The Convergence of the Tangential Scattered Magnetic Field Based on the Vertical Improper Integral
Bibliographic record
Abstract
The tangential scattered magnetic field of a perfectly electric conducting surface is usually expressed as an improper integral. However, the improper integral is divergent. Hence, the field is expressed as a limit of an integral in some references. In this article, the limit of the integral is called a vertical improper integral. A stronger smooth condition of the surface is added to ensure the convergence of the vertical improper integral. The relationship between the vertical improper integral and the Cauchy principle value integral is established. An example shows that the tangential scattered magnetic field is infinite at a first-order smooth point if it is assumed that the surface current density is non-zero at the point. By the boundary condition, it is obtained that the surface current density should be zero at the point. A numerical example is given to demonstrate the effectiveness of the vertical improper integral method. The numerical result also shows that singular integrals need not be calculated when the magnetic field integral equation is computed based on the method of moments.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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 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".