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)     

Ring‐opening grafting polymerization of cyclic monomers onto human hair

Natural human hair was successfully modified by the graft polymerization of trimethylene carbonate, β‐propiolactone, ε‐caprolactone, glycidol, ε‐caprolactam, and 5,5‐dimethyl‐1,3‐dioxane‐2‐thione. In contrast, we could not modify natural human hair by the graft polymerization of oxetane under similar conditions. The model reaction suggested that the main initiating species in these polymerizations were the amino, thiol, and hydroxyl groups in hair, which could induce ring‐opening polymerization. Among the tested monomers, β‐propiolactone was most effective for hair modification with its graft polymer, whose concentration was as high as 0.5 g/g of hair though polymerization under mild conditions. The effects of the hair pretreatment and polymerization temperature on the weight ratio of the grafted polymers were also investigated. Hair modified by grafted polymers was characterized with scanning electron microscopy and Fourier transform infrared measurements. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 736–744, 2007     

WIDE RANGE DETECTOR USING PARABOLIC CYLINDRICAL MIRROR FOR THz APPLICATIONS

A new, wide-band, high-speed and high-sensitivity THz detector has been developed. The prototype detector consists of a parabolic cylindrical mirror, a long wire antenna and a Schottky barrier diode. Direct detection measurements have shown a stable sensitivity of 150 ± 50 V/W for 1–2 THz without any adjustments. The long wire antenna was fixed at the focus of parabolic cylindrical mirror then it has been realized less operation steps, easy coupling to the external THz signals and a dramatic enhancement in the practicality of this system. The optically polished mirror and frosted surface one showed comparable sensitivities, thus easy polishing and less cost mirror fabrication can be applied for this system. The radiation pattern showed a maximum radiation angle of approximately 23° with its dominant main lobe, which was attributed to the wire antenna character and confirmed good agreements with classical antenna theory.     

Synthesis and characterization of norbornene–ethylene–styrene terpolymers with a substituted ansa‐fluorenylamidodimethyltitanium‐based catalyst

This article reports a synthetic method for a norbornene–ethylene–styrene (N‐E‐S) terpolymer, which has not been well investigated so far, via incorporation of styrene (S) into vinyl‐type norbornene–ethylene (N‐E) copolymers catalyzed by a substituted ansa‐fluorenylamidodimethyltitanium [Me₂Si(3,6‐tBu₂Flu)(tBuN)]TiMe₂ catalyst ( I ) activated with a [Ph₃C][B(C₆F₅)₄]/Al(iBu)₃ cocatalyst at room temperature in toluene. The resulting terpolymerization product contained the targeted N‐E‐S terpolymer and the contaminated homopolymers, which were then able to be completely removed by solvent fractionation techniques. While homopolystyrene was easily extracted by fractionation with methylethylketone as a soluble part, homopolyethylene and a trace amount of homopolynorbornene could be perfectly separated by fractionation with chloroform as insoluble parts. The detail characterizations of a chloroform‐soluble polymer with gel permeation chromatography, nuclear magnetic resonance, and differential scanning calorimetry analyses proved that it contained a true N‐E‐S terpolymer with long N‐E sequences incorporated with isolated or short styrene sequences. The homogeneity of the morphology together with a single glass transition temperature that proportionally decreased with the increase of the styrene contents indicated that the N‐E‐S terpolymer obtained in this work is a random polymer with an amorphous structure. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2765–2773, 2007     

Temperature Dependence of the Threshold Current and the Lasing Wavelength in 1.3-μm GalnNAs/GaAs Single Quantum Well Laser Diode

Temperature stability of the threshold current and the lasing wavelength is investigated in a 1.3-μm GaInNAs/ GaAs single quantum-well laser. The measured characteristic-temperature was 88 K. The small wavelength shift per change in temperature of 0.35 nm/°C was obtained, indicating the superior lasing-wavelength stability. Therefore, it is shown experimentally that GaInNAs is very promising material for the fabrication of light source with excellent high-temperature performance for optical fiber communications.     

Copolymers containing a spiro orthoester moiety that undergo no shrinkage during cationic crosslinking

A spiro orthoester with an exomethylene group (exoSOE) was radically copolymerized with acrylonitrile or vinyl acetate at several feed ratios to obtain the corresponding copolymers having spiro orthoester moieties in the side chain. The obtained copolymers could be crosslinked via the double ring‐opening polymerization of the spiro orthoester moieties in their side chain by a treatment with BF₃OEt₂. The volume changes upon the crosslinking of the copolymers were evaluated by density measurements with a micromeritics gas pycnometer. The copolymers experienced less than 1% volume expansion instead of volume shrinkage during typical cationic crosslinking, regardless of the copolymer compositions. Negligible shrinkage was observed during the thermal cationic crosslinking of a film cast from a nitrobenzene solution of the copolymers containing a benzylthiophenium salt as a thermally latent cationic initiator. The constantly low volume changes during the crosslinking of the copolymers from exoSOE probably depended on the almost zero volume change during the cationic polymerizations of spiro orthoester derivatives. This indicates that exoSOE is an effective monomer for crosslinkable polymers without volume changes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3666–3673, 2006     

Anionic grafting polymerization of propylene sulfide onto human hair in water

Natural human hair was modified by the graft polymerization of propylene sulfide in an aqueous medium. The amount of the polymer grafted onto the reduced hair was 0.15–0.19 g on 1.0 g of hair. The grafted polymer was isolated by the hydrolysis of the hair in the polymer‐grafted hair under basic conditions and was confirmed to be poly(propylene sulfide) by ¹H NMR, ¹³C NMR, and Fourier transform infrared spectra. The number‐average molecular weights of the isolated polymers from the grafted products were 10,000–12,000. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3778–3786, 2006     

Simultaneous imaging of the structure and fluorescence of a supramolecular nanostructure formed by the coupling of π‐conjugated polymer chains in the intermolecular interaction

We fabricated a micrometer‐long supramolecular chain in which π‐conjugated polyrotaxane was coupled. A new experimental setup was designed and constructed, and the simultaneous direct imaging of the structure and fluorescent function was achieved. Furthermore, we identified the formation of a polymer intertwined network and observed novel fluorescence due to a long‐range interaction via this intertwined network over a distance of 5 μm or more without quenching over 15 min in the near field. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 801–809, 2006