A Prüfer Angle Approach to the Periodic Sturm-Liouville Problem
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Bibliographic record
Abstract
AbstractIt is shown how to reduce the periodic or antiperiodic Sturm-Liouville problems to an analysis of the Prüfer angle. This provides a simple and flexible alternative to the usual approaches via operator theory or the Hill discriminant. Additional informationNotes on contributorsPaul BindingPAUL BINDING spent much of his early life in England, and obtained his degrees from Cambridge University. Since joining the University of Calgary, he has taken sabbaticals at Memphis, Strathclyde, Warwick and Wuerzburg. He feels very fortunate to be able to indulge in his favourite hobby of collaborative research with friends from many different countries. Over the years he has also played, refereed (and trained referees) at various sports from the Community to the National level, and has coached participants for many types of competitions, including the Mathematical Olympiad.Hans VolkmerHANS VOLKMER received a Ph. D. from the University of Konstanz in 1979, taught at the University of Essen from 1978 to 1990, and joined the University of Wisconsin at Milwaukee in 1990. He works in Special Functions, Differential Equations, Applied Mathematics, Mathematical Statistics and several other areas. He is co-author of the Digital Library of Mathematical Functions, and associate editor for Mathematics of Computation. When he is not doing mathematics, he enjoys walking, bicycling and reading.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.002 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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