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This paper establishes a hypersurface defect relation, that is, ${\sum }_{j=1}^q\delta (D_j,f)\le (n+1)/d$, for a family of meromorphic maps from a generalized p-parabolic manifold M to the projective space ℙⁿ, under some weak non-degeneracy assumptions.

This paper concerns the uniqueness of meromorphic functions and shows that there exists a set S ⊂ ℂ of eight elements such that any two nonconstant meromorphic functions f and g in the open complex plane ℂ satisfying $E_{3)}(S,f)=E_{3)}(S,g)$ and Ē(∞,f) = Ē(∞,g) are identical, which improves a result of H. X. Yi. Also, some other related results are obtained, which generalize the results of G. Frank, E. Mues, M. Reinders, C. C. Yang, H. X. Yi, P. Li, M. L. Fang and H. Guo, and others.

By considering a question proposed by F. Gross concerning unique range sets of entire functions in $ℂ$, we study the unicity of meromorphic functions in ${ℂ}^m$ that share three distinct finite sets CM and obtain some results which reduce $5\le c_3\left(ℳ\left({ℂ}^m\right)\right)\le 9$ to $5\le c_3\left(ℳ\left({ℂ}^m\right)\right)\le 6$.

This paper studies the unicity of meromorphic(resp. entire) functions of the form $f^n{f}^{\text{'}}$ and obtains the following main result: Let $f$ and $g$ be two non-constant meromorphic (resp. entire) functions, and let $a\in ℂ\setminus \left\{0\right\}$ be a non-zero finite value. Then, the condition that $E_{3)}(a,f^n{f}^{\text{'}})=E_{3)}(a,g^n{g}^{\text{'}})$ implies that either $f=dg$ for some $(n+1)$-th root of unity $d$, or $f=c_1{e}^{cz}$ and $g=c_2{e}^{-cz}$ for three non-zero constants $c$, $c_1$ and $c_2$ with ${\left(c_1{c}_2\right)}^{n+1}{c}^2=-a^2$ provided that $n\ge 11$ (resp. $n\ge 6$). It improves a result of C. C. Yang and X. H. Hua. Also, some other related problems are discussed.