References
- Balian , R. and Bloch , C. 1970 . Distribution of eigenfrequencies for the wave equation in a finite domain. I. Three-dimensional problem with smooth boundary surface . Annals Phys , 60 : 401 – 447 .
- Baltes , H.P. and Hilf , E.R. 1976 . Spectra of finite system, B.I , Mannheim : Wissenschafts Verlag .
- Gottlieb , H. P. W. 1985 . Eigenvalues of the Laplacian with Neumann boundary conditions . J. Aust. Math. Soc. Ser , 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 .
- Greiner , P. 1971 . An asymptotic expansion for the heat equation . Arch. Rat. Mech. Anal , 41 : 163 – 218 .
- Kac , M. 1966 . Can one hear the shape of a drum? . Amer. Math. Monthly , 73 : 1 – 23 .
- Mckean , H. P. and Singer , I. M. 1967 . Curvature and the eigenvalues of the Laplacian . J. Diff. Geom , 1 : 43 – 69 .
- Pleijel , A. 1954 . A study of certain Green's functions with applications in the theory of vibrating membranes . Ark. Mat , 2 : 553 – 569 .
- Sleeman , B. D. and Zayed , E.M.E. 1983 . An inverse eigenvalue problem for a general convex domain . J. Math. Anal. Appl , 94 : 78 – 95 .
- Smith , L. 1981 . The asymptotics of the heat equation for a boundary value problem . Invent. Math , 63 : 467 – 493 .
- Stewartson , K. and Waechter , R. T. 1971 . On hearing the shape of a drum: further results . Proc. Comb. Philos. Soc , 69 : 353 – 363 .
- Zayed , E.M.E. and Younis , A.I. 1990 . An inverse problem for a general convex domain with impedance boundary conditions . Quart. Appl. Math , 48 : 181 – 188 .
- Zayed , E.M.E. 1989 . Hearing the shape of a general convex domain . J. Math. Anal. Appl , 142 : 170 – 187 .
- Zayed , E.M.E. 1989 . Heat equation for an arbitrary doubly connected region in R 2 with mixed boundary conditions . Z. Angew. Math. Phys , 40 : 339 – 355 .
- Zayed , E.M.E. 1990 . On hearing the shape of an arbitrary doubly connected region in R 2 . J. Aust. Math. Soc. Ser , 31 : 472 – 483 .
- Zayed , E.M.E. 1990 . Heat equation for an arbitrary multiply connected region in R 2 with impedance boundary conditions . IMA J. Appl. Math , 45 : 233 – 241 .
- Zayed , E.M.E. 1995 . An inverse problem for a general multiply connected bounded domain . Appl, Anal , 59 : 121 – 145 .
- Zayed , E.M.E. 1996 . An inverse problem for a general doubly connected bounded domain with impedance boundary conditions . Portugal. Math. , 53 : 53 – 72 .
- Zayed , E.M.E. 1998 . Short-time asymptotics 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 . Short-time asymptoties of the heat kernel of the Laplacian of a general doubly connected domain in R 2 with Robin boundary conditions . Soochow J. Math , 25 : 71 – 89 .