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The boundary problem of penetrating the monochromatic electromagnetic field which represents the arbitrary combination of E-and H-polarized plane fields, through a thin cylindrical shell made of biisotropic material with arbitrary complex parameters of media has been solved. The solution of the problem has amounted to solving a system of integral equations by means of specialized two-sided boundary conditions on the composite shell surface. The system of integral equations has been numerically solved by a quadrature method.

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