1. K. Aygun, S. E. Fisher, A. A. Ergin, B. Shanker, and E. Michielssen,”Transient analysis of multielement wire antennas mounted on arbitrarily shaped perfectly conducting bodies, ” Radio Science, vol. 34, no. 4, pp. 781–796, April 1999.

   Article  Google Scholar 

2. E. Altshuler and D.S. Linden, “Wire antenna design using genetic algorithms”, IEEE Antennas and Propagation Magazine 39 (1997) 33–43.

   Article  Google Scholar 

3. T.S. Angell and A. Kirsch, “Multicriteria optimization in antenna design”, Math. Methods Appl. Sci. 15 (1992) 647–660.

   Article MathSciNet MATH  Google Scholar 

4. T.S. Angell, R.E. Kleinman, and B. Vainberg, “Asymptotic methods for an optimal antenna problem”, SIAM J. Appl. Math. 59 (1999) 242–260.

   MathSciNet MATH  Google Scholar 

5. G.R. Benitz, “High-Defintion Vector Imaging,”Lincoln Laboratory Journal, vol. 10, pp. 147–169, 1997.

   Google Scholar 

6. M. Cheney and B. Borden, “Microlocal structure of Inverse Synthetic Aperture Radar Data”,Inverse Problems19, pp. 173–194, 2002.

   Article MathSciNet  Google Scholar 

7. M. Cheney and D. Isaacson, “Inverse problems for a perturbed dissipative half-space”, Inverse Problems, 11, 865–888 (1995).

   Article MathSciNet MATH  Google Scholar 

8. J. Cooper and W. Strauss, “Scattering of waves by periodically moving bodies”, J. Functional Analysis 47 (1982) 180–229.

   Article MathSciNet MATH  Google Scholar 

9. Y. Dermenjian and J.C. Guillot, “Scattering of elastic waves in a perturbed half-space with a free boundary. The limiting absorption principle”, Math. Meth. in the Appl. Sci. 10, 87–124 (1988).

   Article MathSciNet MATH  Google Scholar 

10. D. C. Dobson and F. Santosa, “Nondestructive evaluation of plates using eddy current methods”, International Journal of Engineering Science, 36 (1998), 395–409.

    Article MathSciNet MATH  Google Scholar 

11. S. E. Fisher, D. S. Weile, and E. Michielssen,”Pareto genetic algorithm design of log-periodic monopole arrays mounted on realistic platforms, ” Journal of Electromagnetic Waves and Applications, vol. 13, no. 5, pp. 571–598, 1999.

    Article MATH  Google Scholar 

12. A. Karlsson and G. Kristensson, “Constitutive relations, dissipation and reciprocity for the Maxwell equations in the time domain”, J. Electr. Waves Appl. 6 (1992) 437–551.

    Google Scholar 

13. J.B. Keller, H. Primakoff, M.J. Klein and E. Carstensen, Diffraction of Sound Around a Circular Disk, J.A.S.A., 19, 132–142, Jan. 1947; Math. Revs. 8, 545, 1947

    Google Scholar 

14. J.B. Keller and A. Blank, Diffraction and Reflection of Pulses by Wedges and Corners, Comm. Pure Appl. Math., 4, 75–94, June 1951; Math. Revs., 12,564, 1951; 13, 304, 1952.

    Google Scholar 

15. J.B. Keller, Diffraction of a shock or an electromagnetic pulse by a right-angled wedge, J. Appl. Phys., 23, 1267–1268, Nov. 1952.

    Article  Google Scholar 

16. J.B. Keller, The Geometrical Theory of Diffraction,Proc. of the Symp. on Microwave Optics, Eaton Electronics Laboratory, McGill University, Montreal, Canada, June 1953, Vol. 1 (4 pages); Reprinted as, The Geometric Optics Theory of Diffraction, The McGill Symp. on Microwave Optics, B.S. Karasik and F.J. Zucker, eds., AFCRC, Bedford, MA, 1959, Vol. 2, 207–210.

    Google Scholar 

17. J.B. Keller, R.M. Lewis, and B.D. Seckler, Asymptotic Solution of Some Diffraction Problems, 1956 Comm. Pure Appl. Math., 9, 207–265, June 1956; Math. Revs., 17, 41, 1956; 18, 43, 1957.

    Google Scholar 

18. J.B. Keller, Diffraction by a Convex Cylinder,IRE Trans. on Antennas and Prop., Symp. on Electromagnetic Wave Theory, AP-4, 312–321, July 1956; Math. Revs., 19, 103, 1959.

    Google Scholar 

19. J.B. Keller, Diffraction by an Aperture, J. Appl. Phys., 28,426–444, April 1957; Math. Revs., 20, 835, 1959; 21, 105, 1960.

    Google Scholar 

20. J.B. Keller, R.M. Lewis, and B.D. Seckler, Diffraction by an Aperture II, J. Appl. Phys., 28, 570–579, May 1957; Math. Revs. 20, 835, 1959; 21, 105, 1960.

    Google Scholar 

21. J.B. Keller, A Geometrical Theory of Diffraction, Calculus of Variations and Its Applications, Proceedings of Symposia in Applied Mathematics, 8, 27–52, McGraw-Hill, New York, 1958; Math. Revs. 20, 103, 1959.

    Google Scholar 

22. J.B. Keller and B.D. Seckler, The Geometrical Theory of Diffraction in Inhomogeneous Media, J.A.S.A., 31, 192–205, Feb. 1959; Math. Revs. 20, 836 and 1132, 1959.

    Google Scholar 

23. J.B. Keller, and B.D. Seckler, Asymptotic Theory of Diffraction in Inhomogeneous Media, J.A.S.A., 31, 206–216, Feb. 1959; Math. Revs. 20, 836 and 1132, 1959.

    Google Scholar 

24. J.B. Keller and B.R. Levy, Diffraction by a Smooth Object, Comm. Pure Appl. Math., 12, 159–209, Feb. 1959; Math. Revs., 21, 212, 1960.

    Google Scholar 

25. J.B. Keller, How Dark is the Shadow of a Round-Ended Screen ?, J. Appl. Phys., 30, 1452–1454, Sept. 1959.

    Article  Google Scholar 

26. J.B. Keller and B.R. Levy, Diffraction by a Spheroid, Canadian J. of Phys., 38, 128–144, J.n. 1960; Math. Revs. 22 (2B), 228, 1961.

    Google Scholar 

27. J.B. Keller and R.N. Buchal, Boundary Layer Problems in Diffraction Theory, Comm. Pure Appl. Math., 13, 85–114, Feb. 1960; Math. Revs. 22 (10B), 1797, 1961.

    Google Scholar 

28. J.B. Keller, Backscattering from a Finite Cone, IRE Trans. on Antennas and Prop., AP-8, 175–182, Mar. 1960.

    Google Scholar 

29. J.B. Keller and S.I. Rubinow, Shift of the Shadow Boundary and Scattering Cross Section of an Opaque Object, J. Appl. Phys., 32, 814–820, May 1961; Math. Revs. 22 (10B), 1797, 1961.

    Google Scholar 

30. J.B. Keller, Backscattering from a Finite Cone-Comparison of Theory and Experiment, IRE Trans. Antennas and Prop., AP-9, 411–412, July 1961.

    Google Scholar 

31. J.B. Keller and D.G. Magiros, Diffraction by a Semi-Infinite Screen with a Rounded End, Comm. Pure Appl. Math., 14, 475–471, 1961.

    MathSciNet  Google Scholar 

32. J.B. Keller, Geometrical Theory of Diffraction, J. Opt. Soc. Am., 52,116–130, Feb. 1962; Math. Revs. 24, B 1115, 1962.

    Google Scholar 

33. J.B. Keller A Survey of Short Wavelength Diffraction Theory, 1963 Geometrical Methods and Asymptotic Expansions in Wave Propagation, Symposium on Electromagnetic Theory and Antennas, Copenhagen, June 1962, Pergamon Press, New York, 1963, 3–9.

    Google Scholar 

34. J.B. Keller and I. Kay, Asymptotic evaluation of the field at a caustic, J. Appl. Phys., 25, 876–883, 1954.

    Article MathSciNet MATH  Google Scholar 

35. J.B. Keller and B.R. Levy, Scattering of Short Waves, Interdisciplinary Conference on Electromagnetic Scattering, August 1962, Milton Kerker, ed. Clarkson College of Technology, MacMillan, New York, 1963, 3–24.

    Google Scholar 

36. J.B. Keller, Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems, Annals of Phys., 4, 180–188, June 1958; Math. Revs. 20, 934, 1959.

    Google Scholar 

37. J.B. Keller and F.C. Karal, Jr., Effective Dielectric Constant, Permeability, and Conductivity of a Random Medium and the Velocity and Attenuation Coefficient of Coherent Waves, J. Math. Phys., 7, 661–670, 1966.

    Article MathSciNet  Google Scholar 

38. J.B. Keller, Effective Conductivity, Dielectric Constant and Permeability of a Dilute Suspension, Philips Res. Repts., 30, 83–90, 1975.

    Google Scholar 

39. J.B. Keller, Effective Behavior of Heterogeneous Media, Statistical Mechanics and Statistical Methods in Theory and Application, U. Landman, ed., Plenum, New York, 1977, 631–644.

    Book  Google Scholar 

40. J.B. Keller, Effective conductivities of reciprocal media, Random Media, ed. G. Papanicolaou, Springer-Verlag, New York, 1987, pp. 183–188, 1987.

    Google Scholar 

41. J.B. Keller and J. Nevard, Homogenization of rough boundaries and interfaces, SIAM J. Appl. Math., 57, 1660–1686, 1997.

    MathSciNet MATH  Google Scholar 

42. J.B. Keller, Wave Propagation in Random Media, Proc. Symp. in Appl. Math., 13, Hydrodynamic Instability, Am. Math. Soc., 227–246, 1962.

    Google Scholar 

43. J.B. Keller and F.C. Karal, Jr., Elastic, Electromagnetic, and Other Waves in a Random Medium, J. Math. Phys., 5, 537–547, 1964.

    Article MathSciNet MATH  Google Scholar 

44. J.B. Keller, Stochastic Equations and Wave Propagation in Random Media, Proc. Symp. Appl. Math., 16,145–170, Am. Math. Soc., McGraw-Hill, New York, 1964.

    Google Scholar 

45. J.B. Keller, The Velocity and Attenuation of Waves in a Random Medium, Electromagnetic Scattering, R.L. Rowell and R.S. Stein, eds., Proceedings of ICES II, Gordon and Breach Science Publishers, New York, 1967, 823–834.

    Google Scholar 

46. J.B. Keller, A Survey of the Theory of Wave Propagation in Continuous Random Media,Symposium on Turbulence of Fluids and Plasmas, Polytechnic Institute of Brooklyn, N.Y., 1968, 131–142.

    Google Scholar 

47. J.B. Keller, P. Chose, I. Kupiec, L.B. Felsen, and S. Rosenbaum, Reflection and Transmission by a Random Medium, Radio Science, 4, 1067–1077, 1969.

    Article  Google Scholar 

48. J.B. Keller, J.A. Morrison, and G.C. Papanicolaou, Mean Power Transmission Through a Slab of Random Medium, Comm. Pure Appl. Math., 24, 473–489, 1971.

    MathSciNet MATH  Google Scholar 

49. J.B. Keller and G.C. Papanicolaou, Stochastic Differential Equations with Applications to Random Harmonic Oscillators and Wave Propagation in Random Media, SIAM J. Appl. Math., 21, 287–305, 1971.

    MathSciNet  Google Scholar 

50. J.B. Keller and P.-L. Chow, Wave Propagation in a Random Lattice I, J. Math. Phys., 13, 1404–1411, 1972.

    Article MATH  Google Scholar 

51. J.B. Keller and J.G. Watson, Reflection, Scattering, and Absorption of Acoustic Waves by Rough Surfaces,. Acoust. Soc. Amer., 74, 1887–1894, 1983.

    Article MATH  Google Scholar 

52. J.B. Keller and J.G. Watson, Rough Surface Scattering via the Smoothing Method, J. Acoust. Soc. Am., 75, 1705–1708, 1984.

    Article MATH  Google Scholar 

53. J.B. Keller and W. Boyse, Short acoustic, electromagnetic and elastic waves in random media, J. Opt. Soc. Amer. A, 12, 380–389, 1995.

    Article MathSciNet  Google Scholar 

54. J.B. Keller, G. Papanicolaou, and L. Ryzhik, Transport equations for elastic and other waves in random media, Wave Motion, 24, 327–370, 1996.

    Article MathSciNet MATH  Google Scholar 

55. J.B. Keller, Inverse Problems, American Math. Monthly, 83, 107–118, 1976.

    Article  Google Scholar 

56. J.B. Keller, The Inverse Scattering Problem in G.O. and the Design of Reflectors, IRE Trans. on Antennas and Prop., AP-7, 146–149, April 1959.

    Google Scholar 

57. J.B. Keller, The Inverse Problem of Electromagnetic Scattering by a Metallic Object, Proc.First GISAT Symp., Mitre Corp., Bedford, MA., 1965, 13–21.

    Google Scholar 

58. R.M. Lewis, “Asymptotic theory of wave-propagation”, Arch. Rational Mech. Anal. 20 (1965) 191–250.

    Article MathSciNet MATH  Google Scholar 

59. P. Lax and R. Phillips, Scattering Theory, Academic Press, New York, 1967.

    MATH  Google Scholar 

60. R.K. Luneberg, Mathematical Theory of Optics. Brown University, Advanced Instruction and Research in Mechanics, Providence, R. I., 1944.

    Google Scholar 

61. B. Luong and F. Santosa, “Quantitative imaging of corrosion in plates by eddy current methods”, SIAM Journal on Applied Mathematics, 58 (1998), pages 1509–1531.

    Article MathSciNet MATH  Google Scholar 

62. A. Melin and J. Sjöstrand, “Fourier integral operators with complex-valued phase functions”, in Fourier integral operators and partial differential equations, pp. 120–223, Lecture Notes in Math. vol. 459 ( Springer, Berlin, 1975 )

    Google Scholar 

63. A. Melin and J. Sj¨ostrand. Sj¨ostrand, “Fourier integral operators with complex phase functions and parametrix for an interior boundary value problem”, Comm. Partial Differential Equations 1 (1976) 313–400.

    Article MathSciNet MATH  Google Scholar 

64. C.J. Nolan and M. Cheney, Synthetic aperture inversionInverse Problems18 (2002) 221–36.

    Article MathSciNet MATH  Google Scholar 

65. S.M. Nair and J.H. Rose, “Reconstruction of three-dimensional conductivity variations from eddy current (electromagnetic induction) data”, Inverse Problems 6 (1990) 1007–1030.

    Article MATH  Google Scholar 

66. K.E. Oughstun and G.C. Sherman, Electromagnetic Pulse Propagation in Causal Deielectrics, Springer, Berlin, 1994.

    Book  Google Scholar 

67. R. Pike and P. Sabbatier, eds. Scattering and inverse scattering in pure and applied science. Academic Press, Inc., San Diego, CA, 2002.

    Google Scholar 

68. M. Reed and B. Simon, Functional Analysis, Methods of Modern Mathematical Physics, volume 1, Academic Press.

    Google Scholar 

69. M. Reed and B. Simon, Scattering Theory, Methods of Modern Mathematical Physics, volume 3, Academic Press.

    Google Scholar 

70. E. Somersalo and M. Cheney, “Estimates for wave propagation in inhomogenous acoustic media”, J. Math. Anal. and Appls. 162 (1991) 410– 429.

    Google Scholar 

71. K. Sobczyk, Stochastic Wave Propagation, Polish Scientific Publishers, Warsaw, 1985 (distributed by Elsevier).

    Google Scholar 

72. M. Taylor, Pseudodifferential Operators, Princeton University Press, Princeton, NJ (1981).

    MATH  Google Scholar 

73. L. Tsang, J.A. Kong, and R.T. Shin, Theory of Microwave Remote Sensing, Wiley, New York, 1985.

    Google Scholar 

74. D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, and S. Schultz, “Composite media with simultaneously negative permeability and permittivity”, Phys. Rev. Lett. 84 (2000) 4184–4187.

    Article  Google Scholar 

75. P. Stefanov and G. Uhlmann, “Inverse backscattering for the acoustic equation”, SIAM J. Math. Anal. 28 (1997) 1191–1204.

    MathSciNet MATH  Google Scholar 

76. V.G. Veselago, Sov. Phys. USPEKHI 10 (1968) 509.

    Article  Google Scholar 

77. J. Van Bladel, Electromagnetic Fields, Hemisphere Publishing Corporation (Taylor & Francis group), 1985.

    Google Scholar 

78. R. Weder, Spectral and Scattering Theory for Wave Propagation in Perturbed Stratified Media, Springer, New York, 1991.

    Book MATH  Google Scholar 

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