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     

Determination of midodrine in human plasma by high-performance liquid chromatography with fluorescence detection.

A simple and sensitive fluorometric high-performance liquid chromatographic method was developed for the determination of midodrine in human plasma. After liquid-liquid extraction from plasma, the drug and 2-phenylglycinol (internal standard) were convened into the corresponding fluorescent derivatives by reaction with 3,4-dihydro-6,7-dimethoxy-4-methyl-3-oxoquinoxaline-2-carbonyl chloride, a fluorescence derivatization reagent for amines. The derivatives were separated within 30 min on a reversed-phase column using isocratic elution with acetonitrile-methanol-water (10:30:60, v/v) and were detected spectrofluorometrically at 485 nm with excitation at 400 nm. The detection limit for midodrine was 0.3 pmol (76 pg) per mL plasma at a signal-to-noise ratio of 3.     

Stability analysis of abnormal multiplication of plankton using parameter identification technique

This paper presents the mathematical approach for the abnormal multiplication of plankton. An abnormal multiplication can be expressed as an unstable problem and the stability of the system is investigated by introducing eigenvalues of a mathematical equation. The stability of the system can be judged by an eigenvalue based on the Lyapunov's stability theory. In this paper, the Arnoldi‐QR method is used to obtain eigenvalues and eigenvectors of the system. The mode superposition method is employed to create spatial distribution needed to analyse the stability. To obtain the objective eigenvalue, the parameter identification technique is employed. The finite element method is used for the discretization in space. Lake Kasumigaura, which is located in Ibaraki Prefecture in Japan, is selected and actual data in 1975, 1976, 1991 and 2000 are used in order to investigate the stability of the specified lake in Japan. Copyright © 2004 John Wiley & Sons, Ltd.     

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.