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)     

Muonium in silicon tetrachloride

Muonium in liquid SiCl has been observed for the first time at low temperature (−65°C) The observed polarization of muonium is as much as 25% of the total spin polarization and shows a fast relaxation rate.     

Synthesis and properties of polydiene and polypentenamer having formyl or hydroxymethyl groups and their photosensitive derivatives

cis-1,4-Polybutadiene and polypentenamer having pendant functional groups such as formyl, aldoxime, hydroxymethyl, or cinnamoyloxymethyl groups have been prepared, and some of their properties were investigated in terms of structural effect on physical properties of these polymers. cis-1, 4-Polybutadiene and polypentenamer having a different content of formyl group were prepared by the hydroformylation reaction with rhodium catalyst under mild conditions. The pendant formyl group was reduced to a hydroxymethyl group by using various reducing agents such as sodium borohydride or sodium trimethoxyborohydride which were effective to avoid a crosslinking reaction among the formyl groups. Glass transition temperature of polypentenamer having hydroxymethyl groups increased with increasing the content of the hydroxymethyl groups in the polymer. Cinnamoyl group was introduced into the polypentenamer having hydroxymethyl groups by reacting with cinnamoyl chloride so as to prepare a photosensitive rubber. The relationships between the photosensitivity of the cinnamoylated polypentenamer and the mobility of polymer main chains have been elucidated. A linear relationship between the photodimerization rate constant and the difference between ultraviolet (UV) irradiation temperature and the glass transition temperature of the polymer was found. It has become apparent that the photosensitivity of cinnamoylated polypentenamer can be estimated by the glass transition temperature of the original polymer, UV irradiation temperature, activation energy of the dimerization, and γ, which is a coefficient of the relationship between the photosensitive group concentration and the glass transition temperature of the polymer.     

Preparation of crystalline polyamides by the alternating copolymerization of aziridines and cyclic imides

The copolymerization of aziridines and cyclic imides was studied. Aziridines copolymerized alternately with cyclic imides to give crystalline polyamides. Ethylenimine and succinimide copolymerized to nylon 2,4, melting near 300°C., without any catalyst. Similarly, the corresponding crystalline polyamides were obtained from the systems of 1,2-propylenimine–succinimide, ethylenimine–glutarimide, and ethylenimine–phthalimide. The copolymerization of aziridines and cyclic imides in the presence of BF₃OEt₂ gave a copolymer which was rich in aziridine units, whereas, the addition of triethylamine had no influence on the copolymer composition. A mechanism of copolymerization was proposed based on the facts that N-tetramethylenesuccinamide was obtained by the reaction of pyrrolidine and succinimide, N-acetylethylenimine reacted with acetamide to yield N,N′-diacetylethylenediamine and that the rate of this copolymerization was dependent on the electrophilicity of imide.     

Perfluoro-1,3,5-tris(p-oligophenyl)benzenes: Amorphous Electron-Transport Materials with High-Glass-Transition Temperature and High Electron Mobility

Perfluoro-1,3,5-tris(p-quaterphenyl)benzene (PF-13Y) and perfluoro-1,3,5-tris(p-quinquephenyl)benzene (PF-16Y) have been synthesized and characterized. They showed higher glass transition temperatures compared with perfluoro-1,3,5-tris(p-terphenyl)benzene (PF-10Y). Organic light-emitting diodes were fabricated using these materials as the electron-transport layers. PF-13Y and -16Y are better electron transporters than PF-10Y. The electron mobilities of PF-10Y and Alq₃ were measured by the time-of-flight technique. PF-10Y showed higher electron mobilities (10⁻⁴ cm²/V s) and weaker electric field dependence compared with Alq₃.     

Enzyme and Nonenzyme Hydrolyses of End Ester Group in Polyethylene Glycol Esters

The enzyme and nonenzyme hydrolyses of the end ester group in polyethylene glycol (PEG) esters were studied. The end monoester in PEG ester is known to be easily hydrolyzed by alkaline or acidic solution. 2-Methyl-ω-benzoyloxypoly(oxy-1,2-ethanediyl)(Bz-PEG) and 2-methyl-ω-4-nitrobenzoyloxypoly(oxy-1,2-ethanediyl) were found to be hydrolyzed by lipase and esterase in Tris buffer solution (pH 7.7) but 2-methyl-ω-acetoxypoly(oxy-1,2-ethanediyl) was not. The parameters of enzyme reaction in the hydrolysis of ester bonds in Bz-PEG by esterase were estimated to be as follows: V_max = 6.09 × 10^?7 mol/dm^3.s, K_m = 7.63 × 10^?4 mol/dm³.     

Steric effects upon transition states of radical addition polymerizations

Transition states (TSs) of radical addition homopolymerization reactions of methyl acrylate, methyl methacrylate, dimethyl itaconate, and N-methyl itaconimide were examined with two-unit radical models using MOPAC (PM3 UHF) semiempirical method. Calculated activation energies (E_as) show good correlations with experimental values. Calculated activation entropies (−ΔS^‡s) are found to be well proportional to E_as. The entropy terms play an important role as well as E_a in radical additions. E_a depends on the angle (θ_rs) between reaction points of radical and of monomer at TS. The bond length between reaction points at TS is constant regardless of monomers studied. The geometries and thermodynamical properties calculated here for TS indicate the importance of steric effects caused by substituted group(s) rather than electronic perturbation energies reported previously. © 1996 John Wiley & Sons, Inc.