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Record W16013812 · doi:10.4153/cmb-2001-021-5

Growth Estimates on Positive Solutions of the Equation

2001· article· en· W16013812 on OpenAlexvenueno aff
Man Chun Leung

Bibliographic record

VenueCanadian Mathematical Bulletin · 2001
Typearticle
Languageen
FieldMathematics
TopicNonlinear Partial Differential Equations
Canadian institutionsnot available
Fundersnot available
KeywordsMathematicsBounded functionConformal mapMetric (unit)Norm (philosophy)Pure mathematicsEuclidean geometryMathematical analysisGeometry

Abstract

fetched live from OpenAlex

Abstract We construct unbounded positive C2-solutions of the equation in (equipped with Euclidean metric go) such that K is bounded between two positive numbers in , the conformal metric is complete, and the volume growth of g can be arbitrarily fast or reasonably slow according to the constructions. By imposing natural conditions on u, we obtain growth estimate on the -norm of the solution and show that it has slow decay.

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.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.011
Version: metacan-v3-hybrid-931329e0061cValidation 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: Empirical · Consensus signal: Empirical
Teacher disagreement score0.003
Threshold uncertainty score0.012

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.011
Meta-epidemiology (narrow)0.0020.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0020.000
Science and technology studies0.0010.002
Scholarly communication0.0020.003
Open science0.0010.003
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0030.000

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 head0.070
GPT teacher head0.288
Teacher spread0.218 · 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

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations3
Published2001
Admission routes1
Has abstractyes

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Same venueCanadian Mathematical BulletinSame topicNonlinear Partial Differential EquationsFrench-language works237,207