ag-gipp/GoUldI

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data/305.json

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{
  "constraints": [],
  "comment": "NTCIR 12 wiki topic 28",
  "math_inputtex": "\\varphi(\\lambda_1 x_1+\\lambda_2 x_2+\\cdots+\\lambda_n x_n)\\leq \\lambda_1\\,\\varphi(x_1)+\\lambda_2\\,\\varphi(x_2)+\\cdots+\\lambda_n\\,\\varphi(x_n),",
  "correct_tex": "\\varphi(\\lambda_1 x_1+\\lambda_2 x_2+\\cdots+\\lambda_n x_n)\\leq \\lambda_1 \\varphi(x_1)+\\lambda_2\\,\\varphi(x_2)+\\cdots+\\lambda_n \\varphi(x_n)",
  "math_inputtex_semantic": "\\wf{Q11348}{\\varphi}(\\w{Q1413083}{\\lambda}_1 \\w{Q50701}{x}_1+\\lambda_2 x_2+\\cdots+\\lambda_n x_n)\\leq \\lambda_1\\,\\varphi(x_1)+\\lambda_2\\,\\varphi(x_2)+\\cdots+\\lambda_n\\,\\varphi(x_n)",
  "title": "Jensen's inequality",
  "type": "relation",
  "uri": "https://en.wikipedia.org/w/index.php?title=Jensen%27s_inequality&oldid=809566303#Proof_1_(finite_form)",
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id=\"p1.1.m1.1.49.1.2.1.1.2\" xref=\"p1.1.m1.1.49.1.2.1.1.2.cmml\">\n                <mi id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.3.cmml\">λ</mi>\n                <mn id=\"p1.1.m1.1.4.1\" xref=\"p1.1.m1.1.4.1.cmml\">1</mn>\n              </msub>\n              <mo id=\"p1.1.m1.1.49.1.2.1.1.1\" xref=\"p1.1.m1.1.49.1.2.1.1.1.cmml\">⁢</mo>\n              <msub id=\"p1.1.m1.1.49.1.2.1.1.3\" xref=\"p1.1.m1.1.49.1.2.1.1.3.cmml\">\n                <mi id=\"p1.1.m1.1.5\" xref=\"p1.1.m1.1.5.cmml\">x</mi>\n                <mn id=\"p1.1.m1.1.6.1\" xref=\"p1.1.m1.1.6.1.cmml\">1</mn>\n              </msub>\n            </mrow>\n            <mo id=\"p1.1.m1.1.7\" xref=\"p1.1.m1.1.7.cmml\">+</mo>\n            <mrow id=\"p1.1.m1.1.49.1.2.1.2\" xref=\"p1.1.m1.1.49.1.2.1.2.cmml\">\n              <msub id=\"p1.1.m1.1.49.1.2.1.2.2\" xref=\"p1.1.m1.1.49.1.2.1.2.2.cmml\">\n                <mi id=\"p1.1.m1.1.8\" xref=\"p1.1.m1.1.8.cmml\">λ</mi>\n                <mn id=\"p1.1.m1.1.9.1\" xref=\"p1.1.m1.1.9.1.cmml\">2</mn>\n              </msub>\n              <mo id=\"p1.1.m1.1.49.1.2.1.2.1\" xref=\"p1.1.m1.1.49.1.2.1.2.1.cmml\">⁢</mo>\n              <msub id=\"p1.1.m1.1.49.1.2.1.2.3\" xref=\"p1.1.m1.1.49.1.2.1.2.3.cmml\">\n                <mi id=\"p1.1.m1.1.10\" xref=\"p1.1.m1.1.10.cmml\">x</mi>\n                <mn id=\"p1.1.m1.1.11.1\" xref=\"p1.1.m1.1.11.1.cmml\">2</mn>\n              </msub>\n            </mrow>\n            <mo id=\"p1.1.m1.1.7a\" xref=\"p1.1.m1.1.7.cmml\">+</mo>\n            <mi mathvariant=\"normal\" id=\"p1.1.m1.1.13\" xref=\"p1.1.m1.1.13.cmml\">⋯</mi>\n            <mo id=\"p1.1.m1.1.7b\" xref=\"p1.1.m1.1.7.cmml\">+</mo>\n            <mrow id=\"p1.1.m1.1.49.1.2.1.3\" xref=\"p1.1.m1.1.49.1.2.1.3.cmml\">\n              <msub id=\"p1.1.m1.1.49.1.2.1.3.2\" xref=\"p1.1.m1.1.49.1.2.1.3.2.cmml\">\n                <mi id=\"p1.1.m1.1.15\" xref=\"p1.1.m1.1.15.cmml\">λ</mi>\n                <mi id=\"p1.1.m1.1.16.1\" xref=\"p1.1.m1.1.16.1.cmml\">n</mi>\n              </msub>\n              <mo id=\"p1.1.m1.1.49.1.2.1.3.1\" xref=\"p1.1.m1.1.49.1.2.1.3.1.cmml\">⁢</mo>\n              <msub id=\"p1.1.m1.1.49.1.2.1.3.3\" xref=\"p1.1.m1.1.49.1.2.1.3.3.cmml\">\n                <mi id=\"p1.1.m1.1.17\" xref=\"p1.1.m1.1.17.cmml\">x</mi>\n                <mi id=\"p1.1.m1.1.18.1\" xref=\"p1.1.m1.1.18.1.cmml\">n</mi>\n              </msub>\n            </mrow>\n          </mrow>\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.19\" xref=\"p1.1.m1.1.49.1.1.cmml\">)</mo>\n        </mrow>\n      </mrow>\n      <mo id=\"p1.1.m1.1.20\" xref=\"p1.1.m1.1.20.cmml\">≤</mo>\n      <mrow id=\"p1.1.m1.1.49.2\" xref=\"p1.1.m1.1.49.2.cmml\">\n        <mrow id=\"p1.1.m1.1.49.2.1\" xref=\"p1.1.m1.1.49.2.1.cmml\">\n          <mpadded width=\"+1.7pt\" id=\"p1.1.m1.1.49.2.1.2\" xref=\"p1.1.m1.1.49.2.1.2.cmml\">\n            <msub id=\"p1.1.m1.1.49.2.1.2a\" xref=\"p1.1.m1.1.49.2.1.2.cmml\">\n              <mi id=\"p1.1.m1.1.21\" xref=\"p1.1.m1.1.21.cmml\">λ</mi>\n      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xref=\"p1.1.m1.1.41.cmml\">λ</mi>\n              <mi id=\"p1.1.m1.1.42.1\" xref=\"p1.1.m1.1.42.1.cmml\">n</mi>\n            </msub>\n          </mpadded>\n          <mo id=\"p1.1.m1.1.49.2.3.1\" xref=\"p1.1.m1.1.49.2.3.1.cmml\">⁢</mo>\n          <mrow id=\"p1.1.m1.1.49.2.3.3.2\" xref=\"p1.1.m1.1.49.2.3.3.1.cmml\">\n            <mi id=\"p1.1.m1.1.44\" xref=\"p1.1.m1.1.44.cmml\">φ</mi>\n            <mo id=\"p1.1.m1.1.49.2.3.3.2a\" xref=\"p1.1.m1.1.49.2.3.3.1.cmml\">⁡</mo>\n            <mrow id=\"p1.1.m1.1.49.2.3.3.2.2\" xref=\"p1.1.m1.1.49.2.3.3.1.cmml\">\n              <mo stretchy=\"false\" id=\"p1.1.m1.1.45\" xref=\"p1.1.m1.1.49.2.3.3.1.cmml\">(</mo>\n              <msub id=\"p1.1.m1.1.49.2.3.3.2.1\" xref=\"p1.1.m1.1.49.2.3.3.2.1.cmml\">\n                <mi id=\"p1.1.m1.1.46\" xref=\"p1.1.m1.1.46.cmml\">x</mi>\n                <mi id=\"p1.1.m1.1.47.1\" xref=\"p1.1.m1.1.47.1.cmml\">n</mi>\n              </msub>\n              <mo stretchy=\"false\" id=\"p1.1.m1.1.48\" xref=\"p1.1.m1.1.49.2.3.3.1.cmml\">)</mo>\n            </mrow>\n          </mrow>\n        </mrow>\n      </mrow>\n    </mrow>\n    <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n      <apply id=\"p1.1.m1.1.49.cmml\" xref=\"p1.1.m1.1.49\">\n        <leq id=\"p1.1.m1.1.20.cmml\" xref=\"p1.1.m1.1.20\"/>\n        <apply id=\"p1.1.m1.1.49.1.1.cmml\" xref=\"p1.1.m1.1.49.1.2\">\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">Q11348</csymbol>\n          <apply id=\"p1.1.m1.1.49.1.2.1.cmml\" xref=\"p1.1.m1.1.49.1.2.1\">\n            <plus id=\"p1.1.m1.1.7.cmml\" xref=\"p1.1.m1.1.7\"/>\n            <apply id=\"p1.1.m1.1.49.1.2.1.1.cmml\" xref=\"p1.1.m1.1.49.1.2.1.1\">\n              <times id=\"p1.1.m1.1.49.1.2.1.1.1.cmml\" xref=\"p1.1.m1.1.49.1.2.1.1.1\"/>\n              <apply id=\"p1.1.m1.1.49.1.2.1.1.2.cmml\" xref=\"p1.1.m1.1.49.1.2.1.1.2\">\n                <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.49.1.2.1.1.2.1.cmml\" 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}