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Record W2521767117 · doi:10.1515/acv-2016-0023

Relative ∞-capacity and its affinization

2016· article· en· W2521767117 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.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueAdvances in Calculus of Variations · 2016
Typearticle
Languageen
FieldMathematics
TopicPoint processes and geometric inequalities
Canadian institutionsMemorial University of Newfoundland
FundersNatural Sciences and Engineering Research Council of CanadaNational Natural Science Foundation of China
KeywordsMathematicsCombinatorics

Abstract

fetched live from OpenAlex

Abstract In this paper, the so-called relative <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>∞</m:mi> </m:math> {\infty} -capacity is introduced and investigated in a close connection to the viscosity solution of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>∞</m:mi> </m:math> {\infty} -Laplace equation. We not only show that the relative <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>∞</m:mi> </m:math> {\infty} -capacity equals the limit of the p -th root of the relative p -capacity as <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>p</m:mi> <m:mo>→</m:mo> <m:mi>∞</m:mi> </m:mrow> </m:math> {p\to\infty} and hence has a simple geometric characterization in terms of the Euclidean distance, but also establish several basic properties for the relative <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>∞</m:mi> </m:math> {\infty} -capacity. Consequently, we apply the relative <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>∞</m:mi> </m:math> {\infty} -capacity to the embedding theory of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>∞</m:mi> </m:math> {\infty} -Sobolev space. More geometrically, we affinize the relative <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>∞</m:mi> </m:math> {\infty} -capacity and its fundamental features as much as possible.

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)0.003
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: Empirical · Consensus signal: none
Teacher disagreement score0.914
Threshold uncertainty score0.410

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.003
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.001
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 head0.049
GPT teacher head0.331
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