Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity

We study smoothing properties for time-dependent Schrödinger equations , , with potentials which satisfy V(x)=O(|x|^m) at infinity, m?2. We show that the solution u(t,x) is 1/m times differentiable with respect to x at almost all , and explain that this is the result of the fact that the sojourn time of classical particles with energy λ in arbitrary compact set is less than CTλ^−1/m during [0,T] when λ is very large. We also show Strichartz's inequality with derivative loss for such potentials and give its application to nonlinear Schrödinger equations.     

Nonameric porphyrin assemblies--formation and intra-assembly energy transfer reactions

The nonameric porphyrin assemblies constructed with the series of free base tetraphenylporphyrins Pn having four pyrazine moieties linked with alkyl chains of different lengths, (CH2)n (n = 1, 5, 9, 17, 30), and dimeric [meso-tetrakis(2-carboxy-4-nonylphenyl)porphyrinato]zinc(II), ZnP2, show the effective light-collection effect and the typical Forster-type energy transfer from ZnP2 to Pn.     

Control of bacteria adhesion by cell-wall engineering

UDP-MurNAc-pentapeptide derivative bacterial cell-wall precursors were synthesized as effective tools for surface display on living bacteria. Lactobacilli were incubated in the ketone-modified precursor-containing medium, and the ketone moiety was displayed on the bacterial surface through cell-wall biosynthesis. Oligomannose was coupled with the ketone moiety on the bacterial surface via a aminooxyl linker, thereby displaying this oligosaccharide on the surface of the bacteria. The increase in the adhesion of the sugar-displaying bacteria onto a concanavalin A-attached film compared to that of native bacteria was confirmed by microscopic observation and surface plasmon resonance measurement. The incorporation of the artificial cell-wall precursors was enhanced when incubated with fosfomycin, an inhibitor of cell-wall precursor biosynthesis.     

Comparison in fractal dimension between those obtained from structure factor and viscoelasticity of gel networks of 1,3:2,4-bis-O-(p-methylbenzylidene)-D-sorbitol in polystyrene melt at gel point

We investigated time evolution of shear moduli in the physical gelation process of 1,3:2,4-bis-O-(p-methylbenzylidene)-D-sorbitol in polystyrene melt. At the gel point, storage and loss shear moduli, G' and G", were described by the power law of frequency omega, G' approximately G" approximately omegan, with the critical exponent n being nearly equal to 2/3, in agreement with the value predicted by the percolation theory. We also investigated the structure factor over two decades in length scale at gel point by using ultra-small-angle X-ray scattering, and small-angle X-ray scattering. We found the power-law behavior in low-q region, indicating that the gel network forms the self-similar structure with mass-fractal dimension. Comparison between the exponent of mass-fractal dimension from structure factor and that from viscoelasticity indicates that hydrodynamic interactions are completely screened out and the excluded volume effects are dominant in the gel. The gel strength was found to increase with the decrease in the lower limit length scale of fractality.     

Observation of electrostatically released DNA from gold electrodes with controlled threshold voltages

DNA oligo-nucleotides, localized at Au metal electrodes in aqueous solution, are found to be released when applying a negative bias voltage to the electrode. The release was confirmed by monitoring the intensity of the fluorescence of cyanine dyes (Cy3) linked to the 5' end of the DNA. The threshold voltage of the release changes depending on the kind of linker added to the DNA 3'-terminal. The amount of released DNA depends on the duration of the voltage pulse. Using this technique, we can retain DNA at Au electrodes or Au needles, and release the desired amount of DNA at a precise location in a target. The results suggest that DNA injection into living cells is possible with this method.     

Development of a novel analytical method for determination of chondroitin sulfate using an in-capillary enzyme reaction

A novel analytical method for determination of total amount of chondroitin sulfate (CS) based on its conversion to desulfated chondro-disaccharide via an enzyme-catalyzed reaction, was developed. Using the in-capillary enzyme reaction, the method was also applied to the successful construction of an on-line analytical system. Within this system, electrophoretic migration was used to mix zones containing the enzyme mixture (chondroitinase ABC, chondro-4-sulfatase, chondro-6-sulfatase and 2-o-sulfatase) and the substrate (CS). The reaction was then allowed to proceed in the presence of a weak electric field and, finally, the product (desulfated chondro-disaccharide) of enzyme reaction migrated to the detector under the influence of an applied electric field. A polyvinyl alcohol-coated capillary was used to reduce protein adsorption. Desulfated chondro-disaccharide was successfully migrated toward the anode in 10 mM Tris-acetate buffer (pH 7.0) under reversed polarity and detected at 232 nm. The established method was validated and demonstrated to be applicable in the determination of total amount of CS in a commercial ophthalmic solution. No interference from the formulation excipients was observed. Good linearity was obtained, with correlation coefficients above 0.999. Recoveries and precisions ranged from 100.0 to 100.5%, and from 0.2 to 0.6% of the relative standard deviation, respectively. Good agreement was obtained between the established method and traditional photometric method based on carbazole reaction. In this study, application of the method to disaccharide compositional analysis was also performed.     

In situ organogelation at room temperature: direct synthesis of gelators in organic solvents

Organogels are formed through a conventional organogelation involving a heating process and an in situ organogelation at room temperature. The conventional organogelation is carried out by dissolution of gelators by heating, while the in situ organogelation is performed by mixing of highly reactive methyl 2,6-diisocyanatohexanoate (LDI) or 2-isocyanatoethyl 2,6-diisocyanatohexanoate (LTI) and alkylamines. The in situ organogelation produced the organogels within several seconds after mixing. The organogels prepared by the in situ organogelation showed quite similar FT-IR spectra and SEM photographs to those formed by conventional organogelation. Moreover, the in situ organogelation using LTI and octylamine as well as dodecylamine produced organogels of acetone, ethyl acetate, and acetonitrile that gelators 5 and 6 cannot gel through conventional organogelation.     

Syntheses, structures and antimicrobial activities of water-soluble silver(I)-oxygen bonding complexes with chiral and racemic camphanic acid (Hca) ligands

Water-soluble, relatively light-stable, chiral and achiral silver(I) complexes [[Ag(2)(ca)(2)]](n) and [[Ag(2)(ca)(2)(Hca)(2)]](n)(R- and S-Hca =(1R,4S)- and (1S,4R)-4,7,7-trimethyl-3-oxo-2-oxabicyclo[2.2.1]heptane-1-carboxylic acid, respectively) prepared from the reaction of Ag(2)O with chiral and racemic Hca in 1:2 and 1:4 molar ratios were characterized by elemental analysis, TG/DTA, FTIR, and solution ((1)H, (13)C and (109)Ag) and solid-state ((13)C) NMR spectroscopy. Crystallography revealed that unique 2(1) helical polymer and zigzag structures were formed on self-assembly of the dimeric units in the crystals of [[Ag(2)(S-ca)(2)]](n) and three [[Ag(2)(ca)(2)(Hca)(2)]](n). In the crystal of [[Ag(2)(S-ca)(2)]](n) two 2(1) helices and a loop were observed in the stair-like polymer structure, whereas zigzag and a loop were seen in the crystals of three [[Ag(2)(ca)(2)(Hca)(2)]](n). Carbon NMR spectra in the solid state and in D(2)O indicated that these polymeric structures were loosely bound and fast ligand-exchange reactions took place in aqueous solution. The complexes, [[Ag(2)(ca)(2)]](n) and [[Ag(2)(ca)(2)(Hca)(2)]](n), showed a wide spectrum of effective antimicrobial activity as anticipated for weak silver(i)-O bonding complexes. Similar antimicrobial activity of [[Ag(2)(ca)(2)]](n) and [[Ag(2)(ca)(2)(Hca)(2)]](n) against selected microorganisms suggested that ligand exchangeability played an important role as well as the coordination geometry of the silver(i) ion.     

Synthesis of conjugated oligomers having aromatic and enediyne units alternately in the backbone that show intense fluorescence emission

[structure: see text] Synthesis and fluorescence properties of pi-conjugated compounds having alternately an aromatic ring such as benzene, pyridine, and thiophene and an enediyne unit in the backbone are described.     

Data extrapolation method for boundary element method-based near-field acoustical holography

A new data extrapolation method for boundary element method (BEM)-based near-field acoustical holography (NAH) is proposed to reduce an error of the reconstructed result obtained from the pressure measured on an aperture small compared with the structure. The finiteness of the measurement aperture is a serious impediment to actual large-scale implementation of NAH, because NAH requires the measurement of the pressure field over a complete surface of structure. To eliminate the requirement, the wave number-space data extrapolation method for fast Fourier transform (FFT)-based NAH has been proposed. In this paper, the extension of this data extrapolation method to BEM-based NAH is presented. The effectiveness of this method is demonstrated by experiments. The experiment results confirm that the reconstruction error is sufficiently suppressed by the proposed method.