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Apodictic discourse and the Cauchy-Bunyakovsky-Schwarz inequality ; Discours apodictique et inégalité de Cauchy-Bunyakovsky-Schwarz
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In: ISSN: 0970-0307 ; Ganita Bharati (Indian Mathematics): Journal of the Indian Society for History of Mathematics ; https://hal.archives-ouvertes.fr/hal-03643571 ; Ganita Bharati (Indian Mathematics): Journal of the Indian Society for History of Mathematics, Prints Publications Pvt., In press (2022)
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Abstract:
International audience ; Bunyakovsky’s integral inequality (1859) is one of the familiar tools of modern Analysis. We try and understand what Bunyakovsky did, why he did it, why others did not follow the same path, and explore some of the mathematical (re)interpretations of his inequalities. This is achieved by treating the texts as discourses that provide motivation and proofs by their very discursive structure, in addition to what meets the eye at first reading. Bunyakovsky paper is an outgrowth of the mathematical theory of mean-values in Cauchy’s work (1821), but viewed from the point of view of Probability and Statistics. Liouville (1836) gave a result that implies Bunyakovsky’s inequality, but did not identify it as significant because his interests lay elsewhere. Grassmann (1862) stated the inequality in abstract form but did not prove it for reasons that can be identified. Finally, by relating the result to quadratic binary forms, Schwarz (1885) opened the way to a geometric interpretation of the inequality that became important in the theory of integral equations. His argument is the source of one of the proofs most commonly taught nowadays. At about the same time, the Rogers-Hölder inequality suggested generalizations of Cauchy’s and Bunyakovsky’s results in an entirely different direction. Later extensions and reinterpretations show that no single result, even now, subsumes all known generalizations.
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Keyword:
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]; [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]; [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]; [MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO]; [SHS.HISPHILSO]Humanities and Social Sciences/History; algebraic identities; Analysis; Apodicticité; Cauchy-Schwarz; derivations; Discourse Analysis; history of mathematics; invariant theory; Philosophy and Sociology of Sciences; Saint-Petersburg
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URL: https://hal.archives-ouvertes.fr/hal-03643571
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| 2 |
Towards an international lexicon
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In: ISSN: 1863-9690 ; EISSN: 1863-9704 ; ZDM ; https://hal.archives-ouvertes.fr/hal-03625972 ; ZDM, Springer Verlag, 2022, ⟨10.1007/s11858-022-01349-3⟩ (2022)
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Hitchcock, F. L., 1941, The Distribution of a Product from Several Sources to Numerous Localities. Version bilingue et commentée
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In: https://hal.archives-ouvertes.fr/hal-03565874 ; 2022 (2022)
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| 4 |
Exploring elementary teachers’ facilitation of discussion in developing students’ mathematical agency
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| 5 |
The contextual logic
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In: https://hal.archives-ouvertes.fr/hal-03195162 ; 2022 (2022)
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A gentle introduction to Girard's Transcendental Syntax for the linear logician
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In: https://hal.archives-ouvertes.fr/hal-02977750 ; 2022 (2022)
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Evolution and trade-off dynamics of functional load
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In: ISSN: 1099-4300 ; Entropy ; https://hal.archives-ouvertes.fr/hal-03630585 ; Entropy, MDPI, 2022, ⟨10.3390/e24040507⟩ (2022)
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| 8 |
Usages du Dictionnaire Électronique des Synonymes (DES) du CRISCO : focus sur les mots inexistants
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In: ISSN: 2607-0987 ; Le carnet de la MRSH ; https://halshs.archives-ouvertes.fr/halshs-03606075 ; 2022 (2022)
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| 9 |
Dialogical Logic
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In: ISSN: 1095-5054 ; Stanford Encyclopedia of Philosophy ; https://hal.archives-ouvertes.fr/hal-03651225 ; 2022, https://plato.stanford.edu/archives/sum2022/entries/logic-dialogical/ (2022)
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Game of Grounds
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In: Objects, Structures, and Logics ; https://hal.archives-ouvertes.fr/hal-03602786 ; Objects, Structures, and Logics, 339, Springer International Publishing, pp.259-286, 2022, Boston Studies in the Philosophy and History of Science, ⟨10.1007/978-3-030-84706-7_10⟩ (2022)
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| 11 |
Logiciel de calculs statistiques pour des données linguistiques
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In: https://hal.archives-ouvertes.fr/hal-03631733 ; 2022, ⟨swh:1:dir:f3daa115d74f59485bc7249c1ab40dcb5f4af412;origin=https://hal.archives-ouvertes.fr/hal-03631733;visit=swh:1:snp:913acafcd2699ecc9ef1f05543532e454b11b328;anchor=swh:1:rel:d520c0e78ee4276ff8af500da81d99f8f5e4a301;path=/⟩ (2022)
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| 12 |
Calculi of Epistemic Grounding Based on Prawitz’s Theory of Grounds
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In: ISSN: 0039-3215 ; EISSN: 1572-8730 ; Studia Logica ; https://hal.archives-ouvertes.fr/hal-03581352 ; Studia Logica, Springer Verlag (Germany), 2022, ⟨10.1007/s11225-021-09979-6⟩ (2022)
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| 13 |
Semiotic analysis of the scientific measurement of a quantity ; Analyse sémiotique de la mesure scientifique d'une grandeur
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In: La Sémiotique et ses horizons ; https://hal.archives-ouvertes.fr/hal-03556362 ; La Sémiotique et ses horizons, 2022 (2022)
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| 14 |
Plurilinguisme et enseignement des mathématiques ; Plurilinguisme et enseignement des mathématiques: Mise en perspectives des Journées Plurimaths 2020
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In: https://hal.archives-ouvertes.fr/hal-03553842 ; Éditions Lambert-Lucas, 2022 (2022)
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| 15 |
Improving mathematics performance in 7-year-old children: Training the mapping from estimated quantities to Arabic digits ...
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Finding the best way to put media bias research into practice via an annotation app ...
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Are neural language models sensitive to false belief? A computational study. ...
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Structured, flexible, and robust: comparing linguistic plans and explanations generated by humans and large language models ...
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Similarity between person roles in a card sorting experiment ...
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| 20 |
Statistical detection of format dialects using the weighted Dowker complex ...
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