Some m-fold symmetric bi-univalent function classes and their associated Taylor-Maclaurin coefficient bounds
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 The Ruscheweyh derivative operator is used in this paper to introduce and investigate interesting general subclasses of the function class $\Sigma_{m}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>Σ</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:math> of m -fold symmetric bi-univalent analytic functions. Estimates of the initial Taylor-Maclaurin coefficients $\vert a_{m+1} \vert $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>|</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:math> and $\vert a_{2 m+1} \vert $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>|</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:math> are obtained for functions of the subclasses introduced in this study, and the consequences of the results are discussed. Additionally, the Fekete-Szegö inequalities for these classes are investigated. The results presented could generalize and improve some recent and earlier works. In some cases, our estimates are better than the existing coefficient bounds. Furthermore, within the engineering domain, the utilization of the Ruscheweyh derivative operator can encompass a broad spectrum of engineering applications, including the robotic manipulation control, optimizing optical systems, antenna array signal processing, image compression, and control system filter design. It emphasizes the potential for innovative solutions that can significantly enhance the reliability and effectiveness of engineering applications.
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 | 0.001 | 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 | 0.000 | 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