See Jacobian in All languages combined, or Wiktionary
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G. J. Jacobi." ], "id": "en-Jacobian-en-adj-yqVX~MD0", "links": [ [ "mathematical", "mathematical#English" ], [ "object", "object#English" ], [ "C. G. J. Jacobi", "w:Carl Gustav Jacob Jacobi" ] ], "tags": [ "not-comparable" ], "translations": [ { "code": "de", "lang": "German", "sense": "in honor of Jacobi", "word": "Jacobi-" }, { "code": "es", "lang": "Spanish", "sense": "in honor of Jacobi", "word": "jacobiano" } ] } ], "sounds": [ { "enpr": "yä-kõ'-bi-un" }, { "ipa": "/jɑːˈkəʊ.bi.ən/" }, { "ipa": "/d͡ʒəˈkoʊ.bi.ən/" }, { "audio": "LL-Q1860 (eng)-Persent101-Jacobian.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/6/62/LL-Q1860_%28eng%29-Persent101-Jacobian.wav/LL-Q1860_%28eng%29-Persent101-Jacobian.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/6/62/LL-Q1860_%28eng%29-Persent101-Jacobian.wav/LL-Q1860_%28eng%29-Persent101-Jacobian.wav.ogg" } ], "wikipedia": [ "Carl Gustav Jacob Jacobi" ], "word": "Jacobian" } { "etymology_number": 1, "etymology_templates": [ { "args": { "1": "en", "2": "Jacobi", "3": "-an" }, "expansion": "Jacobi + -an", "name": "af" } ], "etymology_text": "From Jacobi + -an, after Carl Gustav Jacob Jacobi, a German mathematician of the 19th century.", "forms": [ { "form": "Jacobians", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "Jacobian (plural Jacobians)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Calculus", "orig": "en:Calculus", "parents": [ "Mathematical analysis", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "43 39 10 8", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "37 36 21 7", "kind": "other", "name": "English terms suffixed with -ian", "parents": [], "source": "w+disamb" }, { "_dis": "40 38 16 7", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "41 40 17 2", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" } ], "examples": [ { "ref": "2016, Kyle E. Niemeyer, Nicholas J. Curtis, Chih-Jen Sung, “pyJac: analytical Jacobian generator for chemical kinetics”, in arXiv:", "text": "As a demonstration, we first establish the correctness of the Jacobian matrices for kinetic models of hydrogen, methane, ethylene, and isopentanol oxidation, then demonstrate the performance achievable on CPUs and GPUs using pyJac via matrix evaluation timing comparisons..", "type": "quote" } ], "glosses": [ "A Jacobian matrix or its associated operator." ], "id": "en-Jacobian-en-noun-BSwHBgdS", "links": [ [ "calculus", "calculus" ], [ "matrix", "matrix" ], [ "operator", "operator" ] ], "raw_glosses": [ "(calculus) A Jacobian matrix or its associated operator." ], "topics": [ "calculus", "mathematics", "sciences" ], "translations": [ { "_dis1": "83 17", "code": "de", "lang": "German", "sense": "Jacobian matrix", "tags": [ "feminine" ], "word": "Jacobi-Matrix" }, { "_dis1": "83 17", "code": "de", "lang": "German", "sense": "Jacobian matrix", "tags": [ "feminine" ], "word": "Funktionalmatrix" }, { "_dis1": "83 17", "code": "de", "lang": "German", "sense": "Jacobian matrix", "tags": [ "feminine" ], "word": "Ableitungsmatrix" }, { "_dis1": "83 17", "code": "he", "lang": "Hebrew", "roman": "matrítzat ya'akóbi", "sense": "Jacobian matrix", "tags": [ "feminine" ], "word": "מטריצת יעקובי" }, { "_dis1": "83 17", "code": "es", "lang": "Spanish", "sense": "Jacobian matrix", "tags": [ "feminine" ], "word": "matriz jacobiana" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Calculus", "orig": "en:Calculus", "parents": [ "Mathematical analysis", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "ref": "2015, Ping Ngai Chung, Craig Costello, Benjamin Smith, “Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes”, in arXiv:", "text": "In terms of per-bit security, elliptic curves and Jacobians of genus 2 curves appear to be roughly equivalent. However, when it comes to efficient and side-channel-aware implementations, we see a curious divergence.", "type": "quote" } ], "glosses": [ "The determinant of such a matrix." ], "id": "en-Jacobian-en-noun-MTDOOUma", "links": [ [ "calculus", "calculus" ], [ "determinant", "determinant" ] ], "raw_glosses": [ "(calculus) The determinant of such a matrix." ], "topics": [ "calculus", "mathematics", "sciences" ] } ], "sounds": [ { "enpr": "yä-kõ'-bi-un" }, { "ipa": "/jɑːˈkəʊ.bi.ən/" }, { "ipa": "/d͡ʒəˈkoʊ.bi.ən/" }, { "audio": "LL-Q1860 (eng)-Persent101-Jacobian.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/6/62/LL-Q1860_%28eng%29-Persent101-Jacobian.wav/LL-Q1860_%28eng%29-Persent101-Jacobian.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/6/62/LL-Q1860_%28eng%29-Persent101-Jacobian.wav/LL-Q1860_%28eng%29-Persent101-Jacobian.wav.ogg" } ], "translations": [ { "_dis1": "54 46", "code": "de", "lang": "German", "sense": "the determinant of the Jacobian matrix", "tags": [ "feminine" ], "word": "Jacobi-Determinante" }, { "_dis1": "54 46", "code": "de", "lang": "German", "sense": "the determinant of the Jacobian matrix", "tags": [ "feminine" ], "word": "Funktionaldeterminante" }, { "_dis1": "54 46", "code": "he", "lang": "Hebrew", "roman": "ya'akobián", "sense": "the determinant of the Jacobian matrix", "tags": [ "masculine" ], "word": "יעקוביאן" }, { "_dis1": "54 46", "code": "es", "lang": "Spanish", "sense": "the determinant of the Jacobian matrix", "tags": [ "masculine" ], "word": "determinante jacobiano" }, { "_dis1": "54 46", "code": "es", "lang": "Spanish", "sense": "the determinant of the Jacobian matrix", "tags": [ "masculine" ], "word": "jacobiano" } ], "wikipedia": [ "Carl Gustav Jacob Jacobi" ], "word": "Jacobian" } { "etymology_number": 2, "etymology_templates": [ { "args": { "1": "en", "2": "Jacob", "3": "-ian" }, "expansion": "Jacob + -ian", "name": "af" } ], "etymology_text": "From Jacob + -ian.", "forms": [ { "form": "more Jacobian", "tags": [ "comparative" ] }, { "form": "most Jacobian", "tags": [ "superlative" ] } ], "head_templates": [ { "args": {}, "expansion": "Jacobian (comparative more Jacobian, superlative most Jacobian)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "categories": [ { "_dis": "43 39 10 8", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "37 36 21 7", "kind": "other", "name": "English terms suffixed with -ian", "parents": [], "source": "w+disamb" }, { "_dis": "40 38 16 7", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "41 40 17 2", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" } ], "glosses": [ "Of or relating to the biblical Jacob." ], "id": "en-Jacobian-en-adj-SqSaU0pC", "links": [ [ "biblical", "biblical" ], [ "Jacob", "Jacob" ] ], "synonyms": [ { "word": "Jacobic" } ] } ], "word": "Jacobian" }
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Niemeyer, Nicholas J. Curtis, Chih-Jen Sung, “pyJac: analytical Jacobian generator for chemical kinetics”, in arXiv:", "text": "As a demonstration, we first establish the correctness of the Jacobian matrices for kinetic models of hydrogen, methane, ethylene, and isopentanol oxidation, then demonstrate the performance achievable on CPUs and GPUs using pyJac via matrix evaluation timing comparisons..", "type": "quote" } ], "glosses": [ "A Jacobian matrix or its associated operator." ], "links": [ [ "calculus", "calculus" ], [ "matrix", "matrix" ], [ "operator", "operator" ] ], "raw_glosses": [ "(calculus) A Jacobian matrix or its associated operator." ], "topics": [ "calculus", "mathematics", "sciences" ] }, { "categories": [ "English terms with quotations", "en:Calculus" ], "examples": [ { "ref": "2015, Ping Ngai Chung, Craig Costello, Benjamin Smith, “Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes”, in arXiv:", "text": "In terms of per-bit security, elliptic curves and Jacobians of genus 2 curves appear to be roughly equivalent. However, when it comes to efficient and side-channel-aware implementations, we see a curious divergence.", "type": "quote" } ], "glosses": [ "The determinant of such a matrix." ], "links": [ [ "calculus", "calculus" ], [ "determinant", "determinant" ] ], "raw_glosses": [ "(calculus) The determinant of such a matrix." ], "topics": [ "calculus", "mathematics", "sciences" ] } ], "sounds": [ { "enpr": "yä-kõ'-bi-un" }, { "ipa": "/jɑːˈkəʊ.bi.ən/" }, { "ipa": "/d͡ʒəˈkoʊ.bi.ən/" }, { "audio": "LL-Q1860 (eng)-Persent101-Jacobian.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/6/62/LL-Q1860_%28eng%29-Persent101-Jacobian.wav/LL-Q1860_%28eng%29-Persent101-Jacobian.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/6/62/LL-Q1860_%28eng%29-Persent101-Jacobian.wav/LL-Q1860_%28eng%29-Persent101-Jacobian.wav.ogg" } ], "translations": [ { "code": "de", "lang": "German", "sense": "Jacobian matrix", "tags": [ "feminine" ], "word": "Jacobi-Matrix" }, { "code": "de", "lang": "German", "sense": "Jacobian matrix", "tags": [ "feminine" ], "word": "Funktionalmatrix" }, { "code": "de", "lang": "German", "sense": "Jacobian matrix", "tags": [ "feminine" ], "word": "Ableitungsmatrix" }, { "code": "he", "lang": "Hebrew", "roman": "matrítzat ya'akóbi", "sense": "Jacobian matrix", "tags": [ "feminine" ], "word": "מטריצת יעקובי" }, { "code": "es", "lang": "Spanish", "sense": "Jacobian matrix", "tags": [ "feminine" ], "word": "matriz jacobiana" }, { "code": "de", "lang": "German", "sense": "the determinant of the Jacobian matrix", "tags": [ "feminine" ], "word": "Jacobi-Determinante" }, { "code": "de", "lang": "German", "sense": "the determinant of the Jacobian matrix", "tags": [ "feminine" ], "word": "Funktionaldeterminante" }, { "code": "he", "lang": "Hebrew", "roman": "ya'akobián", "sense": "the determinant of the Jacobian matrix", "tags": [ "masculine" ], "word": "יעקוביאן" }, { "code": "es", "lang": "Spanish", "sense": "the determinant of the Jacobian matrix", "tags": [ "masculine" ], "word": "determinante jacobiano" }, { "code": "es", "lang": "Spanish", "sense": "the determinant of the Jacobian matrix", "tags": [ "masculine" ], "word": "jacobiano" } ], "wikipedia": [ "Carl Gustav Jacob Jacobi" ], "word": "Jacobian" } { "categories": [ "English adjectives", "English entries with incorrect language header", "English eponyms", "English lemmas", "English terms suffixed with -ian", "Pages with 1 entry", "Pages with entries" ], "etymology_number": 2, "etymology_templates": [ { "args": { "1": "en", "2": "Jacob", "3": "-ian" }, "expansion": "Jacob + -ian", "name": "af" } ], "etymology_text": "From Jacob + -ian.", "forms": [ { "form": "more Jacobian", "tags": [ "comparative" ] }, { "form": "most Jacobian", "tags": [ "superlative" ] } ], "head_templates": [ { "args": {}, "expansion": "Jacobian (comparative more Jacobian, superlative most Jacobian)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "glosses": [ "Of or relating to the biblical Jacob." ], "links": [ [ "biblical", "biblical" ], [ "Jacob", "Jacob" ] ], "synonyms": [ { "word": "Jacobic" } ] } ], "word": "Jacobian" }
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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