For a connected hypergraph H with \(rank(H)=r\) , let \(\mathcal {D}(H)\) and \(\mathcal {A}(H)\) be the diagonal tensor of degrees and the adjacency tensor of H, respectively. For \(0 \le \alpha < 1\), the \(\alpha \)-spectral radius \(\rho _{\alpha }(H)\) of H is defined as \(\rho _{\alpha }(H)=\max \{x^{T}(\mathcal {A}_{\alpha }x)|x \in \mathbf {R}_{+}^{n},\Vert x\Vert _{r}=1\}\), where \(\mathcal {A}_{\alpha }(H)=\alpha \mathcal {D}(H)+(1-\alpha )\mathcal {A}(H)\). In this paper, we present some bounds on entries of the positive unit eigenvector corresponding to the \(\alpha \)-spectral radius of connected uniform hypergraphs. Furthermore, we obtain some bounds on entries of the positive unit eigenvector corresponding to the \(\alpha \)-spectral radius of connected general hypergraphs.

对于具有\（rank（H）= r \）的连通超图H，令\（\ mathcal {D}（H）\）和\（\ mathcal {A}（H）\）为度的对角张量，H的邻接张量。对于\（0 \文件\阿尔法<1 \） ，该\（\阿尔法\） -spectral半径\（\ RHO _ {\阿尔法}（H）\）的ħ被定义为\（\ RHO _ {\阿尔法}（H）= \ max \ {x ^ {T}（\ mathcal {A} _ {\ alpha} x）| x \ in \ mathbf {R} _ {+} ^ {n}，\ Vert x \ Vert _ {r} = 1 \} \），其中\（\ mathcal {A} _ {\ alpha}（H）= \ alpha \ mathcal {D}（H）+（1- \ alpha）\ mathcal {A} （H）\）。在本文中，我们给出了与连接的统一超图的\（\ alpha \）谱半径相对应的正单位本征向量项的一些边界。此外，我们获得了与连接的一般超图的\（\ alpha \）谱半径相对应的正单位本征向量项的某些边界。