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.     

Effect of explicit cationic size and valence constraints on the phase stability of 1:2 B-site-ordered perovskite ruthenates

The related parameters of cation size and valence that control the crystallization of Sr(3)CaRu(2)O(9) into a 1:2 B-site-ordered perovskite structure were explored by cationic substitution at the strontium and calcium sites and by the application of high pressure. At ambient pressures, Sr(3)MRu(2)O(9) stoichiometries yield multiphasic mixtures for M = Ni(2+), Mg(2+), and Y(3+), whereas pseudocubic perovskites result for M = Cu(2+) and Zn(2+). For A-site substitutions, an ordered perovskite structure results for Sr(3-x)Ca(x)CaRu(2)O(9), with 0 相似文献   

Alternative copolymerization of aziridines and carbon monoxide by γ-ray irradiation

The copolymerization of carbon monoxide and aziridines such as ethylenimine and propylenimine was carried out by γ-ray irradiation. Aziridines and carbon monoxide were allowed to copolymerize under γ-ray irradiation from a Co⁶⁰ source and gave a crystalline solid copolymer. The yield of the copolymer increased with reaction temperature. The composition of copolymers obtained did not depend on the feed ratio of monomers and was found to be almost equimolar. The copolymer of ethylenimine and carbon monoxide melted at about 322–335°C. with decomposition and has an infrared spectrum identical with that of poly-β-alanine obtained by the hydrogen-migration polymerization of acrylamide. The hydrolyzed product of the ethylenimine–carbon monoxide copolymer was confirmed to be β-alanine by paper chromatography. These results lead to the conclusion that the copolymerization of aziridines and carbon monoxide took place alternatively by γ-ray irradiation, and produced crystalline poly-β-alanines.     

The cellulose system in viscin from mistletoe berries

The cellulose system of the viscous fibrous cellulosic polysaccharide (viscan) in the viscin tissue of the European mistletoe, Viscum album L., was analyzed by chemical and physicochemical techniques including sugar analysis, optical and transmission electron microscopy, X-ray and electron diffraction together with solid state CP/MAS ¹³C-NMR spectroscopy. The results confirmed that in the elongated thin viscin cells, the cellulose microfibrils (having a diameter of around 3 nm) were tightly coiled with their axes perpendicular to the long axis of the cell. Upon stretching these cells became deformed by more than a hundred fold. In such a deformation, the cellulose microfibrils became unwound to be perfectly aligned along the stretching direction. Based on solid-state CP/MAS ¹³C-NMR spectroscopic analysis of the viscin tissue, it was found that its cellulose consisted of I and I polymorphs in the ratio 1:1.     

Studies on antiallergic agents. I. Synthesis and antiallergic activity of novel pyrazine derivatives.

Various pyrazine derivatives were synthesized and their antiallergic activity was examined. The inhibitory activity on allergic histamine release of the compounds bearing a 5-tetrazolyl group was more potent than that of the corresponding carboxyl derivatives. The introduction of -CONH- or -NHCO- between the pyrazine ring and the 5-tetrazolyl group as a spacer greatly enhanced the activity. N-(1H-Tetrazol-5-yl)-2-pyrazinecarboxamide (I-3) was estimated to exhibit nearly the same potency as disodium cromoglycate (DSCG). The structure-activity relationship among various derivatives modified by introducing some substituents onto the 3-, 5- or 6-position of the pyrazine ring of I-3 was investigated. The activity remained unchanged or was reduced when such substituents as methyl, chloro, methoxy, methylamino and dimethylamino were introduced at the 3- or 5-position. In contrast, 6-substitution with various alkylamino groups more or less increased the activity. Among them, the 6-dimethylamino (I-17c) and 6-(1-pyrrolidinyl) (I-34) derivative were proved to be most potent. The IC50 values (concentration which produces 50% inhibition of the allergic histamine release) of I-17c and I-34 were determined to be 4.7 x 10(-10) and 4.6 x 10(-10) M, respectively. These two compounds produced a potent inhibitory activity on passive cutaneous anaphylaxis (PCA) in rat, not only by the intravenous route (ED50 = 0.0096 mg/kg for both compounds) but also by the oral route (ED50 = 0.19 and 0.18 mg/kg, respectively). On the other hand, when the pyrazine ring of some representative compounds was replaced with a pyridine ring, the inhibitory activity on histamine release was significantly reduced.     

Development of rectangular column structured titanium oxide photocatalysts anchored on silica sheets by a wet process

Commercially available powdered photocatalysts such as P-25 are known to show high photocatalytic performance. However, in practical use, their anchoring onto a substrate without any binders is still very difficult. The purpose of this study is to design and develop high-performance photocatalysts that can be anchored onto a substrate, and to this end we have prepared a titanium oxide photocatalyst using a wet process. The results of this study led to the successful development of rectangular column structured titanium oxide crystals which could be anchored onto silica sheets. The rectangular columnar crystal was 100- 500 nm wide and 1000- 5000 nm long. Moreover, investigations on the complete oxidation reaction of acetaldehyde into CO₂ and H₂O showed a high performance equivalent to that of the most efficient marketed powdered photocatalysts.