On injective enumerability of recursively enumerable classes of cofinite sets

To date the problem of finding a general characterization of injective enumerability of recursively enumerable (r.e) classes of r.e. sets has proved intractable. This paper investigates the problem for r.e. classes of cofinite sets. We state a suitable criterion for r.e. classesC such that there is a boundn with |-A|n for allAC. On the other hand an example is constructed which shows that Lachlan's condition (F) does not imply injective enumerability for r.e. classes of cofinite sets. We also look at a certain embeddability property and show that it is equivalent with injective enumerability for certain classes of cofinite sets. At the end we present a reformulation of property (F).Thank you for technical support, Wolfgang Eppler, for intellectual support, Alistair Lachlan, and for proof-reading, Martin Kummer. Thanks also to the anonymous referee     

Spin coupling in distorted high-valent Fe(IV)-porphyrin radical complexes

In order to study structural influences on the interaction of Fe(IV) (S=1) and porphyrin cation radical (S=1/2) in high-valent iron porphyrin complexes of the type ¦X-(TMP)Fe=O¦⁺(Cl^–), X=I, Br₂, Br₄ were generated by mCPBA oxidation of corresponding Fe(III) porphyrins. The halogen substitution at the peripheral positions of the porphyrin leads to distortion of the planar porphyrin ring of ¦(TMP)Fe=O¦⁺. The new species have beeen investigated by temperature-dependent EPR and field-dependent Mössbauer spectroscopy; for the evaluation of spectra, we adopted the spin-Hamiltonian formalism including exchange interaction explicitly. As in ¦(TMP)Fe=O¦⁺, strong ferromagnetic spin coupling was observed with|J₀|D=0.9–1 and a zero-field spltting ofD32 cm^–1. For consistent parametrization of EPR and Mössbauer results, anisotropic coupling had to be introduced. Compared to ¦(TMP)Fe=O¦⁺ [1], analysis of the spectroscopic data shows that zero-field splitting and spin coupling is only slightly affected by the halogen distortion of the porphyrin structure.     

Curvature and finite domination

Upper bounds obtained by Gromov on the Betti numbers of certain closed Riemannian manifolds are shown to be upper bounds on the minimum number of cells in --spaces dominating such manifolds.

     

Evidence for a monomeric structure of nonribosomal Peptide synthetases

Nonribosomal peptide synthetases (NRPS) are multimodular biocatalysts that bacteria and fungi use to assemble many complex peptides with broad biological activities. The same modular enzymatic assembly line principles are found in fatty acid synthases (FAS), polyketide synthases (PKS), and most recently in hybrid NRPS/PKS multienzymes. FAS as well as PKS are known to function as homodimeric enzyme complexes, raising the question of whether NRPS may also act as homodimers. To test this hypothesis, biophysical methods (size exclusion chromatography, analytical equilibrium ultracentrifugation, and chemical crosslinking) and biochemical methods (two-affinity-tag-system and complementation studies with enzymes being inactivated in different catalytic domains) were applied to NRPS subunits from the gramicidin S (GrsA-ATE), tyrocidine (TycB(1)-CAT and TycB(2-3)-AT.CATE), and enterobactin (EntF-CATTe) biosynthetic systems. These methods had revealed the dimeric structure of FAS and PKS previously, but all three NRPS systems investigated are functionally active as monomers.     

Characterization of individual atmospheric particles by element mapping in electron probe microanalysis

In this paper procedures for the characterization of individual aerosol particles by element mapping in the electron microprobe are presented. The number, size and qualitative chemical composition of particles is derived from a combination of secondary or backscattered electron images and element distribution maps. Accuracy of the size distribution and reliability of the qualitative analysis procedure were checked with silicate samples. In order to obtain a semi-quantitative estimate of the chemical composition of individual particles the count rates taken from element distribution maps are corrected for matrix and geometric effects using particle ZAF procedures.Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday     

Theoretical and experimental analysis of the fine structure and hyperfine structure in the configurations 5p6s and 5p6p of the antimony II spectrum

From 17 transitions in the singly ionized Sb II spectrum the hyperfine structure (A andB splitting constants) of the complete excited configurations 5p6s and 5p6p were determined by means of optical interference spectroscopy. In addition, a theoretical analysis both of the fine structure and also of the hyperfine structure was carried out (in the case of 5p6p of the general typenpn′p for the first time in literature). For the 3 levels 5p6p ³ P ₁, 5p7p ³ D ₂ and 5p6p ¹ P ₁ a different classification was found and consistent values for the fine structure parameters, mixing coefficients and single electron hyperfine structure splitting parametersa _nl ^ik andb _nl ^ik were obtained. The three new determinations in Sb II of the quadrupole moment (in barn) of¹²¹Sb (Q(5p6s)=?0.55(5);Q(5p6p)=?0.57(5) from the 5p-electron andQ(5p6p)=?0.7(2) from the 6p-electron) are well agreeing with each other but differ to former values from SbI. The core polarization and isotope shift of the lines, however, are compatible with our former results in SbI.