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Record W4393971061 · doi:10.1002/9781119763222.ch2

Green's Functions in Free Space

2024· other· en· W4393971061 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

Venuenot available
Typeother
Languageen
FieldMathematics
TopicAdvanced Mathematical Theories
Canadian institutionsUniversity of Manitoba
Fundersnot available
KeywordsSpace (punctuation)MathematicsPhysicsComputer scienceOperating system

Abstract

fetched live from OpenAlex

This chapter examines the homogeneous space scalar Green's function in one, two, and three dimensions. It explains the integral expansions of the homogeneous Green's functions over plane and cylindrical waves. The chapter derives Sommerfeld identify for 3D scalar Green's function. It then represents field from arbitrary source as convolution of source distribution with Green's function. Vector structure of the Hertzian dipole field is explained to provide physical interpretation of the dyadic representation of the electric and magnetic field Green's functions. Interpretation of the electromagnetic field produced by arbitrary current sources as superposition of fields from elementary Hertzian dipoles (dyadic Green's functions) is introduced. Such interpretation explains representation of the fields as the convolution of the source distributions with Green's functions foundational to the integral equations of electromagnetics.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.056
Threshold uncertainty score0.995

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0150.005

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.

Opus teacher head0.036
GPT teacher head0.326
Teacher spread0.290 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Quick stats

Citations0
Published2024
Admission routes1
Has abstractyes

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