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Record W1515301603 · doi:10.1017/cbo9780511805790.011

Orthogonal Curvilinear Coordinate Systems

2009· other· en· W1515301603 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
FieldEngineering
TopicAerospace Engineering and Control Systems
Canadian institutionsUniversity of Victoria
Fundersnot available
KeywordsCurvilinear coordinatesOrthogonal coordinatesCoordinate systemComputer scienceMathematicsGeometry

Abstract

fetched live from OpenAlex

Rectangular Cartesian coordinate systems are well suited for presenting the basic concepts of continuum mechanics since many mathematical complications that arise with other coordinate systems, for example, convected systems, are avoided. However, for the solution of specific problems, the use of rectangular Cartesian coordinate systems may result in considerable difficulties, and the use of other systems may be desirable in order to take advantage of symmetry aspects of the problem. For example, in the analysis of the expansion of a thick-walled cylindrical tube, the use of cylindrical polar coordinates has an obvious advantage. We introduce a simple theory of curvilinear coordinates in this appendix and specialize it for orthogonal curvilinear systems, in particular cylindrical and spherical. We avoid the use of the general theory of tensor components referred to curvilinear coordinates by considering what are known as the physical components of tensors that are derived for orthogonal coordinate systems. Superscripts are used to denote curvilinear coordinates.

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 categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: Not applicable
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.030
Threshold uncertainty score1.000

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)0.0000.001

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.

Opus teacher head0.003
GPT teacher head0.162
Teacher spread0.159 · 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