1. Osteoporosis has syndrome characteristics of bone rarefaction and body pain, which should be carefully differentiated. 骨质疏松症的证候特征应辨别“松”与“痛”，治则常分“肾”与“脾”。
2. Several applications require consideration of rarefaction, which motivates the present thesis to focus on simulation of driven cavity flows in this region. 因此本文的动机是模拟空穴流场在稀薄区域上的应用。
3. Gravity compresses the gas in denser regions and, depending on the phase of the sound wave, can alternately enhance or counteract sonic compression and rarefaction. 重力会压缩致密区域内的气体，并因声波相位的不同，而可能加强或抵消声波所造成的压缩或稀释。
