Translating solitons to symplectic and Lagrangian mean curvature flows

In this paper, we construct finite blow-up examples for symplectic mean curvature flows and we study properties of symplectic translating solitons. We prove that, the K"ahler angle $\alpha$ of a symplectic translating soliton with $\max \mathrm{\mid }A\mathrm{\mid }=1$ satisfies that $\sup \mathrm{\mid }\alpha \mathrm{\mid }>\frac{\pi }{4}\frac{\mathrm{\mid }T\mathrm{\mid }}{\mathrm{\mid }T\mathrm{\mid }+1}$ where $T$ is the direction in which the surface transltes.