{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:13eb108a-e792-47e5-999f-e7000f71deee", "labels": { "zh-CN": "支集", "en": "support" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "d9193de8409af5f9ad5a358c9f408d6c6927c57bad3ec40ffc42e99747d650ed", "occurrences": [ { "concept_id": "urn:uuid:13eb108a-e792-47e5-999f-e7000f71deee", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-12/01-test-functions-and-distributions", "anchor": "first-2f2d8bdeefcf3528a381-zh", "chapter": "12", "section": "12.1", "offset": 393, "range": [ 4648, 4878 ], "source_revision": "1313c447e739f007a893e8a36396d845ca81d5070f59e96e03fc03f2c0d3bce9", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "支集(support)", "context": { "range": [ 4597, 5386 ], "quote": "函数 $f : \\mathbb { R } ^ { n } \\to \\mathbb { R }$ 的 支集(support) 是 $\\mathbb { R } ^ { n }$ 中使 $f ( \\mathbf { x } ) \\neq 0$ 的区域之闭包。若 $\\mathbb { R } ^ { n }$ 上的实值函数 $f$ 的支集为有界闭集，则称该函数具有 紧支集(compact support)； 即， 存在 $R > 0$ 使得 $f ( x _ { 1 } , \\ldots , x _ { n } ) = 0 { \\mathrm { f o r } } | \\mathbf { x } | \\geq R$ 。 称函数 $f$ 为 $C ^ { m }$，如果阶为 $m$ 的所有偏导数，", "quote_sha256": "98624846faeadabffc2aa217ce0d653fb035f675844fc8dd3ff6a516c5e9441b", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-12/01-test-functions-and-distributions", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-a914f2a3221590db47c6e401" }, { "concept_id": "urn:uuid:13eb108a-e792-47e5-999f-e7000f71deee", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-17/02-integration-of-n-forms", "anchor": "section-17-2", "chapter": "17", "section": "17.2", "offset": 1388, "range": [ 4649, 4844 ], "source_revision": "a5d7e1939076e64a9e0069ca7bc699edc9e6b5ecb2099896b26aa7833a647bf1", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "支集(support)", "context": { "range": [ 4417, 4873 ], "quote": "设 $( M , \\omega )$ 为一个 $n$ 维有向可微流形，而 $( U , \\phi ; x ^ { i } )$ 为一个正定向坐标图。在 $U$ 上，我们可以写出 $\\omega = g ( \\mathbf { x } ) \\mathrm { d } x ^ { 1 } \\wedge \\cdot \\cdot \\cdot \\wedge \\mathrm { d } x ^ { n }$，其中 $g > 0$。一个 $n$ 形式 $\\alpha$ 的 支集(support) 定义为使 $\\alpha \\neq 0$ 的集合的闭包，", "quote_sha256": "5284bf104989f0dc4792b5cfc7ddf50e765fc9d2876b6fc336b116abab9a0d99", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-17/02-integration-of-n-forms", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-5c2c564f98ffcc23c283422b" }, { "concept_id": "urn:uuid:13eb108a-e792-47e5-999f-e7000f71deee", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "en", "route": "en/chapter-17/02-integration-of-n-forms", "anchor": "first-2f2d8bdeefcf3528a381-en", "chapter": "17", "section": "17.2", "offset": 1832, "range": [ 4619, 4845 ], "source_revision": "8562e2a5c5b54f793324385976206248e2ec40b5bc5b5879886fb2c474621212", "source_category": "original_transcription", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "support", "context": { "range": [ 4331, 4933 ], "quote": "Let $( M , \\omega )$ be an $n$-dimensional oriented differentiable manifold, and $( U , \\phi ; x ^ { i } )$ a positively oriented chart. On $U$ we can write $\\omega = g ( \\mathbf { x } ) \\mathrm { d } x ^ { 1 } \\wedge \\cdot \\cdot \\cdot \\wedge \\mathrm { d } x ^ { n }$ where $g > 0$ . The support of an $n$-form $\\alpha$ is defined as the closure of the set on which $\\alpha \\neq 0$ ,", "quote_sha256": "be4472d7c39efc7d4b989560f5590239c5c952c54561cddb9e8be37e2d60444f", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "zh/chapter-17/02-integration-of-n-forms", "lang": "zh-CN", "source_category": "translation", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-14018c05f1ee27dd4738a3b1" } ], "registered_positions": [ { "route": "zh/chapter-12/01-test-functions-and-distributions", "lang": "zh-CN", "section": "12.1", "signal": "term-mark", "label": "支集", "english": "support", "offset": 393 }, { "route": "en/chapter-17/02-integration-of-n-forms", "lang": "en", "section": "17.2", "signal": "term-mark", "label": "support", "english": "support", "offset": 1832 }, { "route": "zh/chapter-17/02-integration-of-n-forms", "lang": "zh-CN", "section": "17.2", "signal": "term-mark", "label": "支集", "english": "support", "offset": 1388 } ], "statements": [], "resolved_references": [], "reading_order": [ "occ-a914f2a3221590db47c6e401", "occ-5c2c564f98ffcc23c283422b", "occ-14018c05f1ee27dd4738a3b1" ], "recorded_dependencies": [], "reading_paths": [], "coverage": { "registered_positions": 3, "located_occurrences": 3, "whole_book_search_complete": false, "registered_positions_truncated": false, "independent_human_review_implied": false }, "unresolved": [], "base_revision": "39a9cd8298e60f0ac9f0ce181050a814b21485808702c74c5ec044de5a019ad0", "optional_enrichments": [] }