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)     

Stereoselective synthesis of (25R)-25,26-dihydroxy-23-oxovitamin D3 and its enzymatic conversion to (25R)-1α,25,26-trihydroxy-23-oxovitamin D3, a putative metabolite of vitamin D3

(25$\text{R}$)-25,26-Dihydroxy-23-oxovitamin D₃ was synthesized efficiently and stereoselectively, and it was converted enzymatically to (25$\text{R}$)-1α,25,26-trihydroxy-23-oxovitamin D₃, a putative metabolite of 1α,25-dihydroxyvitamin D₃. The spectral and chemical properties of (25$\text{R}$)-25,26-dihydroxy-23-oxovitamin D₃ and its 1α,hydroxylated derivative disagree with those reported for the isolated metabolite.     

Rapid racemization of chiral non-racemic sec-alcohols catalyzed by (η-C5(CH3)5)Ru complexes bearing tertiary phosphine-primary amine chelate ligands

A ternary catalyst system of Cp*RuCl(cod)-2-diphenylphosphinoethylamine-KOt-Bu (Cp*=η⁵-C₅(CH₃)₅, cod=1,5-cyclooctadiene) causes rapid racemization of chiral non-racemic sec-alcohols, which results from the reversible hydrogen transfer between sec-alcohols and ketones. Both tertiary phosphine and primary amine functionalities in the ligand are responsible for the high rate.     

Measurement of hyperfine structure constants,g values and tensor polarizability of excited states of Sm I

Atomic-beam laser spectroscopy with fluorescence detection is applied to investigate the hyperfine structure (hfs), Stark and Zeeman effects of the electric dipole transitions of Sm i. The measurements are performed for the four transitions of 0 → 15650.55, 292.58 → 15650.55, 292.58 → 15567.32, and 1489.55 → 16890.59 cm^-1. The hfs constants of the upper and lower levels and the isotope shifts of the transitions are determined. The tensor polarizability of the 15650.55 cm^-1 level is found to be α₂ = -556.2 ± 11.8 kHz/(kV/cm)². Thanks to the accurate g values of the lower levels [Childs, W.J., Goodman, L.S.: Phys. Rev. A 6, 2011 (1972)], the g values of the upper levels are obtained from the observed Zeeman splittings. The values are found to be -0.115907(79), 2.22259(20) and 1.599968(51) for the 15650.55 cm^-1 .1, 15567.32 cm^-1 and 16890.59.cm^-1 levels, respectively.     

Hole transfer in DNA: DNA as a scaffold for hole transfer between two organic molecules

Hole transfer process in ODNs conjugated with two organic molecules, pyrene (Py) and phenothiazine (Ptz) was investigated with the pulse radiolysis measurements. Monitoring the transient absorption of Py⁺ and Ptz⁺, it was shown that the hole transfer rate was dependent on the distance and sequence between Py and Ptz.     

Direct observation of the one-electron reduction of methyl viologen mediated by the CO2 radical anion during TiO2 photocatalytic reactions

The one-electron reduction of methyl viologen (MV(2+)) mediated by the carbon dioxide radical anion (CO(2)(*-)) during photocatalytic reactions in a colloidal TiO(2) aqueous solution (pH 2) has been investigated by time-resolved absorption spectroscopy. The formation of MV(*+) generated from the one-electron reduction reaction with CO(2)(*-), which is generated from the one-electron oxidation reactions with the photogenerated holes (h(+)), was directly observed. The spectral features of the photogenerated charge carriers and the kinetic analysis of the formation process of MV(*+) revealed that the CO(2)(*-), desorbed from the surface, reacts with MV(2+) via a homogeneous electron-transfer process in the bulk solution.     

The synthesis of hexahydrooxoepithiopyridinedicarboximides by the reaction of thioamides with N-substituted maleimides

The synthesis of hexahydrooxoepithiopyridinedicarboxyimide (5: X₂ = N-Ph) by the reaction of thioamides 1 with N-substituted maleimide ( 2a ) was examined. The reaction of primary thioamides, such as thiobenzamide and p-toluthioamide with N-phenylmaleimide gives compounds 5 together with corresponding 4-hydroxy-1,3-thiazoles 4 . However, a similar reaction of secondary thioamides, such as N-methylthioacetamide, thiobenzanilide, with N-phenylmaleimide did not provide compounds 5 without addition of acid. The reaction pathway and the configuration of 5 were also investigated.     

Structures of 1,4-benzodioxane derivatives from the seeds of Phytolacca americana and their neuritogenic activity in primary cultured rat cortical neurons

The methanol extract of the seeds of Phytolacca americana was reinvestigated to yield three new 1,4-benzodioxane-type compounds, americanoic acid methyl ester (1), isoamericanoic acid A methyl ester (2), and 9'-O-methylamericanol A (3) along with the previously isolated neolignans 6-9. The structures of 1-3 were characterized by 2D NMR and long-range selective proton-decoupling (LSPD) techniques. The neuritogenic effects of compounds 1-3, and dicarboxilic acids 4 and 5, which had been previously synthesized with horseradish peroxidase-catalyzed oxidative coupling of caffeic acid, were examined in primary cultured rat cortical neurons. Americanoic acid A methyl ester (1) exhibited neurite outgrowth-promoting activity at concentration of 0.01-1.0 microM, whereas dicarboxilic acids 4 and 5 were found to induce neuritogenesis dose dependently at the concentrations from 0.1 microM to 10 microM.     

Lipase-catalyzed transformation of poly(lactic acid) into cyclic oligomers

Enzymatic transformations into cyclic oligomers were carried out with the objective of developing chemical recycling of poly(lactic acid)s, such as poly(D,L-lactic acid) (PDLLA), poly(D-lactic acid) (PDLA) and poly(L-lactic acid) (PLLA), which are typical biodegradable polymers. They were degraded by lipase in an organic solvent to produce the corresponding cyclic oligomer with a molecular weight of several hundreds. PDLLA (with a Mw of 84,000) was quantitatively transformed into cyclic oligomers by lipase RM (Lipozyme RM IM) in chloroform/hexane at 60 degrees C. PLLA (with a Mw of 120,000) was transformed into cyclic oligomer by lipase CA (Novozym 435) at a higher temperature of 100 degrees C in o-xylene. The oligomer structure was identified by 1H and 13C NMR spectroscopy and MALDI-TOF (matrix assisted laser desorption/ionization-time-of-flight) mass spectrometry.