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Summary  

New results for the eigenvalue ratios of vibrating strings are presented partially in connection with previous results concerning Schrdinger operators.

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Abstract  

For vibrating strings with symmetric single-well densities, it is known that the ratio λ211 is maximized when the density is constant. In this note, we extend this result to a class of symmetric densities.

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Abstract  

We establish several comparison results on the eigenvalue gap for vibrating strings with symmetric single-well densities or symmetric double-well densities.

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