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Let $(X, \omega)$ be a compact connected Hermitian manifold of dimension $n$.We consider the Bott-Chern cohomology and let $[\chi ] \inH^{1,1}_{\text{BC}}(X; \mathbb{R})$. We study the deformed Hermitian-Yang-Millsequation, which is the following nonlinear elliptic equation $\sum_{i} \arctan(\lambda_i) = h(x)$, where $\lambda_i$ are the eigenvalues of $\chi$ withrespect to $\omega$.

Deformed Hermitian-Yang-Mills Equation on Compact Hermitian Manifolds