To Nigel Hitchin, with admiration, on the occasion of his 70th birthday.Abstract. We provide an introduction to the mathematics and physics of the deformed Hermitian-Yang-Mills equation, a fully nonlinear geometric PDE on Kähler manifolds which plays an important role in mirror symmetry. We discuss the physical origin of the equation, discuss some recent progress towards its solution. In dimension 3 we prove a new Chern number inequality and discuss the relationship with algebraic stability conditions.

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This study raises a new electric wheel with active control of suspension for in-wheel motor. Proceeding from the reality, we made a simulation analysis on these four models: a sample car with no motor, a motor with fixed joint, and active/inactive control suspension for in-wheel motor. During the analysis, less-than-10mm relative vertical displacement was used as a prerequisite, reducing the car's acceleration, the suspension flexivety, and the wheel's load as basic conditions, reducing the wheel's vertical acceleration as the primary target, LQR control of active suspension as the motive. According to the analysis, by optimizing the parameter of inactive control suspension for in-wheel motor, we can solve the vertical problems caused by the electric wheel's mass, but the vertical impact to in-wheel motor is still heavy. However, using active control suspension for in-wheel motor can not only rise the smoothness and safety of the car, but also reduce 64% of the vertical impact comparing to inactive control suspension. This improves the active control suspension for in-wheel motor can effectively resolve the electric cars' vertical problems both theoretically and practically.