在本项目中，我们将先构造两类单项式理想，并研究它们的深度与Stanley深度。在此基础上，我们将研究这两类单项式理想的幂的深度与Stanley深度，并估计它们的深度稳定指数。之后，我们将研究某些特殊图的边理想的乘子理想的Castelnuovo-Mumford正则度，希望给出一个较好的上界。

In this project, we will construct two classes of monomial ideals first, then study the depth and Stanley depth of them. On this basis, we will study the depth and Stanley depth of powers of these monomial ideals mentioned above, and we want to estimate the indexes of depth stability of these two classes of monomial ideals.. Furthermore, we will study the Castelnuovo-Mumford regularity of multiplier ideals of the edge ideals of some special graphs. And we want to give upper bounds for the regularity of these multiplier ideals.