Some refined families of Jordan-type inequalities and their applications
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract In this paper, the classical Jordan's inequality is studied once again, a new sharpened and generalized version of Jordan's inequality is given by means of polynomial representation, and the result thus derived is then used to obtain several substantially more refined inequalities of Jordan type. Finally, an application of the results presented in this paper toward the improvement of the Yang Le inequality is considered. Keywords: Jordan's inequalitypower seriespolynomial representationhigher-order derivativesYang Le inequalitygeneralizations and refinement of Jordan's inequality Acknowledgements The present investigation was supported, in part, by the Natural Science Foundation of the Fujian Province of the People's Republic of China under Grant S0650003 and, in part, by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0007353.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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)
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