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Point value characterizations and related results in the full Colombeau algebras G^e and G^d

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Eduard Nigsch

Functional Analysis · Submitted 5 Apr 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We present a point value characterization for elements of the elementary full Colombeau algebra G^e and the diffeomorphism invariant full Colombeau algebra G^d.

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arXiv ID1104.0911 (version 1)
Pith IDV2XPD27V, Pith's permanent record of this paper and its review
CitationEduard Nigsch. "Point value characterizations and related results in the full Colombeau algebras G^e and G^d." arXiv:1104.0911 (2011). https://pith.science/paper/V2XPD27V
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,284 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.61 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We present a point value characterization for elements of the elementary full Colombeau algebra G^e and the diffeomorphism invariant full Colombeau algebra G^d. Moreover, several results from the special algebra G^s about generalized numbers and invertibility are extended to the elementary full algebra.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a point value characterization for elements of the elementary full Colombeau algebra G^e and the diffeomorphism invariant full Colombeau algebra G^d. contribution 0.92 0.94 0.74 asserted 1.00
s1 Moreover, several results from the special algebra G^s about generalized numbers and invertibility are extended to the elementary full algebra. contribution 0.54 0.89 0.13 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We present a point value characterization for elements of the elementary full Colombeau algebra G^e and the diffeomorphism invariant full Colombeau algebra G^d. Moreover, several results from the special algebra G^s about generalized numbers and invertibility are extended to the elementary full algebra.

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