Bibliographic record
Abstract
The Stokes Phenomenon The Stokes phenomenon plays a central role in the asymptotic description of the special functions of analysis and in the important class of asymptotic phenomena in mathematical physics known as ‘discontinuities’. Such discontinuities, along with those of a different origin arising in boundary layer theory and shocks in gas dynamics, are not true discontinuities in the mathematical sense but are found to depend on the scale on which the phenomenon in question is considered. When viewed under an appropriate magnification these discontinuities appear as a smooth albeit rapid transition from one form of description to another. An interesting discussion of such asymptotic phenomena is given in Friedrichs (1955). A typical example related to the Stokes phenomenon is the boundary of the shadow which appears when a light wave passes an object. As a first approximation the shadow boundary is a sharp discontinuity, but on a smaller scale there is a transition from light to darkness which takes place in a narrow region along the shadow boundary. This corresponds to the asymptotic expansion of the solution of the wave equation taking on different forms across this boundary. Another example is the change in asymptotic form of a wave function at a caustic surface where the eikonal in the WKBJ description of the wave equation develops a singularity. Indeed, the first account of this phenomenon by Stokes in 1857 arose in this last connection in the theory of the rainbow and the formation of supernumerary arcs.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".