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Constitutive sets of convex static systems

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Wlodzimierz Tulczyjew, Pawel Urbanski

Mathematical Physics · Submitted 20 Dec 2006

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

The authors' main claim The notion of a critical point of a family of convex forms is introduced and discussed.

how it is stated · asserted 0.95 read the record →

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arXiv IDmath-ph/0612067 (version 1)
Pith IDNGZP3O4T, Pith's permanent record of this paper and its review
CitationPawel Urbanski, Wlodzimierz Tulczyjew. "Constitutive sets of convex static systems." arXiv:math-ph/0612067 (2006). https://pith.science/paper/NGZP3O4T
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,393 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.03 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The principle of virtual work for dissipative systems is stated. Partially controlled systems are discussed and the concept of a generating families of forms is introduced. The notion of a critical point of a family of convex forms is introduced and discussed. A number of examples is given.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The principle of virtual work for dissipative systems is stated. background 0.64 0.50 0.07 asserted 0.99
s1 Partially controlled systems are discussed and the concept of a generating families of forms is introduced. contribution 0.97 0.72 0.07 asserted 0.97
s2 The notion of a critical point of a family of convex forms is introduced and discussed. contribution 0.98 0.75 0.08 asserted 0.95
s3 A number of examples is given. contribution 0.61 0.84 0.03 asserted 0.95

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 0.87.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

The principle of virtual work for dissipative systems is stated. Partially controlled systems are discussed and the concept of a generating families of forms is introduced. The notion of a critical point of a family of convex forms is introduced and discussed. A number of examples is given.

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