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Record W2042379731 · doi:10.1139/p99-073

<i>Tutorial / Article didactique</i> Derivatives of curvilinear coordinate unit vectors: A concise matrix-vector approach

2000· article· en· W2042379731 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.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueCanadian Journal of Physics · 2000
Typearticle
Languageen
FieldEngineering
TopicGeophysics and Sensor Technology
Canadian institutionsnot available
Fundersnot available
KeywordsCurvilinear coordinatesCoordinate systemPhysicsUnit vectorComputationEllipsoidal coordinatesCoordinate spaceMatrix (chemical analysis)Orthogonal coordinatesUnit (ring theory)Elliptic coordinate systemMathematical analysisGeometryAlgorithmComputer scienceMathematics

Abstract

fetched live from OpenAlex

The time evolution of a curvilinear coordinate system can be identifiedwith an angular velocity matrix or vector, which contains the complete differentiationrule for all unit coordinate vectors of the curvilinear system, providinga concise method for their computations. When generalized the technique provides a powerful tool fordifferentiation, with respect to any parameter, of not only unit coordinate vectors but any vector that remains fixed in a general orthogonal curvilinear coordinate system. Several curvilinear systems, as well as the normal and tangentialcoordinate system are examined.PACS No.: 46.00

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)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Bench or experimental · Consensus signal: Bench or experimental
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.288
Threshold uncertainty score0.612

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
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)0.0000.000

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.

Opus teacher head0.009
GPT teacher head0.200
Teacher spread0.191 · 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