Zur Fehlerabschätzung näherungsweiser Lösungen von Gleichungen in halbgeordneten Räumen

Ohne Zusammenfassung     

A conjecture of Palamodov about the functors Ext in the category of locally convex spaces

In 1971 Palamodov proved that in the category of locally convex spaces the derived functors Ext^k(E,X) of Hom(E,·) all vanish if E is a (DF)-space, X is a Fréchet space, and one of them is nuclear. He conjectured a “dual result”, namely that Ext^k(E,X)=0 for all if E is a metrizable locally convex space, X is a complete (DF)-space, and one of them is nuclear. Assuming the continuum hypothesis we give a complete answer to this conjecture: If X is an infinite-dimensional nuclear (DF)-space, then

(1)

There is a normed space E such that Ext¹(E,X)≠0.

(2)

where is a countable product of lines.

(3)

Ext^k(E,X)=0 for all k?3 and all locally convex spaces E.

     

Parallel Analysis of the Reaction Products from Combinatorial Catalyst Libraries

No Abstract     

Photochemical cycloaddition of olefie to aromatic compounds -IV. on the mechanism of the photochemical meta-cycloaddition.

The meta-photoadditions of 1,3-dioxoles to benzene are shown to yield predominantly exo-configurated products. The mechanism is considered in the light of these new results.