Application of the Homotopy Analysis Method in Solving Fuzzy Nonlinear Integral Equations for Birthrate
Bibliographic record
Abstract
In this work, we presented the fuzzy generalized integral equation for population includes future surge in birthrates which is great interesting for future planning throughout the world.So, we formulated the fuzzy problem of birthrates to be investigated any surge in fuzzy birthrates.The fuzzy integral equation (FIE) included the fuzzy birthrates at time t and the fuzzy function of a girl living to age r2 and unclear role of a girl giving birth to a female kid at this age in an interval time dr2.This fuzzy integral contributed for fuzzy birthrate from woman in the suitable subinterval of the range of childbearing age r2.The homotopy analysis method (HAM) for explained the numerical fuzzy solution of periodicity in the surge of birthrate of generalized fuzzy dynamical birthrate of girl born at any as well as all the tables and figures are given in details also the behaviors of the birthrate which described the solution of fuzzy integral.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 source (direct Gemma or distilled Codex), 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".