The stability of the exponential equation

We generalize the well-known Baker's superstability result for exponential mappings with values in the field of complex numbers to the case of an arbitrary commutative complex semisimple Banach algebra. It was shown by Ger that the superstability phenomenon disappears if we formulate the stability question for exponential complex-valued functions in a more natural way. We improve his result by showing that the maximal possible distance of an -approximately exponential function to the set of all exponential functions tends to zero as tends to zero. In order to get this result we have to prove a stability theorem for real-valued functions additive modulo the set of all integers .

     

Melanin offers protection against induction of cyclobutane pyrimidine dimers and 6-4 photoproducts by UVB in cultured human melanocytes

The goal of this investigation was to correlate the melanin content in human pigmentary cells with the generation of UVB-induced photoproducts and to examine the relationship between the melanin content and the removal of the photoproducts. Cultured melanocytes from light-skinned individuals synthesized less melanin and produced more cyclobutane pyrimidine dimers and 6-4 photoproducts upon UVB exposure than did melanocytes from black skin. Tyrosine-stimulated melanogenesis provided protection against DNA damage in both cell types. In another set of pigmented cell lines a ratio between eumelanin and pheomelanin was determined. The assessment of association between DNA damage induction and the quantity and quality of melanin revealed that eumelanin concentration correlated better with DNA protection than pheomelanin. Skin type-I and skin type-VI melanocytes, congenital nevus (CN)-derived cells and skin type-II melanocytes from a multiple-melanoma patient were grown in media with low or high L-tyrosine concentration. The cells were irradiated with 200 J/m2 UVB, and the levels of the photoproducts were determined immediately and after 6 and 24 h. Once again the induction of the photoproducts was mitigated by increased melanogenesis, and it was inversely correlated with the skin type. No significant differences were found for the removal of photoproducts in the cultures of skin types I and VI and CN cells. No indications of a delay in the removal of photoproducts in the melanocytes from the multiple-melanoma patient were found either.     

Rearrangements and fragmentations of [C2H5S]+ ions

From deuterium labelling experiments it was concluded that metastable molecular ions of ethyl methyl sulfide lose a methyl radical with the formation of both [CH₃S?CH₂]⁺ amd [CH₃CH?SH]⁺˙ The fragmentation reactions of metastable ions generated with these structure are losses of C₂H₂, H₂S and CH₄. These reactoins and the preceding isomerizations have also been studied by means of deuterium labelling. From the results it is concluded that the three fragmentation reactions most probably occur from ions with a C? C? S skeleton. Appearance energy measurements for ions generated with the two structures above and all give rise to the same ΔH_f value for these three isomeric forms. Ab initio molecular orbitals calculations confirm that these three ions fortuitously have very similar heats of formation. A potential energy diagram rationalizing the isomerizations and the principal fragmentation reaction is presented.     

Electronic transitions and magnetic circular dichroism of the naphthalene monogenegative ion

The optical absorption and magnetic circular dichroism (MCD) spectra of the mononegative ion of naphthalene in a solution of 2-methyltetrahydrofuran have been measured at room temperature over the 25000–41000 cm^?1 spectral region. Experimental values of the MCD parameter B/D are compared with theoretical data obtained by means of an LCAO SCF CI calculation according to Pariser, Parr and Pople. The agreement between theory and experiment is rather good.     

On alienation of two functional equations of quadratic type

Aequationes mathematicae -   We deal with an alienation problem for an Euler–Lagrange type functional equation $$\begin{aligned} f(\alpha x + \beta y) + f(\alpha x - \beta y) =...     

Relativity and the chemistry of UF6: A molecular Dirac—Hartree—Fock—CI study

The electronic structure and bonding of UF₆ and UF₆⁻ are studied within a relativistic framework using the MOLFDIR program package. A stronger bonding but more ionic molecule is found if one compares the relativistic with the nonrelativistic results. The first peak in the photoelectron spectrum of Karlsson et al. is assigned to the 12γ_8u component of the 4t_1u orbital, in agreement with other theoretical and experimental results. Good agreement is found between the experimental and theoretical 5f spectrum UF₆⁻. Some properties, like the dissociation energy and electron affinity, are calculated and the necessity of a fully relativistic framework is shown. The Breit interaction has an effect on the core spinors and the spin-orbit splitting of these spinors but the influence on the valence spectrum is negligible. © 1996 John Wiley & Sons, Inc.     

Homomorphisms and boundedness in topological groups

We consider homomorphisms from a normed space into a topological group. Assuming their boundedness in a neighbourhood (in relative topology) of an extremal point of the unit sphere, we derive their linearity (whenever it makes sense), closedness of the graph or continuity.     

The spin-quadrupole interaction and the 0<Superscript>+</Superscript> excitations in <Superscript>158</Superscript>Gd

In this work, the effect of spin-quadrupole forces on the 0⁺ sates in ¹⁵⁸Gd has been investigated. For this purpose, the model Hamiltonian including monopole pairing, quadrupole-quadrupole and spin-quadrupole forces has been diagonalized in one phonon basis. In conclusion, for the distribution of energies of the states and their collective properties, fairly good results have been obtained.