References
- Balian , R. and Bloch , C. 1970 . Distribution of eigenfrequencies for the wave equatiuon in a finite domain. I. Three—imensional problem with smooth boundary surface . Annals. Phys , 60 : 401 – 447 .
- Baltes , H.P. and Hilf , E.R. 1976 . Spectra of finite system B.I. .
- Gordon , C. , Webb , D.L. and Wolpert , S. 1992 . One cannot hear the shape of a drum . Bull. Amer. Math. Soc , 27 : 134 – 138 .
- Gottlieb , H.P.W. 1985 . Eigenvalues of the Laplacian with Neumann boundary conditions . J. Aust. Math. Soc. Ser. B , 26 : 293 – 309 .
- Gutierrez , G. and Yanez , J.M. 1997 . Can an ideal gas feel the shape of its container? . Amer. J. Phys. , 65 : 739 – 743 .
- Hsu , P. 1992 . On the ø-function of a Riemannian manifold with boundary . Trans. Amer. Math. Soc. , 333 : 643 – 671 .
- Kac , M. 1966 . Can one hear the shape of a drum? . Amer. Math. Month , 73 : 1 – 23 .
- Mckean , H.P. and Singer , I.M. 1967 . Curvature and the eigenvalues of the Laplacian . J. Diff. Geom , 1 : 43 – 69 .
- Milnor , J. 1964 . Eigenvalues of the Laplace operator on certain manifolds . Proc. Nat. Acad. Sci , 51 : 542
- Pleijel , A. 1954 . On Green's functions and the eigenvalue distribution of the three-dimensional membrane equation . Skandinav. Mat , 12 : 222 – 240 .
- Sridhar , S. and Kudrolli , A. 1994 . Experiments on Not hearing the shape of drums . Phys. Rev. Lett , 72 : 2175 – 2178 .
- Waechter , R.T. 1972 . On hearing the shape of a drum: An extension to higher dimensions . Proc. Comb. Philos. Soc , 72 : 439 – 447 .
- Zayed , E.M.E. 1985 . An inverse eigenvalue problem for a general convex domain: An extension to higher dimensions . J. Math. Anal. Appl , 112 : 455 – 470 .
- Zayed , E.M.E. 1990 . Hearing the shape of a general doubly-connected domain in R3 with impedance boundary conditions . J. Math. Phys , 31 : 2361 – 2365 .
- Zayed , E.M.E. 1991 . Heat equation for a general convex domain in R3 with a finite number of piecewise impedance boundary conditions . Appl. Anal , 42 : 209 – 220 .
- Zayed , E.M.E. 1991 . Hearing the shape of a general convex domain: An extension to a higher dimensions . Math , 48 : 259 – 280 .
- Zayed , E.M.E. 1991 . Hearing the shape of a general doubly-connected domain in R3 with mixed boundary conditions . J. Appl. Math. Phys , 42 : 547 – 564 . ZAMP
- Zayed , E.M.E. 1992 . An inverse eigenvalue problem for an arbitrary multiply-connected bounded domain in R3 with impedance boundary conditions . SIAM J. Appl. math , 52 : 725 – 729 .
- Zayed , E.M.E. 1997 . An inverse problem for a general doubly-connected bounded domain: An extension to higher dimensions . Tamkang. J. Math , 28 : 277 – 295 .
- Zayed , E.M.E. 1997 . An inverse problem for a general doubly-connected bounded domain in R3 with a finite number of piecewise impedance boundary conditions . Appl. Anal , 64 : 69 – 98 .
- Zayed , E.M.E. 1998 . Short-time asymptotice of the heat kernel of the Laplacian of a bounded domain with Robin boundary conditions . Houston. J. Math , 24 : 377 – 385 .
- Zayed , E.M.E. 1999 . An inverse problem for a general multiply-connected bounded domain: An extension to higher dimensions . Appl. Anal , 72 : 27 – 41 .
- Zayed , E.M.E. 2000 . On hearing the shape of a bounded domain with Robin boundary conditions . IMAJ. Appl. Math , 64 : 95 – 108 .
- Zayed , E.M.E. 2000 . An inverse problem for a general bounded domain in R3 with piecewise smooth mixed boundary conditions . International J. Theoretical Phys , 39 : 189 – 205 .
- Zayed , E.M.E. 2000 . The asymptotics of the heat semigroup for a general bounded domain with mixed boundary conditions . Acta. Math. Sinica , 16 : 627 – 636 .
- Zayed , E.M.E. 2001 . Short-time asymptotics of the hear kernel of the Laplacian for a multiply-connected domain in R2 with Robin boundary conditions . Appal. Anal , 77 : 177 – 194 .
- Zayed , E.M.E. 2001 . An inverse problem of the heat equation for a general multiconnected drum with applications in physics . Chaos, Solitons & Fractals , 12 : 1861 – 1871 .
- Zayed E.M.E. An inverse problem for a general annular bounded domain in R2 with mixed boundary conditins and its applications in physics. Applied Math. Computation (to appear)
- Zayed E.M.E. An inverse problem for a general vibrating annular membrane in R3 with physical applications: Further results. Applied Math. Computation (to appear)