Bibliographic record
Abstract
This paper presents a thorough study of the time-domain theory of metal cavity resonators.The completeness of the vector modal functions of a perfectly conducting metal cavity is first proved by symmetric operator theory, and analytic solution for the field distribution inside the cavity excited by an arbitrary source is then obtained in terms of the vector modal functions.The main focus of the present paper is the time-domain theory of a waveguide cavity, for which the excitation problem may be reduced to the solution of a number of modified Klein-Gordon equations.These modified Klein-Gordon equation are then solved by the method of retarded Green's function in order that the causality condition is satisfied.Numerical examples are also presented to demonstrate the time-domain theory.The analysis indicates that the time-domain theory is capable of providing an exact picture for the physical process inside a closed cavity and can overcome some serious problems that may arise in traditional time-harmonic theory due to the lack of causality.2 Consequently {∇ × e n } and {∇ • e n } are Cauchy sequences in H.As a result, there exist h ∈ H, and ρ ∈ L 2 (V ) such that ∇ × e n → h and ∇ • e n → ρ as n → ∞.From integration by parts, one may write
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 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) | 0.004 | 0.001 |
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".