Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey–Wilson polynomials

Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey–Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians, which are deformations of those for the Wilson and Askey–Wilson polynomials in terms of a degree ?   (?=1,2,…$?=1,2,\dots$) eigenpolynomial. These polynomials are exceptional in the sense that they start from degree ??1$??1$ and thus not constrained by any generalisation of Bochner's theorem.     

Crystal structure and spin state of Fe0.5Co0.5(NCS)2(bpa)2

Fe(NCS)₂(bpa)₂, Co(NCS)₂(bpa)₂, and Fe_0.5Co_0.5(NCS)₂(bpa)₂ were synthesized. X-ray structural analysis revealed that the structure was the same among the three complexes. Although the metal-ligand distance in the mixed crystals was shorter than the distance in Fe(NCS)₂(bpa)₂ and was similar to that in Co(NCS)₂(bpa)₂, the spin state remained temperature-independent Fe^II high-spin state in ⁵⁷Fe M?ssbauer spectra.     

o-Diketonedioxime compounds as analytical reagents for the spectrophotometric determination of nickel

Sixteen dioxime compounds, including six new compounds, were synthesized and their reactions with nickel, cobalt, iron(II, III) and copper ions were examined. The nickel chelates of the glyoxime derivatives show hardly any absorption in the visible region, and are therefore unsuitable as color reagents. The nickel chelates of the benzildioxime derivatives can be extracted into organic solvents and provide a selective color reaction, so that useful extraction-spectrophotometric methods are possible. The metal complexes of quinonedioximes are extracted into some organic solvents, and the complexes have relatively large molar absorptivities in the visible region, but the reagents are not selective. However, the molar absorptivity of the ternary complex, Ni²⁺-reagent-zephiramine, with 1,2-naphthoquinonedioxime-4-sulfonic acid was 2.03·10⁴ at 480 nm, and that of the nickel complex of 9,10-phenanthrenequinonedioxime was 2.49·10⁴at 456 nm. The compositions of the nickel-dioxime complexes were examined spectrophotometrically.     

Synthesis and polymerization of N‐(4‐tetrahydropyranyl‐oxyphenyl)maleimide

N‐(4‐Tetrahydropyranyl‐oxy‐phenyl)maleimide (THPMI) was prepared and polymerized by radical or anionic initiators. THPMI could be polymerized by 2,2′‐azobis(isobutyronitrile) (AIBN) and potassium tert‐butoxide. Radical polymers (poly(THPMI)r) were obtained in 15–50% yields for AIBN in THF at 65°C after 2–5 h. The yield of anionic polymers (poly(THPMI)a) obtained from potassium tert‐butoxide in THF at 0°C after 20 h was 91%. The molecular weights of poly(THPMI)r and poly(THPMI)a were M_n = 2750–3300 (M_w/M_n = 1.2–3.3) and M_n = 11300 (M_w/M_n = 6.0), respectively. The difference in molecular weights of the polymers was due to the differences in the termination mechanism of polymerization and the solubility of these polymers in THF. The thermal decomposition temperatures were 205 and 365°C. The first decomposition step was based on elimination of the tetrahydropyranyl group from the poly(THPMI). Positive image patterns were obtained by chemical amplification of positive photoresist composed of poly(THPMI) and 4‐morpholinophenyl diazonium trifluoromethanesulfonate used as an acid generator. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 341–347, 1999     

Catalytic property of Europium supported on alumina from its ammoniacal solution

Europium supported on alumina (Eu/Al₂O₃) was prepared by impregnation from an ammoniacal solution of the metal. The catalytic activity of Eu/Al₂O₃ for the isomerization of 2,3-dimethylbut-1-ene to 2,3-dimethylbut-2-ene was examined. Eu/Al₂O₃ showed the highest catalytic activity for the isomerization when heated under a vacuum at 523 K, the yield of 2,3-dimethylbut-2-ene in 20 min being 81.6% at 314 K. IR spectrum shows the presence of two kinds of Eu amides. The change of the IR spectra and the catalytic activities with evacuation temperature suggest that only one of the two Eu amides is catalytically active for this base-catalyzed isomerization.