On the theorem of Barban and Davenport-Halberstam in algebraic number fields

The Barban-Davenport-Halberstam theorem is generalized to arbitrary algebraic number fields of finite degree over the rationals. As an application, we consider a divisor problem and a result of Elliott and Halberstam concerning the least prime in an arithmetic progression.     

Photolyse von Monophenylphosphat und e aq − -Bildung in wäßriger Lösung

At photolysis (253.7 nm) of monophenylphosphate (10^?3 m) in O₂-free neutral aqueous solution were determined: orthophosphate (Φ=0.006), phenol (Φ=0.0029), besides of small amounts of phosphorous acid, benzene, 2.2′-dihydroxybiphenyl and traces of 2.4′- and 4.4′-dihydroxybiphenyl. The yield of the main products is smaller at pH 2 and 12. Polymers were formed at u.v.-doses >2·10¹⁹ hv/ml. The electron yield determined by means of N₂O increases from Φ (N₂)= Φ(e _aq ^? )=0.012 to 0.019 changing the ester concentration from 0.001 to 0.1m. Φ (N₂)-value rises by addition of methanol or increasing pH. As electron ejecting state an excited complex is postulated. The effective ionization potential of phenylphosphate in aqueous solution is ≦4.9 e.v.     

L p -Estimates for the Navier–Stokes Equations for Steady Compressible Flow

We consider the Navier–Stokes equations for compressible isentropic flow in the steady three-dimensional case. The pressure and the kinetic energy are estimated uniformly in L^q with being the density. This is an improvement of known estimates in the case Mathematics Subject Classification (2000): 35Q30, 76N10     

Magnetization reversal in textured NdFeB-Fe composites observed by domain imaging

Textured composite samples consisting of Nd_13.6Fe_73.6Ga_0.6Co_6.6B_5.6 (MQU-F™) and micron-sized Fe particles with weight ratios from 100:0 to 70:30 have been prepared by hot deformation. Microstructure studies revealed a layered structure of both phases with the layer normal parallel to the pressing direction. Magnetic measurements showed single-phase hysteresis curves for all samples when measured along the pressing direction, which is also the easy axis of magnetization. Coercivity decreased drastically from 1.32 T for pure NdFeB samples to 0.154 T for a sample with 30 wt% Fe. Magneto-optical Kerr microscopy with a digitally enhanced imaging technique has been used to examine the evolution of magnetic domains in the hard and soft phase during demagnetizing a sample consisting of 70 wt% NdFeB and 30 wt% Fe. It is shown that demagnetization takes place via domain rearrangements within the soft phase, which lead to and support the nucleation of reversed interaction domains at phase boundaries. Also nucleation of interaction domains within the hard magnetic phase could be revealed.     

Hydrolysis of Cutin by PET-Hydrolases

Functionalisation of synthetic polymers by using enzymes has been recently demonstrated. The major advantage of enzymes over chemical processes lies in their surface specific and endo-wise mode of action. Surface hydrophilisation of PET with lipases and cutinases leads to a dramatic increase of the surfacial acid and hydroxyl group content while conventional chemical treatment does not cause any change. However, this PET-hydrolysing activity by enzymes from distinct classes has not yet been correlated to activity on natural polyesters. Here, we show that lipases, cutinases and a PHA-depolymerase are all capable of hydrolysing PET, while only lipases and cutinases also hydrolysed cutin to various degrees. Lipases showed a higher specificity for terminal fatty acids while the cutinases preferred hydroxy fatty acids during cutin hydrolysis.     

Sierpiński graphs as spanning subgraphs of Hanoi graphs

Hanoi graphs H _p ⁿ model the Tower of Hanoi game with p pegs and n discs. Sierpinski graphs S _p ⁿ arose in investigations of universal topological spaces and have meanwhile been studied extensively. It is proved that S _p ⁿ embeds as a spanning subgraph into H _p ⁿ if and only if p is odd or, trivially, if n = 1.