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In this article, we show a truncated Second Main Theorem of meromorphic mappings from C n into P N ðCÞ for moving targets. The moving targets are only assumed to be nondegenerate. 2000 Mathematics Subject Classification: 32H30, 32A22; 30D35. Brought to you by | University of Miami Authenticated | 129.171.178.62 Download Date | 9/15/13 8:56 PM 2 Basic notions and auxiliary results from Nevanlinna theory 2.1. We set kzk ¼ ðjz 1 j 2 þ Á Á Á þ jz n j 2 Þ 1=2 for z ¼ ðz 1 ; . . . ; z n Þ A C n and define BðrÞ :¼ fz A C n : kzk < rg; SðrÞ :¼ fz A C n : kzk ¼ rg ð0 < r < yÞ: Define d c :¼ ffiffiffiffiffiffi ffi À1 p 4p ðq À qÞ; v nÀ1 ðzÞ :¼ ðdd c kzk 2 Þ nÀ1 and s n ðzÞ :¼ d c logkzk 2 5ðdd c logkzk 2 Þ nÀ1 on C n nf0g: 164 D. T. Do, D. Q. Si Brought to you by | University of Miami Authenticated | 129.171.178.62 Download Date | 9/15/13 8:56 PM Brought to you by | University of Miami Authenticated | 129.171.178.62 Download Date | 9/15/13 8:56 PM Brought to you by | University of Miami Authenticated | 129.171.178.62 Download Date | 9/15/13 8:56 PM

In this article, truncated second main theorems with moving targets are given. Basing on these theorems, the uniqueness problem with truncated multiplicities of meromorphic mappings in several complex variables for moving targets is solved.

In this article, the uniqueness problem with truncated multiplicities of meromorphic mappings in several complex variables is studied. The recent results of Smiley, Ji, Fujimoto and Fujimoto's questions are deduced as consequences.

The purpose of this article is twofold. The first is to prove the unicity theorem with truncated multiplicities of meromorphic functions sharing five small functions. This gives a remarkable improvement of the results of Yuhua–Jianyong, Yao and Yi. The second is to generalize the unicity theorem of Fujimoto to meromorphic functions sharing four small functions with truncated multiplicities.