{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:357477c3-6241-452b-834b-833bbcf1ea71", "labels": { "zh-CN": "轨道", "en": "orbit" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "10db3b1f0db31972234750414fdf5aa3deab8ea52588edea1da6205fe3b579fe", "occurrences": [ { "concept_id": "urn:uuid:357477c3-6241-452b-834b-833bbcf1ea71", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-02/06-group-actions", "anchor": "concept-2-orbit", "chapter": "2", "section": "2.6", "offset": 2174, "range": [ 6439, 6653 ], "source_revision": "ee9ed474b5901e55a5560c8c99524360191a82b2fa608d354831ac9d3ab11f00", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "轨道(orbit)", "context": { "range": [ 6418, 6681 ], "quote": "设$G$有一个左作用在$X$上，点$x$的轨道(orbit)$G x$是可以通过这个作用从$x$到达的所有点的集合：", "quote_sha256": "3a4160988952e7d9045547c499aea53dd3f4034ccc23ff30292622384af339be", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-02/06-group-actions", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-396117a08b75e2840be9d086" }, { "concept_id": "urn:uuid:357477c3-6241-452b-834b-833bbcf1ea71", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-15/05-commutators-flows-and-lie-derivatives", "anchor": "concept-15-orbit", "chapter": "15", "section": "15.5", "offset": 6306, "range": [ 13883, 14098 ], "source_revision": "2f0608b8eac69ae4caf530afbfcbc72c0bbf08ce94d9db8746758c0032aafdce", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "轨道(orbit)", "context": { "range": [ 13759, 14128 ], "quote": "由$\\gamma _ { p } ( t ) = \\sigma _ { t } ( p )$定义的曲线$\\gamma _ { p } : \\mathbb { R } \\to M$显然在$t = 0$处经过$p$。它称为$p$在流$\\sigma$下的轨道(orbit)，并通过下式在$p$处定义一个切向量$X _ { p }$：", "quote_sha256": "1833557906607ca16b7dbb4e6bfe61340b32d1aea7d7e317575e52fc5b7634ec", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-15/05-commutators-flows-and-lie-derivatives", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-02bf7f37444d5be7ae31446a" }, { "concept_id": "urn:uuid:357477c3-6241-452b-834b-833bbcf1ea71", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "en", "route": "en/chapter-15/05-commutators-flows-and-lie-derivatives", "anchor": "first-be5c0d4a8e58f2dac890-en", "chapter": "15", "section": "15.5", "offset": 8339, "range": [ 15405, 15629 ], "source_revision": "b8c69f025d8d682aca940e9c3c2c1374cac6eaec1671872b5a7ec7b3301a1baa", "source_category": "original_transcription", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "orbit", "context": { "range": [ 15242, 15711 ], "quote": "The curve $\\gamma _ { p } : \\mathbb { R } \\to M$ defined by $\\gamma _ { p } ( t ) = \\sigma _ { t } ( p )$ clearly passes through $p$ at $t = 0$ . It is called the orbit of $p$ under the flow $\\sigma$ and defines a tangent vector $X _ { p }$ at $p$ by", "quote_sha256": "5d3260d0250e9483630a869417657261bb8130812d0a0a7d95b387e26fe64d0c", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "zh/chapter-15/05-commutators-flows-and-lie-derivatives", "lang": "zh-CN", "source_category": "translation", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-abb063c814f0666df282e1f1" }, { "concept_id": "urn:uuid:357477c3-6241-452b-834b-833bbcf1ea71", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-19/04-lie-groups-of-transformations", "anchor": "concept-19-orbit", "chapter": "19", "section": "19.4", "offset": 1499, "range": [ 7691, 7906 ], "source_revision": "6b9fb6e6b5795a67066d5fd3a7943c2f835350c01b6fb3e5c32a14545a7a7b79", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "轨道(orbit)", "context": { "range": [ 7667, 8241 ], "quote": "如 2.6 节所述，点 $x \\in M$ 的 轨道(orbit) $G x$ 是集合 $G x = \\left\\{ g x \\mid g \\in G \\right\\}$，并且如果 $M$ 的全部是其中某一点的轨道，则称 $G$ 在 $M$ 上的作用是 传递作用(transitive action)", "quote_sha256": "64db6868ea2d709df8be1381a6adb9dbf12c096c6b92c46476998ca3029ca9f5", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-19/04-lie-groups-of-transformations", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-9c2b0f9d6b425c08ec1a4420" }, { "concept_id": "urn:uuid:357477c3-6241-452b-834b-833bbcf1ea71", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "en", "route": "en/chapter-19/04-lie-groups-of-transformations", "anchor": "xref-04-lie-groups-of-transformations-2", "chapter": "19", "section": "19.4", "offset": 2095, "range": [ 7780, 7969 ], "source_revision": "603b0bc152be28d1376b2bca520097bf4f5c5ce4dde74b2630d942384add1ab5", "source_category": "original_transcription", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "orbit", "context": { "range": [ 7603, 8450 ], "quote": "As in Section 2.6 the orbit $G x$ of a point $x \\in M$ is the set $G x = \\left\\{ g x \\mid g \\in G \\right\\}$ , and the action of $G$ on $M$ is said to be transitive if the whole of $M$ is the orbit of some point in", "quote_sha256": "daa84f1a1a6cddf64d21ae53bc776d605efd64c0740f5c4d158d1759b6f9d330", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "zh/chapter-19/04-lie-groups-of-transformations", "lang": "zh-CN", "source_category": "translation", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-33d9829448d42125523501a4" } ], "registered_positions": [ { "route": "zh/chapter-02/06-group-actions", "lang": "zh-CN", "section": "2.6", "signal": "term-mark", "label": "轨道", "english": "orbit", "offset": 1550 }, { "route": "en/chapter-15/05-commutators-flows-and-lie-derivatives", "lang": "en", "section": "15.5", "signal": "term-mark", "label": "orbit", "english": "orbit", "offset": 7766 }, { "route": "zh/chapter-15/05-commutators-flows-and-lie-derivatives", "lang": "zh-CN", "section": "15.5", "signal": "term-mark", "label": "轨道", "english": "orbit", "offset": 5838 }, { "route": "en/chapter-19/04-lie-groups-of-transformations", "lang": "en", "section": "19.4", "signal": "term-mark", "label": "orbit", "english": "orbit", "offset": 1713 }, { "route": "zh/chapter-19/04-lie-groups-of-transformations", "lang": "zh-CN", "section": "19.4", "signal": "term-mark", "label": "轨道", "english": "orbit", "offset": 1187 } ], "statements": [], "resolved_references": [ { "raw": "href=\"../chapter-02/06-group-actions#section-2-6\"", "href": "../chapter-02/06-group-actions#section-2-6", "range": [ 7612, 7661 ], "relation": "references", "target_route": "en/chapter-02/06-group-actions", "target_anchor": "section-2-6", "resolved": true, "reason": null, "source_revision": "603b0bc152be28d1376b2bca520097bf4f5c5ce4dde74b2630d942384add1ab5", "source_route": "en/chapter-19/04-lie-groups-of-transformations", "occurrence_id": "occ-33d9829448d42125523501a4" } ], "reading_order": [ "occ-396117a08b75e2840be9d086", "occ-02bf7f37444d5be7ae31446a", "occ-abb063c814f0666df282e1f1", "occ-9c2b0f9d6b425c08ec1a4420", "occ-33d9829448d42125523501a4" ], "recorded_dependencies": [], "reading_paths": [], "coverage": { "registered_positions": 5, "located_occurrences": 5, "whole_book_search_complete": false, "registered_positions_truncated": false, "independent_human_review_implied": false }, "unresolved": [], "base_revision": "d280f304f13027831426954abc985102f8bdeb4d389749c496b73583c42a5d84", "optional_enrichments": [] }