Definitions from Unihan Copyright © 1991-2015 Unicode® Inc. All rights reserved.

不胜 * * + +
不胜感激 * * + +

不 no, not / un- / negative prefix

胜 victory / excel, be better than

感 feel, perceive, emotion

激 arouse, excite, incite / quickly

from CC-CEDICT under a Creative Commons Attribution-Share Alike 3.0 License

不勝' + 不胜 * * + cannot bear or stand / be unequal to very
不勝其擾' + 不胜其扰 * * + unable to put up with (sth) any longer /
不勝其煩' + 不胜其烦 * * + to be pestered beyond endurance /
不勝其苦' + 不胜其苦 * * + unable to bear the pain (idiom)/
不勝枚舉' + 不胜枚举 * * + too numerous to mention individually or one by one /

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