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Record W2137912495 · doi:10.1017/s0017089509990036

THE GENERALISED LIÉNARD EQUATIONS

2009· article· en· W2137912495 on OpenAlex
A. Aghajani, Amir Moradifam

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

VenueGlasgow Mathematical Journal · 2009
Typearticle
Languageen
FieldMathematics
TopicAdvanced Differential Equations and Dynamical Systems
Canadian institutionsUniversity of British Columbia
Fundersnot available
KeywordsMathematicsHomoclinic orbitOscillation (cell signaling)Zero (linguistics)Stability (learning theory)Liénard equationMathematical analysisPoint (geometry)Pure mathematicsGeometryDifferential equationPhysicsBifurcation

Abstract

fetched live from OpenAlex

Abstract In this paper we present sufficient conditions for all trajectories of the system to cross the vertical isocline h ( y ) = F ( x ), which is very important in the global asymptotic stability of the origin, oscillation theory and existence of periodic solutions. Also we give sufficient conditions for all trajectories which start at a point on the curve h ( y ) = F ( x ), to cross the y -axis which is closely connected with the existence of homoclinic orbits, stability of the zero solution, oscillation theory and the centre problem. The obtained results extend and improve some of the authors' previous results and some other theorems in the literature.

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)0.001
metaresearch head score (Gemma)0.002
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 score0.914
Threshold uncertainty score0.675

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0010.000
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 head0.047
GPT teacher head0.328
Teacher spread0.282 · 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