Hyers–Ulam stability of linear differential operator with constant coefficients

Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polarization Sensitive Spectral Interferometric Optical Coherence Tomography for Biological Samples

A spectral interferometric optical coherence tomography (OCT) system which has polarization sensitivity is developed. This system reduces the mechanical scanning dimension by employing the principle of spectral interferometry, and measures a two dimensional cross-sectional image of biological tissue with one dimensional mechanical scanning. Sixteen OCT images with different polarization conditions are measured, and two dimensional distributions of each element of the Müller matrix of a sample to be measured are calculated.     

Effect of the pore surface modification of an inorganic substrate on the plasma‐grafting behavior of pore‐filling‐type organic/inorganic composite membranes

We have investigated the effect of the surface state and surface treatment of the pores of an inorganic substrate on the plasma‐grafting behavior of pore‐filling‐type organic/inorganic composite membranes. Shirasu porous glass (SPG) was used as the inorganic substrate, and methyl acrylate was used as the grafting monomer. The grafting rate increased as the density of silanol on the SPG substrate increased. This result suggests that radicals are generated mainly at the silanol groups on the pore surface by plasma irradiation. The SPG substrates were treated with silane coupling agents used to control the mass of organic material bonded to the pore surface. The thickness of the grafted layer became thinner as the mass of organic material bonded to the pore surface of SPG increased. This decrease in the thickness of the grafted layer could be explained by the decrease in the penetration depth of vacuum ultraviolet rays contained in plasma having a wavelength of less than 160 nm that generated radicals in the pores of the substrate. The thickness of the grafted layer inside the SPG substrates could be controlled through the control of the mass of organic material bonded to the pore surface of the SPG substrate. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 846–856, 2006     

Preparation and physical properties of flame retardant acrylic resin containing nano-sized aluminum hydroxide

Poly(methylmethacrylate) (PMMA) shows high strength and transparency but is a flammable material. In this study, the surface of aluminum hydroxide was modified with methacrylate containing phosphoric acid moieties before dispersion in MMA, and organic-inorganic nano-hybrid materials were obtained by bulk polymerization in the presence of the surface-modified aluminum hydroxide. The resulting hybrid materials retained the high transparency of PMMA, with transparency values similar to that of pure PMMA. Moreover, the flame resistance of the hybrid materials was improved in comparison with that of pure PMMA, with depression of the horizontal burning rate becoming a maximum at an inorganic content of 3 wt%. These results suggest that the use of aluminum hydroxide surface-modified with phosphoric acid groups is an efficient method for obtaining good performance fire-resistant polymer materials.     

DESIGN AND PERFORMANCE OF THE OKAZAKI LARGE SPECTROGRAPH FOR PHOTOBIOLOGICAL RESEARCH

A computer-operated spectrograph was recently built at Okazaki, Japan. Different specimens can be placed on a horseshoe-shaped focal curve (10 m long) covering a wavelength range of 250 to 1000 nm so they can be irradiated simultaneously. The linear dispersion is about 0.8 nm/cm. The photon fluence rate on the focal curve is 5 x 10¹⁵. photons x cm^-2 x s^-1 at 300nm and 1 x 10¹⁶ photons x cm^-2 x s^-1 at 600 and at 900 nm. The spectral half width is 5.5 nm or less on the focal curve. The stray light content is about 10^-5 of the main peak at the peak wavelength ± 100 nm. Specimens are set in microcomputer-controlled threshold boxes so that wavelengths, photon fluence rates, photon fluences and timing of irradiations are controlled automatically according to a pre-programmed schedule. An optical fiber system is also provided for remote irradiations.     

Measurement of hyperfine structure constants,g values and tensor polarizability of excited states of Sm I

Atomic-beam laser spectroscopy with fluorescence detection is applied to investigate the hyperfine structure (hfs), Stark and Zeeman effects of the electric dipole transitions of Sm i. The measurements are performed for the four transitions of 0 → 15650.55, 292.58 → 15650.55, 292.58 → 15567.32, and 1489.55 → 16890.59 cm^-1. The hfs constants of the upper and lower levels and the isotope shifts of the transitions are determined. The tensor polarizability of the 15650.55 cm^-1 level is found to be α₂ = -556.2 ± 11.8 kHz/(kV/cm)². Thanks to the accurate g values of the lower levels [Childs, W.J., Goodman, L.S.: Phys. Rev. A 6, 2011 (1972)], the g values of the upper levels are obtained from the observed Zeeman splittings. The values are found to be -0.115907(79), 2.22259(20) and 1.599968(51) for the 15650.55 cm^-1 .1, 15567.32 cm^-1 and 16890.59.cm^-1 levels, respectively.     

Concise and highly stereocontrolled synthesis of 1-deoxygalactonojirimycin and its congeners using dioxanylpiperidene,a promising chiral building block

[reaction: see text] A concise and stereoselective synthesis of the chiral building block, dioxanylpiperidene 4 as a precursor for deoxyazasugars, starting from the Garner aldehyde 5 using catalytic ring-closing metathesis (RCM) for the construction of the piperidine ring is described. The asymmetric synthesis of 1-deoxygalactonojirimycin and its congeners 1-3 was carried out via the use of 4 in a highly stereocontrolled mode.     

ANALYSIS OF PHOTOTRANSFORMATION INTERMEDIATES IN THE PATHWAY FROM THE RED-ABSORBING TO THE FAR-RED-ABSORBING FORM OF AVENA PHYTOCHROME BY A MULTICHANNEL TRANSIENT SPECTRUM ANALYZER

Phototransformation of the red-absorbing form of phytochrome (Pr) to the far-red-absorbing form (Pfr) was followed with a custom-built transient spectrum analyzer. Large phytochrome, which consisted of approximately 120000-dalton monomers, was immunopurified or conventionally purified from etiolated oat (Avena sativa L., cv. Garry) shoots. Phototransformation was initiated by exciting Pr with a 115-mJ, 600-ns half-width, 655-nm laser pulse. Absorption spectra were recorded on a microsecond time scale at predetermined times after the flash. It has been reported earlier that flash excitation of large oat Pr produces a transformation intermediate with maximum absorbance near 700 nm in a difference spectrum and that this intermediate decays by two kinetically distinct reactions. Difference spectra for these two reactions are indistinguishable. Both show bleaching centered at 690 nm with no detectable associated absorbance increase between 570 and 830 nm. Subsequent appearance of absorbance at 724 nm, which presumably but not necessarily represents the appearance of Pfr, had earlier been shown to occur by two kinetically distinct reactions for large oat phytochrome. Data presented here indicate in addition the occurrence of a third, slower reaction. Difference spectra for the two faster reactions are indistinguishable, both with maxima near 728 nm and minima near 650 nm. The difference spectrum for the slowest component, however, was qualitatively different exhibiting a maximum near 722 nm with no corresponding minimum. About 15-20% of the absorbance increase at 724 nm occurred by this slowest reaction, which exhibited a half-life of 3 s at 25°C and a Q₁₀ of 1.2 for immunopurified and 1.5 for conventionally purified phytochrome. The percentage occurring by this reaction was independent of temperature over the range studied (1-25dEC). For immunopurified phytochrome the enthalpy of activation, Gibbs free energy of activation, and entropy of activation of this slowest reaction were found to be about lOkJ-mol^-1, 75kJ.mol^-1, and -220 J.mol^-1 K^-1, respectively, and for conventionally purified phytochrome 25kJ.mol^-1, 75kJ.mol^-1and —170 J.mol^-1 K^-1, respectively. The thermodynamic characteristics of this reaction indicate that it may involve a significant ordering of the protein moiety as it transforms to Pfr.     

Structures of 1,4-benzodioxane derivatives from the seeds of Phytolacca americana and their neuritogenic activity in primary cultured rat cortical neurons

The methanol extract of the seeds of Phytolacca americana was reinvestigated to yield three new 1,4-benzodioxane-type compounds, americanoic acid methyl ester (1), isoamericanoic acid A methyl ester (2), and 9'-O-methylamericanol A (3) along with the previously isolated neolignans 6-9. The structures of 1-3 were characterized by 2D NMR and long-range selective proton-decoupling (LSPD) techniques. The neuritogenic effects of compounds 1-3, and dicarboxilic acids 4 and 5, which had been previously synthesized with horseradish peroxidase-catalyzed oxidative coupling of caffeic acid, were examined in primary cultured rat cortical neurons. Americanoic acid A methyl ester (1) exhibited neurite outgrowth-promoting activity at concentration of 0.01-1.0 microM, whereas dicarboxilic acids 4 and 5 were found to induce neuritogenesis dose dependently at the concentrations from 0.1 microM to 10 microM.     

LIGHT INDUCED FLUORESCENCE SPECTRAL CHANGES IN NATIVE PHYTOCHROME FROM Secale cereale L. AT LIQUID NITROGEN TEMPERATURE

Abstract— Fluorescence spectra of native rye phytochrome were determined under different light conditions at liquid nitrogen temperature. Fluorescence spectrum of the red-light-absorbing form (Pr) had a major peak at about 685 nm (14 600 cm⁻¹) and a broad sub-peak at about 515 nm (19 400 cm⁻¹). The peak height at 685 nm was reduced by irradiation with monochromatic light of 640 nm, and a new peak became obvious at about 702 nm (14250 cm⁻¹). This spectral change was almost completely reversed by subsequent irradiation with 700-nm light. Fluorescence spectrum of the photoequilibrium mixture of Pr and far-red-light absorbing form under continuous red light showed a sharp peak at about 685 nm having a peak height ca. 12% of Pr, and a broad sub-peak at about 508 nm (19 700 cm⁻¹). Light of 730 nm did not reduce the peak height at about 685 nm but induced a new shoulder at about 699 nm (14300 cm⁻¹). Monochromatic light of 640 and 700 nm given following the light of 730 nm could not reverse the spectral change at 699 nm induced by the irradiation with 730-nm light. Fluorescence spectrum of Pr in partially degraded phytochrome was similar to that in native phytochrome but the peak position in the red region was shifted by about 5 nm (100 cm⁻¹) to the blue.