{"id":10505,"date":"2025-07-15T15:19:39","date_gmt":"2025-07-15T06:19:39","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=10505"},"modified":"2025-07-21T10:16:31","modified_gmt":"2025-07-21T01:16:31","slug":"%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e5%be%ae%e5%88%86%e3%81%ae%e6%81%92%e7%ad%89%e5%bc%8f%e3%81%ae%e7%a9%8d%e5%88%86%e3%81%a8%e6%b7%b7%e4%b9%b1%e3%81%ae%e6%ad%a3%e3%81%97%e6%96%b9\/","title":{"rendered":"\u30d9\u30af\u30c8\u30eb\u5834\u306e\u5fae\u5206\u306e\u6052\u7b49\u5f0f\u306e\u7a4d\u5206\u3068\u6df7\u4e71\u306e\u6b63\u3057\u65b9"},"content":{"rendered":"

\u30d9\u30af\u30c8\u30eb\u5834\uff08\u542b\u30b9\u30ab\u30e9\u30fc\u5834\uff09\u306e2\u968e\u504f\u5fae\u5206\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\boldsymbol{0}$ \u3068 $\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) = 0$ \u306e\u9762\u7a4d\u5206\u3084\u4f53\u7a4d\u7a4d\u5206\u306b\u3064\u3044\u3066\uff0c\u3042\u3089\u305f\u3081\u3066\u307e\u3068\u3081\u3066\u304a\u304f\u3002<\/p>\n

<\/p>\n

$\\nabla \\times (\\nabla\\psi)$ \u306e\u9762\u7a4d\u5206<\/h3>\n

\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi)=\\boldsymbol{0}$ \u306e\u5de6\u8fba\u3092\uff0c\u9589\u66f2\u7dda $C$ \u3092\u7e01\u3068\u3059\u308b\u4efb\u610f\u306e\u66f2\u9762 $S$ \u3067\u9762\u7a4d\u5206\u3059\u308b\u3068\uff0c\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u304b\u3089<\/p>\n

\\begin{eqnarray}
\n\\iint_S \\bigl( \\nabla \\times (\\nabla\\psi)\\bigr)\\cdot\\boldsymbol{n}\\, dS
\n&=& \\oint_C\\ (\\nabla\\psi)\\cdot d\\boldsymbol{r} \\\\
\n&=& \\oint_C\\ d\\psi \\\\
\n&=& \\int_{\\boldsymbol{r}_1}^{\\boldsymbol{r}_1}\\ d\\psi \\\\
\n&=& \\bigl[ \\psi\\bigr]_{\\boldsymbol{r}_1}^{\\boldsymbol{r}_1} \\\\
\n&=& \\psi(\\boldsymbol{r}_1) -\\psi(\\boldsymbol{r}_1) \\\\
\n&=& 0
\n\\end{eqnarray}<\/p>\n

\u4e00\u65b9\uff0c\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi)=\\boldsymbol{0}$ \u306e\u53f3\u8fba\u306e\u9762\u7a4d\u5206\u306f<\/p>\n

\\begin{eqnarray}
\n\\iint_S \\boldsymbol{0}\\cdot\\boldsymbol{n}\\, dS
\n&=& 0
\n\\end{eqnarray}<\/p>\n

\u3067\u3042\u308b\u304b\u3089\uff0c\u78ba\u304b\u306b\u5de6\u8fba\u306e\u9762\u7a4d\u5206\u3068\u53f3\u8fba\u306e\u9762\u7a4d\u5206\u304c\u7b49\u3057\u3044\u3053\u3068\u304c\u7c21\u5358\u306b\u308f\u304b\u308b\u3002\u3053\u306e\u5834\u5408\u306b\u306f\u4f55\u306e\u6df7\u4e71\u3082\u306a\u3044\u3002<\/p>\n

$\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) $ \u306e\u4f53\u7a4d\u7a4d\u5206\uff1a\u6df7\u4e71\uff1f<\/h3>\n

\u6052\u7b49\u5f0f $\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) = 0$ \u306e\u5de6\u8fba\u3092\uff0c\u9589\u66f2\u9762 $S$ \u3067\u56f2\u307e\u308c\u305f\u4f53\u7a4d $V$ \u3067\u4f53\u7a4d\u7a4d\u5206\u3059\u308b\u3068\uff0c\u30ac\u30a6\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u3068\uff0c\u3055\u3089\u306b\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u304b\u3089\uff08\u5b57\u9762\u3060\u3051\u3092\u307f\u308b\u9650\u308a\u3067\u306f\uff09<\/p>\n

\\begin{eqnarray}
\n\\iiint_V\\ \\nabla\\cdot (\\nabla\\times \\boldsymbol{a})\\ dV &=& \\iint_S\\ (\\nabla\\times \\boldsymbol{a})\\cdot\\boldsymbol{n}\\ dS \\qquad\\mbox{(\u30ac\u30a6\u30b9\u306e\u5b9a\u7406\u304b\u3089)}\\\\
\n&=& \\oint_C\\ \\boldsymbol{a}\\cdot d\\boldsymbol{r}\\qquad\\qquad\\qquad\\mbox{(\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406\u304b\u3089\uff1f)}
\n\\end{eqnarray}<\/p>\n

\u3068\u66f8\u3051\u308b\u3088\u3046\u306b\u601d\u3048\u308b\u3002\u4e00\u65b9\uff0c\u6052\u7b49\u5f0f $\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) = 0$ \u306e\u53f3\u8fba\u306e\u4f53\u7a4d\u6210\u5206\u306f\u76f4\u3061\u306b<\/p>\n

\\begin{eqnarray}
\n\\iiint_V\\ 0\\\u00a0 dV &=& 0
\n\\end{eqnarray}<\/p>\n

\u3067\u3042\u308b\u304b\u3089\uff0c\u4e00\u898b\uff0c\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb\u5834 $\\boldsymbol{a}$ \u306b\u5bfe\u3057\u3066<\/p>\n

\\begin{eqnarray}
\n\\oint_C\\ \\boldsymbol{a}\\cdot d\\boldsymbol{r} &=& 0
\n\\end{eqnarray}<\/p>\n

\u3068\u306a\u3063\u3066\u3057\u307e\u3046\u3088\u3046\u306b\u898b\u3048\u308b\u3002\u3061\u3087\u3063\u3068\u6df7\u4e71\u3057\u305d\u3046\u3060\u3002\u3044\u3063\u305f\u3044\u3053\u308c\u306f\u6b63\u3057\u3044\u306e\u3067\u3042\u308d\u3046\u304b\uff1f<\/p>\n

\u6df7\u4e71\u306e\u6b63\u3057\u65b9<\/h3>\n

\u4e0a\u8a18\u306e\u8a08\u7b97\u3067\u554f\u984c\u3068\u306a\u308b\u306e\u306f\u9589\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/strong><\/span>\u306b\u5bfe\u3057\u3066\uff08\u5b57\u9762\u3060\u3051\u3092\u307f\u3066\uff09\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u3092\u4f7f\u3063\u3066\u5909\u5f62\u3059\u308b\u3068\u3053\u308d\u3067\u3042\u308b\u3002<\/p>\n

\u305d\u3082\u305d\u3082\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u3068\u306f\uff0c\u9589\u66f2\u7dda $C$ \u3092\u5883\u754c\u30fb\u7e01\u3068\u3059\u308b\u958b\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/strong><\/span>\u306b\u3064\u3044\u3066\u9069\u7528\u3055\u308c\u308b\u3082\u306e\u3067\u3042\u3063\u305f\u306f\u305a\u3067\u3042\u308b\u3002\u3057\u304b\u3057\uff0c\u3044\u3063\u305f\u3093\u30ac\u30a6\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u3092\u4f7f\u3063\u3066\u4f53\u7a4d\u7a4d\u5206\u304b\u3089\u9762\u7a4d\u5206\u306b\u5909\u5f62\u3057\u305f\u3068\u304d\uff0c$S$ \u306f\u4f53\u7a4d $V$ \u3092\u56f2\u3080\u9589\u66f2\u9762<\/strong><\/span>\u3068\u306a\u3063\u3066\u3044\u308b\u3002\u9589\u66f2\u9762 $S$<\/strong><\/span>\u00a0\u3068\u306f\u5883\u754c\u30fb\u7e01\u304c\u306a\u3044\u306e\u3067\u3042\u308b\u304b\u3089\uff0c\u9589\u66f2\u9762 $S$ \u306e\u5883\u754c\u30fb\u7e01\u3068\u306a\u308b\u9589\u66f2\u7dda $C$ \u306f\u7121\u3044\u3002\u3042\u3048\u3066\u8a00\u3048\u3070\uff0c\u9589\u66f2\u9762 $S$<\/strong><\/span> \u306e\u5883\u754c\u30fb\u7e01\u3068\u306a\u308b $C$ \u306f\u9577\u3055\u30bc\u30ed\u306e\u9589\u66f2\u7dda\uff0c\u3068\u3067\u3082\u8a00\u3046\u3079\u304d\u304b\u3002<\/p>\n

\u3053\u306e\u3088\u3046\u306a\u6df7\u4e71\u3092\u907f\u3051\u308b\u305f\u3081\u306b\uff0c\u9762\u7a4d\u5206\u306e\u8868\u8a18\u3092\u533a\u5225\u3059\u308b\u3079\u304d\u3060\u3068\u3044\u3046\u306e\u304c\u79c1\u306e\u4e3b\u5f35\u3067\u3042\u308b\u3002<\/p>\n

\u4e00\u822c\u306b\uff0c\u9589\u66f2\u7dda $C$ \u3092\u7e01\u3068\u3059\u308b\u958b\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/span><\/strong><\/span>\u306b\u3064\u3044\u3066\u306f\u901a\u5e38\u306e $\\displaystyle \\iint_S$<\/span> \u3092\u4f7f\u3063\u3066<\/p>\n

$${\\color{blue}\\iint_S}\\ \\boldsymbol{a}\\cdot\\boldsymbol{n}\\ dS$$<\/p>\n

\u306e\u3088\u3046\u306b\u66f8\u304f\u3002\u958b\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/span><\/strong><\/span>\u306b\u3064\u3044\u3066\u306f\uff0c\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u304c\u6210\u308a\u7acb\u3061\uff0c<\/p>\n

$${\\color{blue}\\iint_{S}} \\ (\\nabla\\times \\boldsymbol{a})\\cdot \\boldsymbol{n}\\ dS = \\oint_{C}\\\u00a0 \\boldsymbol{a}\\cdot d\\boldsymbol{r}$$<\/p>\n

\u6b21\u306b\uff0c\u9589\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/strong><\/span>\u306f $\\displaystyle \\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}$<\/span> \u3092\u4f7f\u3063\u3066<\/p>\n

$${\\displaystyle \\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}}\\ \\boldsymbol{a}\\cdot\\boldsymbol{n}\\ dS$$<\/p>\n

\u306e\u3088\u3046\u306b\u66f8\u304f\u3002\u9589\u66f2\u9762 $S$ \u4e0a\u306e\u9762\u7a4d\u5206<\/strong><\/span>\u306f\u30ac\u30a6\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u306b\u8868\u308c\uff0c<\/p>\n

$$\\iiint_V \\nabla\\cdot \\boldsymbol{a}\\, dV = {\\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}}\\\u00a0 \\boldsymbol{a}\\cdot\\boldsymbol{n} \\ dS$$<\/p>\n

\u9589\u66f2\u9762 $S$ <\/strong><\/span>\u306b\u306f\u5883\u754c\u30fb\u7e01\u304c\u5b58\u5728\u3057\u306a\u3044\u305f\u3081\uff0c\u7e01\u3068\u306a\u308b\u00a0\u9589\u66f2\u7dda $C$\u306e\u5b58\u5728\u3092\u524d\u63d0\u3068\u3059\u308b\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/strong><\/span>\u306f\u9069\u7528\u3067\u304d\u306a\u3044\u3002<\/p>\n

$$ {\\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}} \\ (\\nabla\\times \\boldsymbol{a})\\cdot \\boldsymbol{n}\\ dS \\ {\\color{red}\\neq} \\oint_{C}\\\u00a0 \\boldsymbol{a}\\cdot d\\boldsymbol{r}$$<\/p>\n

\u5f37\u3044\u3066\u8a00\u3048\u3070\uff0c\u9577\u3055\u30bc\u30ed\u306e\u9589\u66f2\u7dda $C$ \u4e0a\u306e\u7dda\u7a4d\u5206\u3067\u3042\u308b\u304b\u3089\u30bc\u30ed\uff0c<\/p>\n

$$ {\\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}} \\ (\\nabla\\times \\boldsymbol{a})\\cdot \\boldsymbol{n}\\ dS =0$$<\/p>\n

\u3068\u3067\u3082\u3059\u308c\u3070\u3088\u3044\u3060\u308d\u3046\u3002<\/p>\n

\u3053\u3046\u3059\u308b\u3068\uff0c$\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) $ \u306e\u4f53\u7a4d\u7a4d\u5206\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\uff0c<\/p>\n

\\begin{eqnarray}
\n\\iiint_V\\ \\nabla\\cdot (\\nabla\\times \\boldsymbol{a})\\ dV
\n&=& {\\color{red}\\int\\!\\!\\!\\!\\!\\!\\bigcirc\\!\\!\\!\\!\\!\\!\\int_{S}}\\ (\\nabla\\times \\boldsymbol{a})\\cdot\\boldsymbol{n}\\ dS \\\\
\n&=& 0
\n\\end{eqnarray}<\/p>\n

\u6df7\u4e71\u306f\u7121\u304f\u306a\u308b\u3068\u601d\u3046\u306e\u3067\u3042\u308b\u304c\uff0c\u3044\u304b\u304c\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n

\u304a\u3055\u3089\u3044\u3068\u3057\u3066\u306e\u7df4\u7fd2\u554f\u984c<\/h3>\n

\u4ee5\u4e0a\u306e\u8a71\u3092\u7df4\u7fd2\u554f\u984c\u3068\u3057\u3066\u307e\u3068\u3081\u3066\u307f\u305f\u3002<\/p>\n

1. \u52fe\u914d\u306e1\u5468\u7dda\u7a4d\u5206<\/h4>\n

\u4efb\u610f\u306e\u30b9\u30ab\u30e9\u30fc\u5834\uff08\u7a7a\u9593\u5ea7\u6a19\u306e\u95a2\u6570\u3067\u3042\u308b\u30b9\u30ab\u30e9\u30fc\u95a2\u6570\uff09 $\\psi(\\boldsymbol{r})$ \u306e\u52fe\u914d $\\nabla \\psi$ \u306b\u3064\u3044\u3066\uff0c\u4ee5\u4e0b\u3092\u793a\u305b\u3002<\/p>\n

$$\\oint_C\\ (\\nabla \\psi)\\cdot d\\boldsymbol{r} = 0$$<\/p>\n

\u3053\u3053\u3067 $C$ \u306f\u4efb\u610f\u306e\u9589\u66f2\u7dda\u3067\u3042\u308b\u3002<\/p>\n

2. \u56de\u8ee2\u306e\u5782\u76f4\u6210\u5206\u306e\u9589\u66f2\u9762\u7a4d\u5206<\/h4>\n

\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb\u5834\uff08\u5404\u6210\u5206\u304c\u7a7a\u9593\u5ea7\u6a19\u306e\u95a2\u6570\u3067\u3042\u308b\u30d9\u30af\u30c8\u30eb\uff09 $\\boldsymbol{a}$ \u306e\u56de\u8ee2 $\\nabla\\times\\boldsymbol{a}$ \u306b\u3064\u3044\u3066\uff0c\u4ee5\u4e0b\u3092\u793a\u305b\u3002<\/p>\n

$$\\iint_S\\ (\\nabla\\times\\boldsymbol{a})\\cdot\\boldsymbol{n}\\, dS = 0$$<\/p>\n

\u3053\u3053\u3067\uff0c$S$ \u306f\u4efb\u610f\u306e\u9589\u66f2\u9762\u3067\u3042\u308a\uff0c$\\boldsymbol{n}$ \u306f\u9589\u66f2\u9762 $S$ \u306b\u5782\u76f4\u306a\u5358\u306b\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u3002<\/p>\n

\u7df4\u7fd2\u554f\u984c\u306e\u89e3\u7b54\u4f8b<\/h3>\n

1. \u306b\u3064\u3044\u3066\u306f\uff0c\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406\u3092\u4f7f\u3063\u3066\u9762\u7a4d\u5206\u306b\u3057\u3066…<\/p>\n

\\begin{eqnarray}
\n\\oint_C\\ (\\nabla \\psi)\\cdot d\\boldsymbol{r} &=&
\n\\iint_S \\bigl( \\nabla \\times (\\nabla\\psi)\\bigr)\\cdot\\boldsymbol{n}\\, dS\\\\
\n&=& \\iint_S \\boldsymbol{0}\\cdot\\boldsymbol{n}\\, dS \\\\
\n&=& 0
\n\\end{eqnarray}<\/p>\n

\u3053\u3053\u3067 $S$ \u306f\u9589\u66f2\u7dda $C$ \u3092\u5883\u754c\u3068\u3059\u308b\u66f2\u9762\u3067\u3042\u308a\uff0c\u30d9\u30af\u30c8\u30eb\u89e3\u6790\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\boldsymbol{0}$ \u3092\u4f7f\u3063\u305f\u3002<\/p>\n

2. \u306b\u3064\u3044\u3066\u306f\uff0c\u601d\u308f\u305a\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406\u3092\u4f7f\u3063\u3066…<\/p>\n

\\begin{eqnarray}
\n\\iint_S\\ (\\nabla\\times\\boldsymbol{a})\\cdot\\boldsymbol{n}\\, dS &=&
\n\\oint_C \\ \\boldsymbol{a}\\cdot d\\boldsymbol{r} \\\\
\n&=& \\cdots
\n\\end{eqnarray}<\/p>\n

\u3068\u3057\u3066\u3057\u307e\u3044\u305d\u3046\u3060\u304c\uff0c\u306f\u3066\uff0c\u9589\u66f2\u9762 $S$ \u306e\u5883\u754c\u3068\u306a\u308b $C$ \u306f\u3069\u3093\u306a\u9589\u66f2\u7dda\u3068\u306a\u308b\u3093\u3060\u308d\u3046\u304b\uff1f\u3068\u60a9\u3093\u3067\u3057\u307e\u3046\u306e\u3067\uff0c\u3053\u3053\u306f\u30ac\u30a6\u30b9\u306e\u5b9a\u7406\u3092\u4f7f\u3063\u3066\u4f53\u7a4d\u7a4d\u5206\u306b\u3057\u3066…<\/p>\n

\\begin{eqnarray}
\n\\iint_S\\ (\\nabla\\times\\boldsymbol{a})\\cdot\\boldsymbol{n}\\, dS &=&
\n\\iiint_V\\ \\nabla\\cdot(\\nabla\\times\\boldsymbol{a})\\, dV \\\\
\n&=& 0
\n\\end{eqnarray}<\/p>\n

\u3053\u3053\u3067 $V$ \u306f\u9589\u66f2\u9762 $S$ \u3067\u56f2\u307e\u308c\u305f\u9818\u57df\u306e\u4f53\u7a4d\u3067\u3042\u308a\uff0c\u30d9\u30af\u30c8\u30eb\u89e3\u6790\u306e\u6052\u7b49\u5f0f $\\nabla\\cdot(\\nabla\\times\\boldsymbol{a}) = 0$ \u3092\u4f7f\u3063\u305f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u30d9\u30af\u30c8\u30eb\u5834\uff08\u542b\u30b9\u30ab\u30e9\u30fc\u5834\uff09\u306e2\u968e\u504f\u5fae\u5206\u306e\u6052\u7b49\u5f0f $\\nabla \\times (\\nabla\\psi) = \\boldsymbol{0}$ \u3068 $\\nabla\\cdot (\\nabla\\times \\boldsymbol{a}) = 0$ \u306e\u9762\u7a4d\u5206\u3084\u4f53\u7a4d\u7a4d\u5206\u306b\u3064\u3044\u3066\uff0c\u3042\u3089\u305f\u3081\u3066\u307e\u3068\u3081\u3066\u304a\u304f\u3002<\/p>

\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":2615,"menu_order":20,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-10505","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/10505","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=10505"}],"version-history":[{"count":43,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/10505\/revisions"}],"predecessor-version":[{"id":10556,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/10505\/revisions\/10556"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2615"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=10505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}