In one-dimension simulation, the approach taken is a hybrid model where the ions are treated as distinct particles in one-dimension while the electron beam is treated using the beam envelope equation.
在一维模拟中，采用混合模型研究离子噪声，用包络方程描述电子束的，用离散的宏粒子模型描述离子。
This paper uses the method of establishing the convex envelope, giving a proof in Partial Differential Equation.
本文利用构造凸包络的方法，给出了该定理偏微分上的证明。
In 1985, prove Theorem 1.1 from the point of Brown Motion. This paper USES the method of establishing the convex envelope, giving a proof in Partial Differential Equation.
在1985年从布朗运动的角度证明了定理1.1，本文利用构造凸包络的方法，给出了该定理偏微分上的证明。
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