On the Modified Standard Nield-Kuznetsov Functions
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Bibliographic record
Abstract
This work represents part of the detailed calculations of the Plenary Talk presented by the corresponding author at the International Conference on Engineering, Economy, Computer Applications for Natural Sciences and Medicine (EEACS 2025) in Lisbon, Portugal. Modified forms of the standard Nield-Kuznetsov functions of the first- and second-kind are introduced in this work in which power series solutions to the inhomogeneous Airy’s equation are investigated. The forms of solutions for the cases of constant and variable forcing functions are expressed in terms of the modified standard Nield-Kuznetsov functions, and graphs illustrating the two linearly independent power series solutions are obtained using a four-term truncated series. These results illustrate the behaviour of the solutions and of the modified Nield-Kuznetsov functions.
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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 | 0.001 | 0.001 |
| 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) | 0.001 | 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 it