Subsolidus phase relations and crystal structure of compounds in the PrOx-CaO-CuO system

The subsolidus phase relations of the PrO_x-CaO-CuO pseudo-ternary system sintered at 950-1000°C have been investigated by X-ray powder diffraction. In this system, there exist one compound Ca₁₀Pr₄Cu₂₄O₄₁, one Ca₂Pr₂Cu₅O₁₀-based solid solution, seven three-phase regions and two two-phase regions. The crystal structures of Ca₁₀Pr₄Cu₂₄O₄₁ and Ca₂Pr₂Cu₅O₁₀-based solid solution have been determined. Compound Ca₁₀Pr₄Cu₂₄O₄₁ crystallizes in an orthorhombic cell with space group D_2h²⁰−Cccm, Z=4. Its lattice parameters are a=11.278(2) Å, b=12.448(3) Å and c=27.486(8) Å. The crystal structure of Ca₂Pr₂Cu₅O₁₀-based solid solution is an incommensurate phase based on the orthorhombic NaCuO₂ type subcell. The lattice parameters of the subcell of the Ca_2.4Pr_1.6Cu₅O₁₀ are a₀=2.8246(7) Å, b₀=6.3693(5) Å, c₀=10.679(1) Å, and those of the orthorhombic superstructure are with a=5a₀, b=b₀, c=5c₀. The Ca_2.4Pr_1.6Cu₅O₁₀ structure can also be determined by using a monoclinic supercell with space group C_2h⁵−P2₁/c, Z=4, a=5a₀, b=b₀, and β=104.79(1)° or 136.60(1)°, V=5a₀b₀c₀.     

Theoretical Study of Weakly Bound Dimers between Hydrogen Fluoride and Some Polar Molecules

Weakly bound linear and bent dimers, FH—X (where X = CO, OC, CNH, NCH, N₂O and ON₂), are investigated using the DFT B3LYP and ab initio MP2 methods with the same basis sets (6–311++G(3df,2pd)). The strengths of the H—C or H—N H‐bonds in dimers FH—CO, FH—CNH, and FH—N₂O are compared with those of the H—O or H—N H‐bonds in dimers FH—OC, FH—NCH, and FH—ON₂. The results obtained for the H‐bond distances, the elongation effect of the HF bond, the red shift of the HF stretching frequency, and the energy difference between the dimer and the charge transfer reveal that the H‐bonds of the first group of dimers are stronger than those of the second. The Gibbs energies calculated for the six dimer formations indicate that the weakly bound dimers are unstable at room temperature (T = 298 K) (FH—X's → FH + X's, ΔG < 0).     

Quantum chemistry study on B32 and B32H2–32

The structures of B32 and B₃₂H^2–₃₂ with I_h symmetry have been investigated by means of ab initio calculations at STO-3G level. The relationship between molecular orbitals of them has been analyzed and their bonding properties have been discussed. Then the possibility of their existence, as well as the similarity and difference between B₃₂ (B₃₂H^2–₃₂) and C₆₀ (C₆₀H₆₀) have been inferred.     

Kupplungsreaktionen von Diazoniumbetainen mit 1,6-Methano[10]-annulenderivaten und ihre Cyclisierungsreaktionen zu Heterocyclen

Summary Coupling reactions of the diazoniumbetaines2, 4, 6a, 6b, 6c with derivatives of 1,6-methano[10]annulene1a–c and/or -naphthol7 yield the dyes3a–c, 5a, 5c, 8a–c, 9, 11. The syntheses of different triazine derivatives12a–c, 13a–c, 15, 16, and17a, 17c are described.

Herrn Kollegen Gerhard Schwenker mit den besten Wünschen zum 65. Geburtstag gewidmet     

Search

This paper reviews the theory of search. The main viewpoint is statistical but considerable space is spent on connections with other fields such as logic and optimisation. Three primitive ideas dominate: consistency, entropy, and Bayes' methods. The theory of screening provides one of the central examples and there is a section on nonsequential random search deriving from the work of Renyi. The game of Bulls and Cows provides a motivating example for both sequential and nonsequential algorithms.     

KT-nearfields of rank 2

Summary Nearfields of rank 2 over their kernel which are not Dickson nearfields have recently been constructed by H. Zassenhaus. Here it is shown that KT-nearfields of rank 2 over their kernels and of characteristic 2 are necessarily Dickson nearfields which are coupled to quadratic field extensions and their Dickson group is isomorphic to ₂. Using results of Gröger one obtains all KT-nearfields of rank 2 over the field of rational numbers.     

On the support of midconvex operators

Summary LetX be a real vector space,D a convex subset ofX and (Y, K) an order complete ordered vector space. The following sandwich theorem holds: Iff: D Y is midconvex,g: D Y {– } is midconcave andg f onD, then there exists a Jensen mappingh: D Y {– } such thatg h f onD. Using this theorem we show that a mappingf: D Y is midconvex if and only if it has Jensen support at every point ofD. Moreover, ifX is a Baire topological vector space and (Y, K) is an ordered topological vector space satisfying some additional conditions, then a mappingf: D Y is continuous whenever it has continuous Jensen support at every point ofD. As an application of these results we obtain the equality of some set-classes connected with additive and midconvex operators.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth     

Numerical implementation of coherence for the example of the “Swiss Cross”

Summary We consider the two-dimensional Helmholtz equation u+u=0 inD with the boundary conditionsu=0 on D. D is the Swiss Cross — a region consisting of five unit squares. A method based on the concept of Coherence is utilized to determine an approximation for the first eigenvalue= ₁ more accurate than calculated by classical difference methods. The numerical result is used to illustrate isoperimetric upper and lower bounds for ₁, and to test some conjectures on its relations with torsional rigidity.Dedicated to the memory of Professor Lathar Collatz     

Problems with the ζ-function method

The -function method for evaluating effective actions is applied to an operator containing a potential localized on two parallel planes. This operator is characterized by a continuous spectrum and broken translation invariance. In this case, the -method leads to a divergent volume factor independent of the physical parameters. In a suitable regularization scheme, only the next to leading order term reproduces a physically interesting result.