Two Numerical Methods (RO (MSuM) and RO (SuMSu)) for Triple Integrals with for Continuous Functions
Bibliographic record
Abstract
The main goal of this research is to calculate a triple integral included continuous integrands numerically by two composite rules. The first rule is the Mid-point method on the third dimension Z and the first dimension X with a suggested method on the second dimension Y, that is denoted by MSuM. The second rule is the suggested method on the third dimension Z and the first dimension X with a Mid-point method on the second dimension Y, that is denoted by SuMSu. The number of partial intervals is equals on the three dimensions. The study represented two theorems with the proofs to get such rules and the correction terms (the error terms) for each of rule. Moreover, to accelerate convergence and get better results, Romberg acceleration is used with both rules. These rules recalled by RO(MSuM) and RO(SuMSu) respectively such that the obtained results were high accuracy by relatively few partial intervals and shorter times.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 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".