Evaluation of quadrature schemes for the discrete ordinates method

After reviewing the presently available quadrature schemes for the discrete ordinates method, the accuracy of different schemes is analyzed and evaluated. It is shown from a comprehensive error analysis that the moment conditions have to satisfied not only for the principal coordinates directions, as it is mostly carried out, but for any arbitrary test direction. Among the schemes with approximately 50 discrete ordinates the DCT-020-2468 quadrature was found to give the best accuracy. The highest accuracy among all schemes is achieved by the LC-11 quadrature which requires 96 discrete ordinates. This scheme is rarely used up to date and deserves more attention for high accuracy predictions.     

Rückbezüge des Mathematikunterrichts und der Methodik des Mathematikunterrichts in der DDR auf historische Vorausentwicklungen

The author discusses at some examples exemplarily, how the pedagogy of mathematics education in the GDR from curricular and educational/psychological knowledge from the time before 1945 has developed scientifically.     

Direct fission versus sequential evaporation mechanism of sputtered caesium iodide cluster ions

A triple stage hybrid mass spectrometer was scanned for the trapping of the reaction intermediates of the over-all loss of two CsI-moieties from size-selected caesium iodide cluster ions of the general formula Cs (CsI)⁺ _n . In addition to appropriate MS/MS/MS-methods an electrically floated collision cell has been applied to trap intermediates of unimolecular and collision-induced evaporations. In comparison with other experimental findings the features of the evaporation mechanism are discussed.     

Krichever-Novikov-like bases on punctured Riemann surfaces

Bases of holomorphic -differentials on N-punctured Riemann surfaces of arbitrary genus are constructed. The resulting extension of the Virasoro algebra on N-punctured spheres is displayed explicitly.     

Decomposition of EuPdIn and EuPtIn at high temperature and high pressure—formation of the hexagonal Laves phases EuPd0.72In1.28 and EuPt0.56In1.44

EuPd_0.72In_1.28 and EuPt_0.56In_1.44 were prepared under multianvil high-pressure (10.5 GPa) high-temperature (1500 and 1400 K) conditions from the precursor compounds EuPdIn and EuPtIn. They were investigated by X-ray diffraction on both powders and single crystals: MgZn₂-type, space group P6₃/mmc, a=578.7(1) pm, c=944.9(3) pm, wR2=0.0734, 263 F² values for EuPd_0.72In_1.28 and a=591.1(2) pm, c=933.8(2) pm, wR2=0.0853, 151 F² values for EuPt_0.56In_1.44 with 13 variable parameters per refinement. Both structures are built up from face- and corner-sharing tetrahedra of palladium (platinum) and indium atoms. The europium cations are located in cavities within the three-dimensional [Pd_0.72In_1.28] and [Pt_0.56In_1.44] networks. The 2a and 6 h positions of the tetrahedral networks show mixed Pd/In and Pt/In occupancy in EuPd_0.72In_1.28 and EuPt_0.56In_1.44, respectively. The crystal chemistry of these indides is briefly discussed.     

[2+2]-Photocycloaddition von Cyclohexen an 2-Acetyl-5,5-dimethyl-1,3-cyclohexandion und 3-Acetyl-1,5,5-trimethyl-2,4-pyrrolidindion

Summary Irradiation of solutions of excess cyclohexene and 2-acetyl-5,5-dimethyl-1,3-cyclohexanedione (1), and 3-acetyl-1,5,5-trimethyl-2,4-pyrrolidinedione (4) results mainly in the formation of 1,5-diones2 and5. These originate from intermediate cycloadducts of cyclohexene and theexo-enols of the cyclic 1,3-diketones. The yields decrease with increasing polarity of the solvent. In solution2 and5 are in equilibrium with the cyclic hemiacetales3 and6.