中文摘要：

我们考虑决定作为生气的节有一条开的弧的薄绝缘的无限的柱体的形状的反的散布问题。假设电场在 TM 模式被极化，这为在 R2 在一条开的弧的外表定义的 Helmholtz 方程导致一个混合边界价值问题。我们假定弧混合了 Dirichlet 阻抗边界状况，并且试着由使用因式分解方法通过远地模式恢复弧的形状。然而，我们不能使用樱桃酒介绍对待远地操作员 F 的基本定理，并且一些辅助操作员不得不被考虑。到我们的问题的因式分解方法的理论确认在这份报纸被给，并且一些数字结果被介绍显示出我们的方法的生存能力。[从作者抽象]

英文摘要：

We consider the inverse scattering problem of determining the shape of a thin dielectric infinite cylinder having an open arc as cross section. Assuming that the electric field is polarized in the TM mode, this leads to a mixed boundary value problem for the Helmholtz equation defined in the exterior of an open arc in R2. We suppose that the arc has mixed Dirichlet impedance boundary condition, and try to recover the shape of the arc through the far field pattern by using the factorization method. However, we are not able to apply the basic theorem introduced by Kirsch to treat the far field operator F, and some auxiliary operators have to be considered. The theoretical validation of the factorization method to our problem is given in this paper, and some numerical results are presented to show the viability of our method.