| 1. | These frequencies are the eigenvalues of the Laplacian in the space.
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| 2. | The Laplacian is given above in terms of spherical polar coordinates.
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| 3. | Beginning in 1718, Thomas Twinin used the Laplacian differential operator.
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| 4. | As remarked above, the Laplacian is diagonalized by the Fourier transform.
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| 5. | Laplacian eigenmaps builds a graph from neighborhood information of the data set.
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| 6. | For the quadratic Casimir invariant, this is the Laplacian.
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| 7. | Multi-dimensional version replaces the second spatial derivative by the Laplacian.
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| 8. | Note that the standard Laplacian is just \ Delta ( 1 ).
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| 9. | All eigenvalues of the normalized Laplacian are real and non-negative.
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| 10. | Where \ scriptstyle \ nabla ^ 2 is the Laplacian.
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