Bibliographic record
Abstract
Spectral properties of an invariant functional, denoted by H, for the linear stability equation associated with the modon, or solitary drift vortex, solutions of the quasi‐geostrophic equivalent barotropic potential vorticity, or Charney–Hasegawa–Mima (CHM), equation are investigated. It is shown that H, which is the only known quadratic invariant in modon stability theory, is identical in form to the second variation of a “Benjamin‐like” variational principle for solitary vortices. However, such a principle does not exist for the modon. The discrete spectrum of the “form operator” in H contains two simple negative eigenvalues and the simple zero eigenvalue. For the leftward‐traveling solution there are only a finite number of positive eigenvalues. For the rightward‐traveling solution, there are a countable infinity of positive eigenvalues. A sharp lower bound on the spectrum, for both the rightward‐ and leftward‐traveling solutions, and a sharp upper bound for the leftward traveling solution, is determined. For the leftward‐traveling solutions, the eigenfunctions span a finite‐dimensional vector space and are orthogonal with respect to an inner product which is valid for all of L2. For the rightward‐traveling solutions, the eigenfunctions span an infinite‐dimensional Hilbert space, but are orthogonal with respect to an inner product, which is not valid for all of L2.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".