Some Generalized Trigonometric Sine Functions and Their Applications
Bibliographic record
Abstract
In this paper, it is shown that D. Shelupsky's generalized sine func- \ntion, and various general sine functions developed by P. Drabek, R. \nManasevich and M. Otani, P. Lindqvist, including the generalized Ja- \ncobi elliptic sine function of S. Takeuchi can be defned by systems of \nfirst order nonlinear ordinary differential equations with initial condi- \ntions. The structure of the system of differential equations is shown to \nbe related to the Hamilton System in Lagrangian Mechanics. Numer- \nical solutions of the ODE systems are solved to demonstrate the sine \nfunctions graphically. It is also demonstrated that the some of the gen- \neralized sine functions can be used to obtain analytic solutions to the \nequation of a nonlinear spring-mass system.
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How this classification was reachedexpand
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 | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".