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)     

Syntheses and characterization of 16‐arm star and star diblock copolymer and AB8 9‐miktoarm star copolymer via NMRP and ROP from dendritic multifunctional macroinitiators

A dendritic macroinitiator having 16 TEMPO‐based alkoxyamines, Star‐16 , was prepared by the reaction of a dendritic macroinitiator having eight TEMPO‐based alkoxyamines, [G‐3]‐OH , with 4,4′‐bis(chlorocarbonyl)biphenyl. The nitroxide‐mediated radical polymerization (NMRP) of styrene (St) from Star‐16 gave 16‐arm star polymers with PDI of 1.19–1.47, and NMPR of 4‐vinylpyridine from the 16‐arm star polymer gave 16‐arm star diblock copolymers with PDI of 1.30–1.43. The ring‐opening polymerization of ε‐caprolactone from [G‐3]‐OH and the subsequent NMRP of St gave AB₈ 9‐miktoarm star copolymers with PDI of 1.30–1.38. The benzyl ether linkages of the 16‐arm star polymers and the AB₈ 9‐miktoarm star copolymers were cleaved by treating with Me₃SiI, and the resultant poly(St) arms were investigated by size exclusion chromatography (SEC). The SEC results showed PDIs of 1.23–1.28 and 1.18–1.22 for the star polymers and miktoarm stars copolymers, respectively, showing that they have well‐controlled poly(St) arms. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1159–1169, 2007.     

Ion-interaction chromatography of several metallocyanide complexes stabilized by adding cyanide in a neutral mobile phase.

Standard solutions (at 10(-5) M levels) of Cu(I)- and Fe(II)-cyanide complexes were stabilized for at least 5 h using 0.5 mM cyanide solution (around pH 9) as a medium. Complexes of Cu(I)- and Fe(III)-cyanide also could be stabilized without any dissociation by adding 1 mM cyanide to an acetonitrile-water (18:82, v/v) mobile phase (pH 7.0) containing 10 mM tetra-n-propylammonium salt (TPA). Under the optimal conditions, the six complexes of Cu(I)-, Ag(I)-, Ni(II)-, Fe(II)-, Fe(III)- and Au(I)-cyanides were resolved from their mixtures within about 45 min, with well-shaped chromatographic peaks.     

Phase Measurement Algorithm in Wavelength Scanned Fizeau Interferometer

Wavelength scanned interferometry allows the simultaneous measurement of top surface shape and optical thickness variation of a transparent object consisting of several parallel surfaces. Interference signals from these surfaces can be separated in frequency space, and their phases are detected by discrete Fourier analysis. However, these signal frequencies are shifted from the detection frequency by the refractive index dispersion of the object and a nonlinearity of the wavelength scanning. The Fourier analysis is sensitive to the detuning of the signal frequency and suffers from the multiple-beam interference noise. Conventional error-compensating algorithms cannot be applied to an object consisting of more than three reflecting surfaces. We derive a new 2N-1 sample error-compensating algorithm, which allows the phase detection of any order of harmonic frequency among the interference signals. The new algorithm suppresses the effect of signal frequency detuning as well as the multiple-beam interference noise and can be applied to the measurement of complex objects consisting of more than three reflecting surfaces.     

Synthesis and characterization of 6‐ and 12‐arm star polymers by nitroxide‐mediated radical polymerization of St and MA from dendritic TIPNO‐based hexafunctional and dodecafunctional macroinitiators

Dendritic multifunctional macroinitiators having six and 12 TIPNO‐based alkoxyamines, TIPNO‐6 and TIPNO‐12 , were synthesized and used in the living radical polymerization of styrene (St), methyl acrylate (MA), N,N‐dimethylacrylamide (DMAAm), and isoprene (IP). The polymerizations of St initiated with TIPNO‐6 gave 6‐arm star polymers with narrow polydispersities of 1.14–1.18. In the polymerizations of MA initiated with TIPNO‐6 and TIPNO‐12 , the influences of added TIPNO on the polydispersity indexes (PDIs) of the resulting star polymers were first investigated, and this led to the successful formation of poly(MA) star polymers with narrow polydispersities (1.10–1.18). Moreover, the polymerizations of DMAAm and IP from TIPNO‐6 in the presence or absence of TIPNO were briefly investigated. The benzyl ether bonds of the poly(St) and poly(MA) star polymers were cleaved by treating with Me₃SiI or Pd/C, and the resulting arm's parts were analyzed with SEC. The PDIs of the resulting arm parts were low (1.19–1.23), and the M_ns agreed with the M_n,theor, indicating that the poly(St) and poly(MA) star polymers had well‐controlled arms. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4364–4376, 2007     

Synthesis of spherical and hemispherical sugar‐containing poly(ornithine) dendrimers

A novel sugar‐containing poly(ornithine) dendrimer is synthesized for possible antigen delivery and related applications. The dendrimer contains an ornithine dendron as interior scaffolding and oligosaccharides on the periphery, which provide an attachment site for a peptide antigen. Maltose or lactose is bound to both hemispherical and spherical poly(ornithine) dendrimer generation 3 (G3) by reductive amination between its reducing end and the peripheral amino group of the dendrimer using a borane‐pyridine complex in a buffer solution at 50 °C. The degree of substitution of sugar is changed by varying the molar ratio of sugar to dendrimer. When the surface of spherical poly(ornithine) dendrimer G3 is modified by binding β‐alanine to the 16 amino groups, highly substituted maltose‐ or lactose‐β‐alanine‐poly(ornithine) dendrimer G3 is obtained in high yield after 7 days of reaction. The structures of these sugar‐containing dendrimers are characterized by NMR and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry analyses. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1400–1414, 2004     

Synthesis of well‐defined syndiotactic poly(methyl methacrylate) with low‐temperature atom transfer radical polymerization in fluoroalcohol

The copper‐mediated atom transfer radical polymerization of methyl methacrylate (MMA) in 1,1,1,3,3,3‐hexafluoro‐2‐propanol (HFIP) was studied to simultaneously control the molecular weight and tacticity. The polymerization using tris[2‐(dimethylamino)ethyl]amine (Me₆TREN) as a ligand was performed even at ?78°C with a number‐average molecular weight (M_n) of 13,400 and a polydispersity (weight‐average molecular weight/number‐average molecular weight) of 1.31, although the measured M_n's were much higher than the theoretical ones. The addition of copper(II) bromide (CuBr₂) apparently affected the early stage of the polymerization; that is, the polymerization could proceed in a controlled manner under the condition of [MMA]₀/[methyl α‐bromoisobutyrate]₀/[CuBr]₀/[CuBr₂]₀/[Me₆TREN]₀ = 200/1/1/0.2/1.2 at ?20°C with an MMA/HFIP ratio of 1/4 (v/v). For the field desorption mass spectrum of Cu^IBr/Me₆TREN in HFIP, there were [Cu(Me₆TREN)Br]⁺ and [Cu(Me₆TREN)OCH(CF₃)₂]⁺, indicating that HFIP should coordinate to the Cu^I/Me₆TREN complex. The syndiotacticity of the obtained poly(methyl methacrylate)s increased with the decreasing polymerization temperature; the racemo content was 84% for ?78°C, 77% for ?30°C, 75% for ?20°C, and 63% for 30°C. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1436–1446, 2006     

Factors affecting polyhydroxybutyrate biosynthesis in the marine photosynthetic bacteriumRhodopseudomonas sp. strain W-1S

Applied Biochemistry and Biotechnology - A marine photosynthetic bacterium,Rhodopseudomonas sp. strain W-1S, accumulated polyhydroxybutyrate (PHB) to 56% of the dry cell weight under microaerobic...