flows in a 3D exterior domain

We study the time-decay of weighted norms of weak and strong solutions to the Navier-Stokes equations in a 3D exterior domain. Moment estimates for weak solutions and weighted Lq-estimates for strong solutions are deduced, both of which seem to be optimal. The relation is discussed between the space-time decay and the vanishing of the total net force exerted by the fluid to the body. A class of initial data is given so that the total net force associated to the corresponding fluid flows does not vanish.     

In situ and ex situ observations of the growth dynamics of single perylene nanocrystals in water

The growth dynamics of fluorescent perylene nanocrystals, which are fabricated by the reprecipitation method, was investigated using in situ and ex situ single-particle fluorescence measurements. A red shift in the emission maxima as the aging time increased was observed by single-particle fluorescence spectral measurements. The number and size of the nanocrystals increased with the increasing aging time in water. It was concluded that the metastable intermediates, such as clusters and initial nanoparticles, are relevant for the early stages of nucleation and growth of the perylene nanocrystals.     

Mg-promoted reductive coupling of aromatic carbonyl compounds with trimethylsilyl chloride and bis(chlorodimethylsilyl) compounds

Mg-promoted reductive coupling of aromatic carbonyl compounds (1) with chlorosilanes, such as trimethylsilyl chloride (TMSCl:2), 1,2-bis(chlorodimethylsilyl)ethane (3) and 1,5-dichlorohexamethyltrisiloxane (4), in N,N-dimethylformamide (DMF) at room temperature brought about selective and facile reductive formation of both of carbon-silicon and oxygen-silicon bonds to give the corresponding α-trimethylsilylalkyl trimethylsilyl ethers (5) and cyclic siloxanes (6), (7) in moderate to good yields, respectively. The present facile and selective coupling may be initiated through electron transfer from Mg metal to aromatic carbonyl compounds (1).     

Autoxidized phospholipids in hexane: nano-self-assemblies studied by synchrotron small-angle X-ray scattering

Synchrotron small-angle X-ray scattering (SAXS) was used to analyze the structure of self-assembled autoxidized phospholipids in a very dilute solution of hexane. In addition, it was used to build a self-consistent model of the aggregates, taking into account their inner heterogeneities and polydispersity. The scattering intensity from a dilute mixture of different types of noninteracting components of the phospholipid system was represented as a linear combination of partial intensities from the components weighted by their volume fractions. Applying this approach the final model of the system was described as a mixture of polydisperse reverse micelles and aggregates with spherical and cylindrical shapes. Spherical aggregates were represented as hollow spheres with inner radius 0.7 nm (occupied by water or hexane) and outer radius 1.5 nm. Geometrical parameters of the aggregates did not change much during the oxidation process, while the ratio of reverse micelles and aggregates in solution varied. The amount of the reverse micelles increased from very low to about 80%, whereas the content of other aggregates constantly reduced. The analysis performed in this study helps one to better understand the processes of phospholipid oxidation, which may occur in biological membranes.     

Acceleration of laser-induced formation of gold nanoparticles in a poly(vinyl alcohol) film

Gold nanoparticles (AuNps) were fabricated in a poly(vinyl alcohol) (PVA) film using the photochemically generated benzophenone ketyl radical and PVA radical by laser irradiation as a reducing agent. The measurements of the surface plasmon band of AuNps indicated that AuNps continued growing in the PVA film for several hours or days after the laser irradiation. The formation process of AuNps in the PVA film was investigated by using laser flash photolysis and UV-vis absorption spectroscopy. Additive doping (formic acid or sodium 2-mercaptoethanesulfonate) in the PVA film dramatically accelerated or inhibited the formation rate of the AuNps, respectively. The doping of formic acid accelerated the formation rate of the AuNps by a factor of 10-20. On the contrary, doping of 2-mercaptoethanesulfonate inhibited the formation of AuNps. The mechanisms of the acceleration and inhibition were investigated by using laser flash photolysis. The effects of additives on the formation process of AuNps are discussed.     

Nepalensinols D-G, new resveratrol oligomers from Kobresia nepalensis (Cyperaceae) as potent inhibitors of DNA topoisomerase II

Four new resveratrol oligomers, nepalensinols D-G, were isolated from the stem of Kobresia nepalensis (Cyperaceae). The structures were determined by detailed NMR spectral analysis. The compounds were assessed for their inhibitory activity against human topoisomerase II, a potential target of anti-tumor agents. These stilbenoids showed potent inhibitory activity against human topoisomerase II with IC50 values of 5-15 microM.     

Resveratrol oligomers and their O-glucosides from Cotylelobium lanceolatum

Three new resveratrol oligomers, cotylelophenol C (1) (resveratrol tetramer) and cotylelosides A (2) and B (3) (O-glucosides of resveratrol trimer), together with four known glucosides of resveratrol oligomers (vaticasides A, B, C, D) and piceid, were isolated from an acetone soluble part of stem of Cotylelobium lanceolatum (Dipterocarpaceae). The structures of new compounds were determined by spectral data analysis. The characteristic properties observed in the NMR spectra of 1 were also discussed.     

Emission from charge recombination during the pulse radiolysis of 9-cyano-10-phenylethynylanthracenes with donor and acceptor substituents

Emission from 9-cyano-10-phenylanthracene and 9-cyano-10-phenylethynylanthracenes having donor and acceptor substituents (RA = PA, PEA, OEA, NEA, and DEA) was studied with the time-resolved fluorescence measurement during the pulse radiolysis of RAs in benzene (Bz). PA and DEA showed only monomer emission, while other RAs (PEA, OEA, and NEA) showed both monomer and excimer emissions with much lower intensities. On the basis of the steady-state and transient absorption and emission measurements, the formation of RA in the singlet excited state ((1)RA*) can be attributed to the charge recombination between RA radical cation and anion (RA*+ and RA*-, respectively) which are initially generated from the radiolytic reaction in Bz. It is expected that for PA with a twisted geometry, the charge recombination between PA*+ and PA*- occurs to give (1)PA* during the pulse radiolysis in Bz. For PEA and OEA, pi-stacking interaction is possible for the formation of an encounter complex during the charge recombination between RA*+ and RA*-. For NEA, it is expected that NEA*+ and NEA*- collide neck-to-neck to generate the excimer due to the twisted geometry. For DEA, a considerably twisted structure is assumed to give (1)DEA* with strong ICT character but not (1)(DEA)2* because of the bulky donor substituent.     

Electro-optic transparent frequency conversion of a continuous light wave based on multistage phase modulation

Frequency conversion of a continuous light wave based on multistage phase modulation has been investigated both analytically and numerically. The proposed frequency-conversion process consists of three stages: (i) phase modulation and chirp compression to generate a pulse train, (ii) Doppler shift of the pulse center frequency in a second phase modulation, and (iii) demodulation of the pulse train. By controlling the modulation power we can select the destination frequency from an equally spaced grid separated by the modulation frequency. A conversion efficiency of approximately 40% has been numerically confirmed with respect to a destination frequency of +/- 50 channels. Carrier frequency conversion of an analog data stream is numerically demonstrated.