Canonical Problems of Vertical and Horizontal Dipoles Radiation in Layered Media
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Bibliographic record
Abstract
This chapter demonstrates solution of canonical dipole radiation problems in layered media foundational to the definition of both the potential and field dyadic Green's functions. Spectral solutions of the vertical dipole and horizontal dipoles are presented in the analytic form in case of simple layered media. These solutions are also used to demonstrate the definitions of the boundary value problems both in spectral and spatial domains in case of general layered media. The chapter also introduces the reader to the multivaluedness of Green's function spectral as the functions of the lateral wavenumber k p and transversal wavenumbers k z and their definitions in the form of Riemann surfaces. It then considers the problem of four-layer medium backed with a PEC half-space (ground plane) excited by the horizontal electric dipole situated in the upper half-space.
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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 | 0.001 |
| 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) | 0.001 | 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 it