中文摘要：

在这份报纸，我们给三二项式的系数不平等的证明。这些不平等是关键成分在[皮脂腺囊瘤和吉姆 J。Comput。数学。 26 ，( 2008 )， 1-22 ]挥动速度和状况，它进一步过去常建立L错误估计的一个一般接口与一个 piecewise 常数为迎风的差别计划建立L1错误估计到线性移流方程因为一个 保存Hamiltonian 计划发展了在[ Jin 和世界， Commun 。数学。Sci。3，(2005 ) ， 285-315 ] 到有 piecewise 常数潜力的 Liouville 方程[皮脂腺囊瘤和 Jin，暹罗 J。Numer。肛门。16，(2008 ) ， 2688-2714 ] 。[从作者抽象]

英文摘要：

In this paper we give proof of three binomial coefficient inequalities. These inequalities are key ingredients in [Wen and Jin, J. Comput. Math. 26, （2008）, 1-22] to establish the L^1-error estimates for the upwind difference scheme to the linear advection equations with a piecewise constant wave speed and a general interface condition, which were further used to establish the L^1-error estimates for a Hamiltonian-preserving scheme developed in [Jin and Wen, Commun. Math. Sci. 3, （2005）, 285-315] to the Liouville equation with piecewise constant potentials [Wen and Jin, SIAM J. Numer. Anal. 46, （2008）, 2688-2714].