Bounds for the rth Characteristic Frequency of a Beaded String or of an Electrical Filter
The fundamental mode of vibration of a beaded string has a shape without change of sign. The rth higher normal mode of vibration has r changes of sign. Given any virtual shape of the string with r changes of sign, an algorithm is found that gives upper and lower bounds for the rth characteristic fre...
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| Veröffentlicht in: | Proceedings of the National Academy of Sciences - PNAS 1980-06, Vol.77 (6), p.3120-3124 |
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| container_issue | 6 |
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| container_title | Proceedings of the National Academy of Sciences - PNAS |
| container_volume | 77 |
| creator | Barnsley, Michael F. Duffin, Richard J. |
| description | The fundamental mode of vibration of a beaded string has a shape without change of sign. The rth higher normal mode of vibration has r changes of sign. Given any virtual shape of the string with r changes of sign, an algorithm is found that gives upper and lower bounds for the rth characteristic frequency as a function of the virtual shape. By making a certain transformation it is found that this algorithm holds for the characteristic frequencies of an inductor-capacitor network. Other transformations show that it applies to the rth eigenvalue of a Hermitian matrix. |
| doi_str_mv | 10.1073/pnas.77.6.3120 |
| format | Article |
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| identifier | ISSN: 0027-8424 |
| ispartof | Proceedings of the National Academy of Sciences - PNAS, 1980-06, Vol.77 (6), p.3120-3124 |
| issn | 0027-8424 1091-6490 |
| language | eng |
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| source | JSTOR Archive Collection A-Z Listing; PubMed Central; Alma/SFX Local Collection; Free Full-Text Journals in Chemistry |
| subjects | Boundary conditions Eigenfunctions Eigenvalues Eigenvectors Inductors Mathematical functions Mathematical theorems Mathematical vectors Matrices Physical Sciences: Mathematics |
| title | Bounds for the rth Characteristic Frequency of a Beaded String or of an Electrical Filter |
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