Subclasses of analytic functions with respect to symmetric and conjugate points connected with the q-Borel distribution
Bibliographic record
Abstract
In this article, by making use of a q-analogue of the familiar Borel distribution, we introduce two new subclasses: S?,?,q symmetric(b, A, B) and S?,?,q conjugate(b,A, B) of starlike and convex functions in the open unit disk ? with respect to symmetric and conjugate points. We obtain some properties including the Taylor-Maclaurin coefficient estimates for functions in each of these subclasses and deduce various corollaries and consequences of the main results. We also indicate relevant connections of each of these subclasses S?,?,q symmetric(b,A, B) and S?,?,q conjugate(b,A, B) with the function classes which were investigated in several earlier works. Finally, in the concluding section, we choose to comment on the recent usages, especially in Geometric Function Theory of Complex Analysis, of the basic (or q-) calculus and also of its trivial and inconsequential (p, q)-variation involving an obviously redundant (or superfluous) parameter p.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.003 |
| 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 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".