Large time behavior of small solutions to subcritical derivative nonlinear Schrödinger equations

We consider the derivative nonlinear Schrödinger equations

where the coefficient satisfies the time growth condition

is a sufficiently small constant and the nonlinear interaction term consists of cubic nonlinearities of derivative type

where and . We suppose that the initial data satifsfy the exponential decay conditions. Then we prove the sharp decay estimate , for all , where . Furthermore we show that for there exist the usual scattering states, when and the modified scattering states, when

     

Formation of cyclic organosilicon compounds via organopolysilyl anions starting from methoxymethyldisilanes. A mechanistic study

In the presence of a catalytic amount of sodium methoxide, sym-dimethoxytetramethyldisilane was converted into α,ω-dimethoxypermethylpolysilanes, MeO(SiMe₂)_nOMe where n ? 3, at room temperature. On the other hand, similar treatment of the disilane in THF solution gave cyclic polysilanes, (Me₂Si)_n where n = 5–7. Decomposition of the disilane in the presence of diphenylacetylene afforded a trisilacyclopentene derivative under similar conditions. This compound was obtained also by the reaction between α,ω-dimethoxypermethylpolysilanes and diphenylacetylene in the presence of sodium methoxide. These cyclic products most likely were formed via permethyl polysilyl anion intermediates derived from α,ω-dimethoxypermethylpolysilanes. Also, the formation of α,ω-dimethoxypermethylpolysilanes could be elucidated in terms of the mechanism involving the base-assisted, concerted nucleophilic substitution or stepwise substitution by silyl anions, rather than the successive dimethylsilylene (Me₂Si:) insertion reaction.     

Quantum mechanical single-gold-nanocluster electroluminescent light source at room temperature

Electrically contacted gold-nanocluster arrays formed within electromigration-induced break junctions exhibit bright, field-dependent electroluminescence in the near infrared (650-800 nm). Intensity autocorrelation of spatially isolated individual nanocluster emission driven at high electrical frequency (f(ac)= approximately 200 MHz) reveals antibunched electroluminescence at room temperature. These results demonstrate the single quantum nature of several-atom gold molecules and suggest their use as room-temperature electrically driven single-photon sources.     

Validity of retinal oxygen saturation analysis: Hyperspectral imaging in visible wavelength with fundus camera and liquid crystal wavelength tunable filter

The purpose of this paper was to investigate the feasibility of a newly developed hyperspectral fundus imaging camera with a liquid crystal tunable filter. The intensities of different wavelengths of light transmitted through an artery, vein, and the area surrounding these vessels and reflected out were measured, and the differential spectral absorptions were analyzed. Measurements were made from 16 normal eyes and from two artificial capillaries. The ratios of absorption (ROA) of arteries to veins from 500 to 580 nm (range 1) and from 600 to 720 nm (range 2) were calculated. For all eyes, the ROA_range1 was larger than ROA_range2. The ROA obtained from the artificial capillary filled with blood saturated with oxygen or nitrogen was similar to that of simulated data of oxy- and deoxyhemoglobin extinction rate. Most ROAs of human eyes were lower than those of the simulated data and the artificial capillaries. Oxygen saturation analysis by hyperspectral fundus imaging of retinal vessels were qualitatively in agreement with thein vitro analysis or simulated values. However, further improvements are necessary to evaluate the oxygen saturation quantitatively in the retinal blood vessels.     

Binding properties of alginic acid and chitin

The binding properties of granular alginic acid(H-alg.) and chitin to iodine, bromine, cadmium ion, calcium ion and cholesterol were investigated. Chitin-iodine and chitin-bromine compounds closely resemble those of H-alg. The amount of iodine included by these polysaccharides increased with a decrease in the concentration of potassium iodide (KI). The number of sugar residues bound to one iodine molecule extrapolated to 0 g of KI was around 6.0 for H-alg. and 6.4 for chitin. These saccharides, which do not form a gel in water, were found to also absorb KI and radioactive iodide or iodine in aqueous solution. H-alg. did not show as much affinity to cadmium ion and calcium ion and cholesterol in iso-propyl alcohol as metalalginates.Presented at the Fourth International Symposium on Inclusion Phenomena and the Third International Symposium on Cyclodextrins, Lancaster, U.K., 20–25 July 1986.     

Design and fabrication of a dielectrophoresis-based cell-positioning and cell-culture device for construction of cell networks

In this paper, we describe the design and fabrication of a dielectrophoresis (DEP)-based cell-positioning and cell-culture device for the construction of cell networks. This device enables both individual cell positioning and cell culture. Titanium electrodes were fabricated by deposition. Furthermore, microchambers and microchannels composed of SU-8, which is a negative photoresist, were used to carry out cell culture and enable cell differentiation. Using our device, N1E-115 cells were individually positioned in the microchambers, and the positioning yield was 45%. After positioning, the cells could be continuously cultured in the microchambers. Furthermore, the cells differentiated, and their neurites extended through the microchannels after cultivation for several days. These results indicate that our device greatly increases the prospects for individual cell positioning and can be used to construct cell networks that have several applications in the medical field, for example, in drug screening.     

Investigation of individual micrometer-size Kosa particle with on-site combination of electron microscope and synchrotron X-ray microscope.

The Kosa (yellow sand) aerosol affects the global environment as well as human health because it migrates from the interior of China to other areas, absorbing various atmospheric elements. Investigation into individual Kosa aerosol particles, which are submicroscopic to several tens of micrometers in diameter, is required to resolving the issue. We installed a scanning electron microscope (SEM) equipped with an energy dispersive X-ray spectrometer (EDX) on a synchrotron radiation (SR) beam line and introduced the SR beam into the SEM chamber for combinatorial application of SEM-EDX and SR X-ray fluorescence (SR-XRF) spectrometry to individual particles. It should be noted that detailed topographic observation by SEM and sensitive elemental analysis by SR-XRF, both crucial for individual particle measurement but which previously had to be carried out separately, were jointly performed inside the SEM chamber in this setup. Here, we show that SR-XRF results, in conjunction with SEM images, contributed toward resolving individual particle dispositions. Atmospheric sulfur primarily adheres to calcium in the aerosol particles and the particle surface roughens as a consequence of the chemical reaction between the two elements.     

Some properties of invariant polynomials with matrix arguments and their applications in econometrics

Summary Further properties are derived for a class of invariant polynomials with several matrix arguments which extend the zonal polynomials. Generalized Laguerre polynomials are defined, and used to obtain expansions of the sum of independent noncentral Wishart matrices and an associated generalized regression coefficient matrix. The latter includes thek-class estimator in econometrics.