关于一类一阶非线性常微分方程解空间的显易结构

文章以定理１．１为基础,引入标准可积方程的概念,进而根据已知方程ｗ′＝∑sum from ｉ＝０ to n ａ_ｉ（ｚ）ｗ^ｉ（ｚ）的ｎ＋１个系数,给出了该方程解空间具有显易结构的判别准则．一方面,根据该准则,可以对该类非线性常微分方程解空间结构作出显易结构的判定,从而可以对其解空间进行定性解析分析;另一方面,该准则可以作为判定该类非线性常微分方程在复域上能否变量分离之准则     

Resolution of (±)-[2.2]paracyclophane-4,12-dicarboxylic acid

The resolution of (±)-[2.2]paracyclophane-4,12-dicarboxylic acid (±)-1 has been realized through the diastereomeric esters of (1S)-hydroxymethyl-4,7,7-trimethyl-2-oxabicyclo-[2.2.1]heptan-3-one, simply separated by flash chromatography and hydrolyzed with ^tBuOK/H₂O. (R)-(−)-1 and (S)-(+)-1 were obtained in high enantiomeric excesses (>97%) while the determinations of the absolute configurations of (R)-1 and (S)-1 were carried out by X-ray diffraction.