Book ChapterDOI
An inverse eigenvalue problem for the Laplace operator
E M E Zayed
- pp 718-726
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The article was published on 1982-01-01. It has received 6 citations till now. The article focuses on the topics: Inverse Laplace transform & Inverse iteration.read more
Citations
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Journal ArticleDOI
Can an ideal gas feel the shape of its container
Gonzalo Gutiérrez,Julio M. Yáñez +1 more
TL;DR: In this article, the authors used an asymptotic expansion for high temperatures to obtain the partition function of an ideal gas, both in two and three dimensions, showing the leading corrections to the internal energy due to a finite container.
Journal ArticleDOI
Eigenvalues of the laplacian for rectilinear regions
TL;DR: In this paper, the geometry and boundary conditions of isosceles right-angle triangles with Dirichlet or Neumann boundary conditions are derived from knowledge of the eigenvalue spectrum of the Laplacian on a domain.
Journal ArticleDOI
Eigenvalues of the Laplacian: an Extension to Higher Dimensions
TL;DR: In this article, the inverse eigenvalue problem of determining the shape of smooth and convex regions and the unknown attendent boundary conditions from a knowledge of the spectrum of the eigenvalues of the Laplacian was rigorously studied in Gottingen by D. Hilbert, R. Courant and H. Weyl.
Journal ArticleDOI
The wave equation approach to the two-dimensional inverse problem for a general bounded domain with piecewise smooth mixed boundary conditions
E. M. E. Zayed,I.H. Abdel-Halim +1 more
TL;DR: In this paper, the spectral distribution of a bounded domain ω in R2 with a smooth boundary ∂ω is studied for a variety of domains, where the dependence of connectivity of a domain and the boundary conditions are analyzed.
Journal ArticleDOI
An inverse problem of the wave equation for a general doubly connected region in R2 with a finite number of piecewise smooth Robin boundary conditions
E. M. E. Zayed,I. H. Abdel-Halim +1 more
TL;DR: The spectral distribution of the eigenvalues of the negative Laplacian-@D=-@?"k"="1^2@?@?x^k^2in the (x^1,x^2)-plane, is studied for a variety of domains.
References
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Journal ArticleDOI
Can One Hear the Shape of a Drum
TL;DR: Can one hear the shape of a drum? as discussed by the authors, 1966; The American Mathematical Monthly: Vol. 73, No. 4P2, pp. 1-23.
Journal ArticleDOI
Curvature and the Eigenvalues of the Laplacian
TL;DR: In this paper, the authors defined the spectrum of the problem of bounded regions of R d with a piecewise smooth boundary B and showed that if 0 > γ1 ≥ γ2 ≥ ≥ ≥ β3 ≥ etc.
Journal ArticleDOI
A study of certain Green's functions with applications in the theory of vibrating membranes
Journal ArticleDOI
An inverse eigenvalue problem for a general convex domain
TL;DR: In this paper, the shape of a membrane is deduced from the complete knowledge of the eigenvalues of the Lapace operator A = cf=,(a/ax) in the x 1x2-plane.
Journal ArticleDOI
Frequency Distribution of Normal Modes
TL;DR: In this paper, the frequency distribution of the normal modes for a rectangular enclosure has been verified by a more direct computation and extended to apply to a cylinder, a sphere, and to a number of derived shapes.
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