Kristallstruktur von Na3(NH4)12[Mo57Fe6(NO)6O174(OH)3(H2O)24]·76H2O,einer Verbindung mit einem ungewöhnlichen Clusteranion

Summary The X-ray crystal structure of the compound Na₃(NH₄)₁₂[Mo₅₇Fe₆(NO)₆O₁₇₄(OH)₃(H₂O)₂₄]·76H₂O (3) [P6₃/mmc;a=2380.6(5),c=2763.4(7),Z=2], the giant cluster anion of which has the shape of a doughnut, shows remarkable details: The cluster [{Fe(H₂O)₂}₆{Mo(-H₂O)₂(-OH)Mo}₃{ Mo₁₅(MoNO) ₂ ³⁺ O₅₈(H₂O)₂}₃]^15– can be described as being composed of three transferable {Mo₁₇} ligands bridged by cationic centers and contains a novel nanodimensional central cavity.

     

A -normal, not densely normal Tychonoff space

We give an example of a -normal space which is not densely normal.

     

Synthese arylsubstituierter 2-Pyrimidinamine,Dihydro-2-pyrimidinamine und Pyrimido[1,2-a]pyrimidine durch Reaktion von Guanidin mit Chalkonen

4- and 4-methoxy-, 4-hydroxy- and 2-hydroxychalcone4 e,k,f andg, respectively, are transformed by action of guanidine in benzene to yield 4-(4-methoxyphenyl)-6-phenyl-2-pyrimidinamine (6 e=6 k) and hydroxyphenylpyrimidinamines6 f andg, respectively. In contrast, 4- and 4-chlor-, 4-brom- and 4-phenylchalcone4 h,l–n resp. react with guanidine under analogous conditions to give 4,6-diaryl-1,4-dihydro-2-pyrimidinamines5 h,l–n. The bases5 h,l–n also tend to aromatize, but they can be stabilized by transformation into salts5 h,l–n · HCl with hydrochloric acid. Heating of5 n inDMF under atmospheric oxygen yields 4-(4-biphenyl)-6-phenyl-2-pyrimidinamine (6 n). Action of guanidine on 4-nitrochalcone4 o in chloroform affords 2-amino-4-nitrophenyl-6-phenyl-tetrahydro-4-pyrimidinol8 o, which is transformed by hydrochloric acid into 6-nitrophenyl-dihydropyrimidinamine-hydrochloride5 o · HCl. Treating of the latter with sodiummethylat in methanol yields the very stable dihydropyrimidinamine5 o. Action of guanidine on 4-chlor- and 4-bromchalcone4 h andm respectively (in addition to5 h andm) yields 2,4,6,8-tetraaryl-1,4-dihydro-2H-pyrimido[1,2-a]pyrimidines7 h andm, respectively.

Herrn Prof. Dr.Erwin Schauenstein mit den besten Wünschen zum 65. Geburtstag gewidmet.     

Optical metrics and birefringence of anisotropic media

The material tensor of linear response in electrodynamics is constructed out of products of two symmetric second rank tensor fields which in the approximation of geometrical optics and for uniaxial symmetry reduce to “optical” metrics, describing the phenomenon of birefringence. This representation is interpreted in the context of an underlying internal geometrical structure according to which the symmetric tensor fields are vectorial elements of an associated two-dimensional space.     

A Short Remark on Weierstrass Points at Infinity on <Emphasis Type="Italic">X</Emphasis><Subscript>0</Subscript>(<Emphasis Type="Italic">N</Emphasis>)

We point out that the formalism of the trace map and reduction modulo p can be used to give a short proof for the fact first proved by Ogg that is not a Weierstrass point on X₀(pM) where p is a prime not dividing M and the genus of X₀(M) is zero.     

Letter: Statefinder Parameters for Interacting Dark Energy

We argue that the recently introduced statefinder parameters (Sahni et al., JETP Lett. 77, 201 (2003)), that include the third derivative of the cosmic scale factor, are useful tools to characterize interacting quintessence models. We specify the statefinder parameters for two classes of models that solve, or at least alleviate, the coincidence problem.