Study on the Stability of Ion-exchange Resin Catalysts:Ⅰ. TGA as a Rapid Evaluating Method

The thermal stability of five commercial ion-exchange resin catalysts was studied by means of thermal gravimetric analysis （TGA） at elevated temperatures of up to 600℃ and isothermal temperatures in the range of 150℃ and 200 ℃. Resin samples with different initial water contents were also investigated. The study indicated that TGA, as a complementary evaluating method for the plug flow reactor system approach, could be used as a fast analyzing means for study on the thermal stability of ion-exchange resin catalysts. The stoichiometric calculation of the isothermally treated resin catalysts based on the FTIR analysis and acid capacity confirmed that the weight loss of the resins at 150℃ and 200℃ was caused by the desulfonation process and that desulfonation occurred mainly at the para-position of the benzene ring in the resins. H＋ ions and moisture played an important role in the desulfonation process.

拟对角扩张的近似等距提升

设0→I→A—A/I→0为C~*-代数的短正合列且A含有单位元.如果扩张0→I→A→A/I→0为拟对角扩张,则证明对任给的A/I中正元(投影,部分等距,酉元)均有同形式的提升且提升与I中一列由投影组成的拟中心近似单位元相交换.进而证明对任给正数ε,任意A/I中的两正元(投影,部分等距,酉元)a^-和b^-,以及a^-的正元(投影,部分等距,酉元)的提升a,存在b^-的正元(投影,部分等距,酉元)的提升b,使得‖a-b‖<‖a^--b^-‖+ε.作为上述结论的应用证明了对任意的正数ε和u^-∈U(A/I)_0,存在u^-的提升u∈U(A)_0,使得cel(u)<cel(u^-)+ε.