By Sierpinski W.
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Vol. 27, pp. 1708–1718, August 1957.  A. Michaeli, “Equivalent edge currents for arbitrary aspects of observation,” IEEE Trans. , vol. 23, pp. 252–258, March 1984.  H. Ling, S. W. Lee, and R. Chou, “Shooting and bouncing rays: calculating the RCS of an arbitrarily shaped cavity,” IEEE Trans. , vol. 37, pp. 194–205, February 1989.  H. Ling, S. W. Lee, and R. Chou, “High-frequency RCS of open cavities with rectangular and circular cross sections,” IEEE Trans. , vol. 37, pp. 648–652, May 1989.
Doing so yields ∆x 4πǫ = a1 0 1 dx′ + · · · + aN (x1 − x′ ) + a2 N∆x (N−1)∆x 1 dx′ (x1 − x′ ) + a2 .. 10) which comprises a matrix system of the form ⎤⎡ ⎡ Z11 Z12 Z13 . . Z1N ⎥⎢ ⎢Z ⎢ 21 Z22 Z23 . . Z2N ⎥ ⎢ ⎥⎢ ⎢ ⎢ Z31 Z32 Z33 . . Z3N ⎥ ⎢ ⎥⎢ ⎢ ⎢ ⎢ . . .. ⎥ .. ⎥⎢ ⎢ . . ⎦⎣ ⎣ . . Z N 1 ZN 2 ZN 3 . . Z N N a1 ⎤ ⎡ ⎢ a2 ⎥ ⎥ ⎢ ⎥ ⎢ ⎢ a3 ⎥ ⎥=⎢ ⎥ .. ⎥ ⎢ ⎢ . ⎦ ⎣ aN b1 ⎤ b2 ⎥ ⎥ ⎥ b3 ⎥ ⎥ .. ⎥ ⎥ . 12) can be evaluated in closed form. 14) where xb = n∆x and xa = (n − 1)∆x . Note that the linear geometry of this problem yields a matrix that has a symmetric Toeplitz structure of the form ⎡ ⎢ ⎢ ⎢ ⎢ Z=⎢ ⎢ ⎢ ⎣ Z1 Z2 Z3 .
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