Extraction of Singular Integrals from MoM Reaction Integrals and Their Analytic Evaluation
Bibliographic record
Abstract
This chapter presents details how the singular integrals can be extracted from the method of moments (MoM) reaction integrals and integrated analytically for both shape-to-shape function interactions via diagonal components of the vector potential kernels and pulse-to-pulse function interactions via the scalar potential kernel. It helps the reader to use Duffy transformation or equivalent singularity suppression technique for evaluation of singular integrals arising in interactions of shape functions through the off-diagonal components of the vector potential kernels. Efficiency and accuracy in evaluation of the integrals arising from the Rao-Wilton-Glisson MoM discretization of the Mixed-Potential-Integral-Equation is greatly assisted by extraction of the singular integrals from them with the latter being subsequently evaluated either analytically or numerically through a singularity suppression method such as the Duffy transformation.
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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 | 0.000 |
| 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) | 0.008 | 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".