Smooth projective translation planes

A projective plane is called smooth if both the point space and the line space are smooth manifolds such that the geometric operations are smooth. We prove that every smooth projective translation plane is isomorphic to one of the classical planes over , , or .Dedicated to Professor Dr. H. Salzmann on the occasion of his 65th birthday     

Franck-Condon matrix elements for bound-continuum vibrational transitions calculated by numerical integration and basis set expansion techniques

Franck-Condon factor distributions for bound-to-continuum transitions of one-dimensional vibrational states are calculated by a) using numerical integration, b) employing a finite number of square integrable harmonic oscillator functions. The methods are generally applicable to any kind of bound or repulsive potential involved. Results are presented and compared to model potential calculations previously reported by Krüger [1].     

Polyol-Metall-Komplexe. 25. rac-Mannose,rac-Arabit und L-Threit als deprotonierte Liganden in Ferraten(III)

Polyol Metal Complexes. 25. rac-Mannose, rac-Arabitol and L -Threitol as Deprotonated Ligands in Ferrates(III ) Ba₂[Fe₂(β-rac-ManfH_?5)₂] · 12H₂O ( 1 ), Sr₄[Fe₄(rac-Arab1,2,3,5H_?4)₄(OH)₂]CO₃ · 33 H₂O ( 2 ), and Ba₂[Fe₂(L-ThreH_?4)₂(OH)₂] · 12.5 H₂O ( 3 ) (Man = mannose, Arab = arabitol, Thre = threitol) have been crystallized from alkaline aqueous solution. Crystal structure analysis revealed dinuclear ferrate(III ) ions for 1 and 3 , the former being a C_i-symmetrical homoleptic ferric complex with pentadentate pentaanions derived from racemic β-mannofuranose. In 3 , besides tetradentate L -threitolato ligands, there is one terminal hydroxo ligand at each ferric center. Hydroxo ligands are also present in the C_i-symmetrical hexaanions of 2 , which are tetranuclear planar entities built up from four edge-sharing FeO₆ octahedra. However arabitol is a pentitol, the tetraanionic ligands are only tetradentate for steric reasons.     

Geminale Azo- und Heteroelement-Funktionen,II: α-Substituierte 2-(4-Chlorphenylazo)-propan-Derivate

The reaction of acetone-4-chlorophenylhydrazone (6) with bromine in the presence of acetamide yields 2-bromo-2-(4-chlorophenylazo)-propane (7) and 2,2-bis(4-chlorophenylazo)propane (8). The unstable heteroallylic bromide7 was subjected without isolation to nucleophilic displacements with a series of heteronucleophiles thereby affording the corresponding 2-(4-chlorophenylazo)-2-propane derivatives9 with the azo- and heteroelement-functions in a geminal position to each other.

Herrn Prof. Dr. Dr. h. c.K. Kratzl mit den besten Wünschen zum 70. Geburtstag gewidmet.     

Formation of the First Trimeric Monoterpenoid Indole Alkaloids

Under O², the Aspidosperma alkaloid tabersonine ( 1 ) was converted by a crude enzyme preparation from leaves of mature plants of Catharanthus roseus G DON into the trimeric 3-hydroxy-14′-(3α″-tabersonyl)voafrine B ( 4 ) which was easily reduced by NaBH₄ to 14′-(3α″-tabersonyl)voafrine B ( = tertabersonine; 5 ). Compounds such as 4 and 5 are the first trimeric alkaloids in the series of monoterpenoid indole alkaloids.     

Novel stereoselective molecularly imprinted polymers via ring-opening metathesis polymerisation

Stereoselective molecularly imprinted polymers (MIPs) have been synthesised via ring-opening metathesis polymerisation, in essentially, quantitative yield. A covalent imprinting strategy was followed during the network formation of the chiral sorbent. Recognition of the substrate however involved non-covalent interactions; a combination of hydrogen bonding and the chiral environment presented by the imprinted cavities. The enantiomeric excess achievable with these new MIPs is solvent dependent and stereoselectivities of up to 20% e.e. (separation factor α=2.2) were found in batch equilibrations.     

Synthesis of 5-alkylidene-2,5-dihydropyrrol-2-ones and their ring-transformation into 5,6-dihydrobenzo[h]chromones, 5,6,7,8-tetrahydrochromones and pyran-4-ones

Acid-mediated ring-transformations of 5-alkylidene-2,5-dihydropyrrol-2-ones, available by cyclization of 1,3-diketone dianions with bis(imidoyl) dichlorides of oxalic acid, resulted in formation of functionalized pyran-4-ones, such as 5,6-dihydrobenzo[h]chromones and 5,6,7,8-tetrahydrochromones.     

Quantitative depth profiling in glow discharge spectroscopies – A new deconvolution technique to separate effects of an uneven erosion crater shape

An algorithm is presented as a concept for the quantification in direct current and radiofrequency glow discharge (GD) modes for GD optical emission spectroscopy. The algorithm is divided into excitation and sputtering part and thus it is possible to distinguish between the different excitation processes and to consider equivalent sputtering crater formations in both modes. Intensity-time profiles are affected corresponding to the method by several effects. One important effect is that sputtering occurs at a single time in different depths because of curved crater bottoms, this is usually called crater effect. The main purpose is to introduce an iterative deconvolution technique which for the quantification numerically takes into account the curved sputtering crater bottom. Input data for the deconvolution technique are the calibrated mass-time profile, the partial densities of the sample constituents and the measured final shape of the sputtering crater. Using a relatively simple model for ion sputtering the deconvolution technique improves iteratively the calculated layer structure by means of information on crater formation. The mathematical handling is illustrated for the quantification of a depth profile of a multilayer sample of ten 100 nm layers. The resulting concentration-depth profile reflects excellently the real elemental distribution of the multilayer system.     

Analytical Detectors Based on Microplasma Spectrometry

Miniaturizing all dimensions of apparatus, such as electronics and computers, is the current trend followed by scientists in various fields. The idea of Lab-on-a-Chip has significantly expanded and found its broad applications in analytical chemistry. Microplasmas can act as a sample excitation source and are the miniaturized versions of full-sized plasmas. These can be created in various forms, such as direct current, microwave induced, capacitively coupled and inductively coupled plasmas. Scaling down the size would reduce the amount of gases, liquids and consumables required, as well as the sample analysis time, which in turn would decrease the operating costs. Therefore, several research groups are involved in the development of microplasmas for utilisation in analytical instruments.