Mellin and Green symbols for boundary value problems on manifolds with edges

We introduce the algebra of smoothing Mellin and Green symbols in a pseudodifferential calculus for manifolds with edges. In addition, we define scales of weighted Sobolev spaces with asymptotics based on the Mellin transform and analyze the mapping properties of the operators on these spaces. This will allow us to obtain complete information on the regularity and asymptotics of solutions to elliptic equations on these spaces.     

Darstellung,Eigenschaften und Molekülstrukturen von Dimethylaminomethylferrocenyl‐Verbindungen ausgewählter Elemente der Gruppen 13 und 14

Preparation, Properties, and Molecular Structures of Dimethylaminomethyl Ferrocenyl Compounds of selected Elements of Group 13 and 14 Dimethylmetalchlorides of gallium and indium react with dimethylaminomethylferrocenyllithium (FcNLi) to give the corresponding dimethylmetaldimethylaminomethylferrocenes 1 and 2 [Me₂MFcN; M=Ga, In]. In a similar manner dialkylmetaldichlorides of germanium and tin yield the expected chlordialkylmetaldimethylaminomethylferrocenes 3 – 5 [R₂(Cl)MFcN; M=Ge; R = Me ( 3 ), M=Sn; R=Me ( 4 ), Ph ( 5 )]. In a reaction of Me₃Al and Me₂AlCl with dimethylaminomethylferrocene the formation of the 1 : 1 adducts 7 and 8 could be observed. All compounds were characterised by ¹H and ¹³C nmr spectroscopy. The molecular structures of 1 , 3 , 4 and 7 were determined. 3 and 4 build in contrast to 1 monomeric molecules with chelat rings as a result of the M–N coordination. Compound 7 consist of monomeric molecules with 4 coordinated Al atoms.     

Intra- and inter-chain fluctuations in entangled polymer melts in bulk and confined to pore channels

It is known that topological restraints by “chain entanglements” severely affect chain dynamics in polymer melts. In this field-cycling NMR relaxometry and fringe-field NMR diffusometry study, melts of linear polymers in bulk and confined to pores in a solid matrix are compared. The diameter of the pore channels was 10 nm. It is shown that the dynamics of chains in bulk dramatically deviate from those observed under pore constraints. In the latter case, one of the most indicative signatures of the reptation model is verified 28 years after its prediction by de Gennes: The frequency and molecular mass dependencies of the spin-lattice relaxation time obey the power law T_! ∝ M⁰ v^3/4 on a time scale shorter than the longest Rouse relaxation time τ_R. The mean squared segment displacement in the pores was also found to be compatible to the reptation law < r²>∝ M^−1/2t^1/2 predicted for τ_R < t < τ_d, where τ_d is the so-called disengagement time. Contrary to these findings, bulk melts of entangled polymers show frequency and molecular mass dependencies significantly different from what one expects on the basis of the reptation model. The data can however be described with the aid of the renormalized Rouse theory.     

Coupling of a Nucleoside with DNA by a Methyltransferase

How to outwit a methyltransferase: Methyltransferases (Mtases) catalyze the transfer of the activated methyl group from the cofactor S-adenosyl-L -methionine ( 1 ) to acceptors R within a large variety of biomolecules. Through the use of the cofactor analogue 2 a whole nucleoside was coupled to DNA in a Mtase-catalyzed reaction.     

Measurements of L-shell X-ray emission lines of neonlike europium on an electron beam ion trap

We report a measurement of the two X-ray transitions that proceed from the and (1s²2s_1/22p⁶3p_1/2)_{J = 1} upper levels to the (1s²2s²2p⁶)_{J = 0} ground level in neonlike Eu⁵³⁺ (Z = 63), that is,  near the previously documented avoided crossing of the two upper levels at Z = 68. The measurement was carried out using the calorimeter spectrometer on the Livermore EBIT-I electron beam ion trap. It affirms the trends set by the neighboring neonlike ions both in terms of the relative intensity of the two lines and in terms of the magnitude of disagreement with theoretical energy level predictions.     

Development of an automated bacterial luminescence test for biomonitoring of environmental contaminants

The development of the bacterial luminescence test to an automated biomonitor is described. The computer controlled system was optimized by varying the following parameters: intermixture of the analyte solution and bacteria suspension, intensity and period of stirring during intermixture, delay time for temperature equalization, long-time stability of the bacteria and evaluation of the measured signals. All measurements were carried out using organic and inorganic pollutants, e.g. formaldehyde, phenol, 2,4-dichlorophenol, cyanide and lead ions. Five-minute inhibition curves from a number of single runs are presented.