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)     

A Discrete Korovkin Theorem and BKW-Operators

We give a functional Korovkin-type theorem onB(X), the space of bounded complex-valued functions on an arbitrary setXand investigate a BKW-operator onB(X) for a finite collection of test functions with a suitable property and a seminorm defined by a finite subset ofX.     

Dielectric-field effect correction on i.r. band shapes in the liquid phase

The dielectric-field correction on i.r. band shape in the liquid has been studied by using the Lorentz internal field. The deformation of the band shape is inappreciable for a weak absorption band that becomes measurable only at a sample thickness larger than 10μ. The shapes of the strong singlet and doublet bands of hexafluorobenzene at 1530 cm^?1 and near 1000 cm^?1, respectively, and also of the doublet band of carbon tetrachloride near 790 cm^?1 have been measured in dilute solutions and compared with those for the pure liquid.     

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.     

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.     

BKW-operators on the interval [0,1]

Uniqueness sets inC([0, 1]) are studied for test functions {1,t,…,t ⁿ}. As an application, we investigateBKW-operators on the interval [0,1].