"グリーンの第一定理" meaning in All languages combined

See グリーンの第一定理 on Wiktionary

Noun [日本語]

Forms: グリーンのだいいちていり
  1. スカラー場ϕ,ψに対して∮_S(ϕ∇ψ)·d⃑S=∫_V(ϕΔψ+∇ϕ·∇ψ)dVが成り立つという定理。
    Sense id: ja-グリーンの第一定理-ja-noun-HkpdVBSW Categories (other): 日本語 ベクトル解析
The following are not (yet) sense-disambiguated
Related terms: ガウスの発散定理, ストークスの定理, グリーンの第二定理
{
  "categories": [
    {
      "kind": "other",
      "name": "日本語",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "日本語 仮名混用",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "日本語 名詞",
      "parents": [],
      "source": "w"
    }
  ],
  "forms": [
    {
      "form": "グリーンのだいいちていり"
    }
  ],
  "lang": "日本語",
  "lang_code": "ja",
  "pos": "noun",
  "pos_title": "名詞",
  "related": [
    {
      "word": "ガウスの発散定理"
    },
    {
      "word": "ストークスの定理"
    },
    {
      "word": "グリーンの第二定理"
    }
  ],
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "日本語 ベクトル解析",
          "parents": [],
          "source": "w"
        }
      ],
      "glosses": [
        "スカラー場ϕ,ψに対して∮_S(ϕ∇ψ)·d⃑S=∫_V(ϕΔψ+∇ϕ·∇ψ)dVが成り立つという定理。"
      ],
      "id": "ja-グリーンの第一定理-ja-noun-HkpdVBSW",
      "raw_tags": [
        "ベクトル解析"
      ]
    }
  ],
  "word": "グリーンの第一定理"
}
{
  "categories": [
    "日本語",
    "日本語 仮名混用",
    "日本語 名詞"
  ],
  "forms": [
    {
      "form": "グリーンのだいいちていり"
    }
  ],
  "lang": "日本語",
  "lang_code": "ja",
  "pos": "noun",
  "pos_title": "名詞",
  "related": [
    {
      "word": "ガウスの発散定理"
    },
    {
      "word": "ストークスの定理"
    },
    {
      "word": "グリーンの第二定理"
    }
  ],
  "senses": [
    {
      "categories": [
        "日本語 ベクトル解析"
      ],
      "glosses": [
        "スカラー場ϕ,ψに対して∮_S(ϕ∇ψ)·d⃑S=∫_V(ϕΔψ+∇ϕ·∇ψ)dVが成り立つという定理。"
      ],
      "raw_tags": [
        "ベクトル解析"
      ]
    }
  ],
  "word": "グリーンの第一定理"
}

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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-07-19 from the jawiktionary dump dated 2025-07-02 using wiktextract (45c4a21 and f1c2b61). 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.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.