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Record W2006635326 · doi:10.1002/mma.358

A hierarchy of Sturm–Liouville problems

2003· article· en· W2006635326 on OpenAlex
Paul Binding

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

VenueMathematical Methods in the Applied Sciences · 2003
Typearticle
Languageen
FieldMathematics
TopicSpectral Theory in Mathematical Physics
Canadian institutionsUniversity of Calgary
Fundersnot available
KeywordsSturm–Liouville theoryMathematicsEigenvalues and eigenvectorsCompleteness (order theory)Boundary value problemVariety (cybernetics)Oscillation (cell signaling)Mathematical analysisHierarchyOscillation theoryBoundary (topology)Pure mathematicsApplied mathematicsDifferential equation

Abstract

fetched live from OpenAlex

Abstract Sturm–Liouville equations will be considered where the boundary conditions depend rationally on the eigenvalue parameter. Such problems apply to a variety of engineering situations, for example to the stability of rotating axles. Classesof these problems will be isolated with a rather rich spectral structure, for example oscillation, comparison and completeness properties analogous to thoseof the ‘usual’ Sturm–Liouville problem which has constant boundary conditions.In fact it will be shown how these classes can be converted into each other, andinto the ‘usual’ Sturm–Liouville problem, by means of transformations preserving all but finitely many eigenvalues. Copyright © 2003 John Wiley & Sons, Ltd.

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)0.018
metaresearch head score (Gemma)0.005
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.556
Threshold uncertainty score0.675

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0180.005
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.002
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0010.000
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 head0.168
GPT teacher head0.460
Teacher spread0.292 · 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