所说的

所吹嘘的

cracked up to be───断定（指对某人某事某物的优点夸大地宣扬）

came up to───v.达到；等于

check up on───检查，核对，校对

crack a smile───展颜微笑

crack house───破房子

crack of doom───世界末日的霹雳

crack of dooms───世界末日的霹雳

This paper presents a fundamental solution which can be used to solve the general radial crack system on half-plane. An example is given for check up.───本文给出了可用于解决半平面上一般射线裂纹系的基本解。文中作了例题验证。

Oh wow, I don't know whether to vomit or just crack up laughing. This is really sad. Disney Corp must be doing well in China.───哇，我不知道是该作恶还是该捧怀大笑。这真的很糟糕。迪士尼公司在中国一定是发展的很好吧。