Infinite-dimensional Langevin equations: uniqueness and rate of convergence for finite-dimensional approximations

The paper deals with the infinite-dimensional stochastic equation dX= B(t, X) dt + dW driven by a Wiener process which may also cover stochastic partial differential equations. We study a certain finite dimensional approximation of B(t, X) and give a qualitative bound for its rate of convergence to be high enough to ensure the weak uniqueness for solutions of our equation. Examples are given demonstrating the force of the new condition. Received: 6 November 1999 / Revised version: 21 August 2000 / Published online: 6 April 2001     

含长链亚烷基桥的芳炔类共轭大环的合成

采用模板导向法高产率地合成了两个含长链亚烷基桥的芳炔类共轭大环. 通过四碘化合物与单保护双炔化合物的四重Hagiraha偶合反应构建了环化所需要的复杂前体. 通过相应的模板四炔衍生物的分子内Glaser 偶合反应环化得到大环. 大环的结构用NMR, GPC 及UV-Vis表征确证.     

Die Palladium‐katalysierte Bildung von Arylaminen und ‐ethern: Synthesemethoden

Arylamines and arylethers are basic structural elements and of great importance in all areas of chemistry. The transformation of aryl halides into these structures is text book knowledge, however it often requires special substrates or additiona activation steps. In the past few years methodologies have been investigated which enable these transformations under palladium catalysis, using mild conditions to produce high product yields. The progress of these investigations is the subject of this article.     

Synthesis of highly phenylene substituted p-phenylene oligomers from pyrylium salts

A transition metal free route to phenyl substituted oligophenylenes that tolerates halogens is described.