COMPUTATION OF SIMPLEST NORMAL FORMS OF DIFFERENTIAL EQUATIONS ASSOCIATED WITH A DOUBLE-ZERO EIGENVALUE
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Bibliographic record
Abstract
In this paper a method is presented for computing the simplest normal form of differential equations associated with the singularity of a double zero eigenvalue. Based on a conventional normal form of the system, explicit formulae for both generic and nongeneric cases are derived, which can be used to compute the coefficients of the simplest normal form and the associated nonlinear transformation. The recursive algebraic formulae have been implemented on computer systems using Maple. The user-friendly programs can be executed without any interaction. Examples are given to demonstrate the computational efficiency of the method and computer programs.
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Full frame distilled prediction
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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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