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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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Within and Beyond Stereotypes of Arab Women: A Corpus-based Approach to Jordanian Women’s Portrayal in English Digital News
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In: Journal of International Women's Studies (2022)
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From "violence against women" to "violence against women and girls". The reconceptualisation of violence against women in United-Nations discourse
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In: ISSN: 0960-4545 ; EISSN: 2518-3567 ; The European English Messenger ; https://hal.archives-ouvertes.fr/hal-03587067 ; The European English Messenger, European Society for the Study of English ESSE, 2022 (2022)
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Pragmatique de l’insulte en politique : l’art d’accuser l’autre ou la performativité en perspective
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In: Les usages politiques de l'insulte ; https://halshs.archives-ouvertes.fr/halshs-03648831 ; Cédric Passard, Sciences Po, Lille. Les usages politiques de l'insulte, A paraître (2022)
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"What It Means to Discriminate". Presentation of The Volume ; « Ce que discriminer veut dire ». Présentation du volume
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In: ISSN: 1638-5748 ; EISSN: 1638-573X ; CORELA - COgnition, REprésentation, LAngage ; https://halshs.archives-ouvertes.fr/halshs-03648818 ; CORELA - COgnition, REprésentation, LAngage, CERLICO-Cercle Linguistique du Centre et de l'Ouest (France), 2022, ⟨10.4000/corela.14510⟩ (2022)
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Cyberhate in the Context of Migrations
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In: https://hal.archives-ouvertes.fr/hal-03572743 ; Springer International Publishing, 2022, 978-3-030-92105-7. ⟨10.1007/978-3-030-92103-3⟩ ; https://link.springer.com/book/10.1007/978-3-030-92103-3 (2022)
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The Experiences of Migrant Job Seekers, Looking for Work Online ...
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Legitimacy and legality in national identity construction ...
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РЕЧЕВЕДЕНИЕ: ИСТОРИЯ, ТЕОРИЯ, ПРАКТИКА ... : SPEECHSCIENCE: HISTORY, THEORY, PRACTICE ...
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Соловьева Наталья Васильевна. - : Вестник Пермского государственного гуманитарно-педагогического университета. Серия № 3. Гуманитарные и общественные науки, 2022
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« Ne pas parler à la place des premiers concernés ». Étude d’une pratique politique d’éthique langagière chez des militants politiques pour les droits des étrangers en France
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Veniard, Marie. - : University of Guelph, School of Languages and Literatures, 2022. : Érudit, 2022
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The Impact of George W. Bush's Political Discourses on the Invasion of Iraq: A Corpus-Based Rhetoric Discourse Analysis ...
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The Impact of George W. Bush's Political Discourses on the Invasion of Iraq: A Corpus-Based Rhetoric Discourse Analysis ...
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A Dialectic of Race Discourses: The Presence/Absence of Mixed Race at the State, Institution, and Civil Society and Voluntary and Community Sector Levels in the United Kingdom
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In: Social Sciences; Volume 11; Issue 2; Pages: 86 (2022)
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| 17 |
Strategisches Framing bei Björn Höcke - wie ein rechtsextremer Politiker den Rahmen sprengt
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In: ZRex - Zeitschrift für Rechtsextremismusforschung ; 2 ; 1 ; 128-140 (2022)
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| 18 |
Teachers’ narratives of resistance to Madrid's bilingual programme: an exploratory study in secondary education
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| 19 |
Valuing the local within the global: A discourse analysis of professional development in a U.S.-Kurdish transnational university partnership
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In: Journal of Global Education and Research (2022)
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Critical analysis of the main discourses of the Spanish press about the rescue of the ship Aquarius
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