Homotopiemengen von Multiplikationen auf Sphären und ihre algebraische Struktur

In an earlier paper [E4] we introduced an algebraic structure on sets of homotopy classes [S ^p ×S ^q ;S ⁿ ], given by the reflecting product on spheresS ⁿ , which makes these sets symmetric groupoids. In this article we determine precisely the algebraic structure of the symmetric groupoids ([S ⁿ ×S ⁿ ;S ⁿ ], ) forn 1, 3, 7.

     

Edge partitions of the Rado graph

We will prove that for every colouring of the edges of the Rado graph, (that is the countable homogeneous graph), with finitely many coulours, it contains an isomorphic copy whose edges are coloured with at most two of the colours. It was known [4] that there need not be a copy whose edges are coloured with only one of the colours. For the proof we use the lexicographical order on the vertices of the Rado graph, defined by Erdös, Hajnal and Pósa.Using the result we are able to describe a Ramsey basis for the class of Rado graphs whose edges are coloured with at most a finite number,r, of colours. This answers an old question of M. Pouzet.Supported by the French PRC Math-Info.Supported by NSERC of Canada Grant # 691325.     

Photochemical Reactions. 129th Communication. Photochemistry of a conjugated diepoxydiene: Product formation via carbonyl ylide and carbene intermediates with participation of neighbouring epoxy functions

On singlet excitation (λ=254 nm, acetonitrile) the diepoxydiene (E)- 7 undergoes photocleavage to the carbonyl ylide VII and the carbenes X and XI . The carbonyl ylide VII rearranges to the thermally labile dioxabicyclo [3.2.1]octene 20 or fragments via VIII to the aldehyde 9 and propyne. The carbene X , showing behaviour typical of vinyl carbenes, undergoes addition to the adjacent double bond furnishing the cyclopropene 11 . The carbene XI , however, undergoes an insertion reaction into the neighbouring oxirane C,C-bond leading to the oxetene (E)- 21 which can be isolated at ?78°, but at room temperature is rapidly transformed to the aldehyde 10 . On triplet excitation (acetone, λ>280 nm), however, (E)- 7 shows the typical behaviour of epoxydienes, undergoing C, O-cleavage of the oxirane and isomerization to 22, 23 and (E/Z)- 24 .     

[Ph2P(O)CH2Im][F3B(μ‐OH)BF3]. Erste strukturanalytische Charakterisierung des Hexafluoro(μ‐hydroxo)diborat‐Ions [1]

[Ph₂P(O)CH₂Im][F₃B(μ‐OH)BF₃]. First Structural Characterization of the Hexafluoro(μ‐hydroxo)diborate Ion [1] The hexafluoro(μ‐hydroxo)diborate ion has been isolated as it's Ph₂P(O)CH₂Im salt [Im = 2‐(1, 3, 4, 5‐tetramethylimidazolio)] ( 2 ) through basic hydrolysis of [Ph₂P(OBF₃)CH₂Im]BF₄ ( 1 ). The crystal structure of 2 · CH₂Cl₂ reveals the presence of ion pairs linked by unsymmetrical O‐H‐O hydrogen bonds.     

Mass spectrometric investigations of water extracts of the river Elbe for the determination of potential inputs of pollutants into the North Sea

A non-target screening by gas chromatography-mass spectrometry has been carried out on water extracts of the river Elbe in order to obtain an overview of organic compounds being dissolved or bound to suspended matter in the Elbe. Samples of 1001 volume were taken at the freshwater border at Stade and extracted by liquid-liquid extraction with pentane. Before GC-MS analysis, the water extracts were fractionated into 15 subsamples by HPLC on an SiO₂ column. A sensitivity of ca. 50 to 250 pg/l was reached for the GC-MC analysis. Several hundreds of natural and anthropogenic compounds could be identified or at least grouped into a compound class. The presence of a number of compounds could be verified from earlier investigations, in addition a great number of anthropogenic compounds were described which have previously not been reported for the river Elbe.     

18C6-Kronenkomplex der Amidoschwefelsäure

18C6 Crown Complex of Amidosulfuric Acid The title compound ( 3 ) has been obtained from reaction of the crown ether 18C6 ( 1 ) with amidosulfuric acid ( 2 ) in water, methanol, and ethanol. The structure of the substance was elucidated with X-ray diffraction and IR data. The two constituents of 3 are connected through three oxygen-hydrogen bridges. 3 is ideally suited for the isolation and recovery of 1 from aqueous solutions.     

Ozonolyse von Olefinen,III: Säurekatalysierte Ozonolyse von 3-Hexen-1,6-und 2-Penten-1,5-dicarbonylderivaten

Summary The ozonolysis of mono-unsaturated compounds containing the structural element =CH-CH₂-R [R=COOH, COOCH₃, CH(OCH₃)₂] was investigated. Reductive ozonolysis of (E)-3-hexene-1,6-dioic acid gives methyl 3,3-dimethoxypropanoate (2), whereas ozonolysis of dimethyl (E)-3-hexene-1,6-dioate (1a) and (Z)-1,1,6,6-tetramethoxy-3-hexene (1b) in a methanolic solution of HCl leads to a mixture of2, dimethyl malonate (3 a) and 1,1,3,3-tetramethoxypropane (3 b). The homologuos derivatives, dimethyl glutaconate (4 a) and 1,1,5,5-tetramethoxy-2-pentene (4 b), were ozonized to give mixtures of2, 3, dimethyl oxalate (5), methyl 2,2-dimethoxyacetate (6 a), and 1,1,2,2-tetramethoxyethane (6 b). The ratios of the various reaction products were determined by gas chromatography. In each case the formation of the bifunctional derivatives2 and6 a was favoured.