Theory of Periodic Sequence: A Generalized Formalism of Maxwell's Equations in Discrete Transform Domain
Bibliographic record
Abstract
Time-periodic form or expression is commonly observed in both natural and man-made phenomena across a wide range of scientific and engineering disciplines. In this article, we propose the theory of periodic sequence (TPS), marking the first effort to mathematically formalize Maxwell's equations in the discrete transform domain (corresponding to time domain) and to legitimize the application of the discrete Fourier transform to the temporal aspect of Maxwell's equation. TPS is intended to serve as a comprehensive theory to depict the physical behavior of electromagnetic (EM) periodic sequential fields and waves. Within the TPS framework, periodic-sequential Maxwell's curl equations are decomposed and decoupled to independent and paralleled instances via designated mappings. The fundamental solutions of EM periodic sequential excitation are elucidated and corroborated by radio-frequency (RF)/microwave measurements. This involves potential applications in the analysis of broadband RF transmission and the design of high-speed RF devices.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".