id stringlengths 9 9 | relative_image_path stringlengths 19 19 | conversations listlengths 2 2 | image imagewidth (px) 12 5.38k | task stringclasses 1
value |
|---|---|---|---|---|
000000000 | 00000/000000000.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[g _ {k} (v, 0) = e ^ {- v ^ {2}},\\]"
}
] | fr | |
000000001 | 00000/000000001.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[(\\gamma , v _ {2}, \\theta_ {*}),\\]"
}
] | fr | |
000000002 | 00000/000000002.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\mathrm{H} _ {3} ^ {+} + \\mathrm{X} \\longrightarrow \\mathrm{XH} ^ {+} + \\mathrm{H} _ {2},\\]"
}
] | fr | |
000000003 | 00000/000000003.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\mathrm {BASIC\\_GSEE} (w / 2, \\delta / 3, \\eta , 2, m + 2)\\]"
}
] | fr | |
000000004 | 00000/000000004.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\begin{array}{r l} {T (r)} & {= \\frac {R _ {2} ^ {2}}{4 D} \\log r - \\frac {r ^ {2}}{8 D} + \\frac {R _ {1} ^ {2}}{8 D} - \\frac {R _ {2} ^ {2}}{4 D} \\log R _ {1}} \\\\ & {= \\frac {R _ {2} ^ {2}}{4 ... | fr | |
000000005 | 00000/000000005.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[65 \\%\\]"
}
] | fr | |
000000006 | 00000/000000006.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\kappa\\]"
}
] | fr | |
000000007 | 00000/000000007.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[J\\]"
}
] | fr | |
000000008 | 00000/000000008.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\tau\\]"
}
] | fr | |
000000009 | 00000/000000009.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\rho_ {j}\\]"
}
] | fr | |
000000010 | 00000/000000010.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[t _ {0}\\]"
}
] | fr | |
000000011 | 00000/000000011.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[r _ {\\mathrm{crit}} = \\ell / 5\\]"
}
] | fr | |
000000012 | 00000/000000012.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\sum_ {m} [ U _ {\\mathrm{O}} ] _ {m, n _ {\\mathrm{min}}} \\cdot [ U _ {\\mathrm{O}} ] _ {m, n _ {\\mathrm{min}} + 1} = 0\\]"
}
] | fr | |
000000013 | 00000/000000013.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\Phi_ {R}, \\Psi_ {R}\\]"
}
] | fr | |
000000014 | 00000/000000014.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[k = \\nu + \\mu \\bar {b}\\]"
}
] | fr | |
000000015 | 00000/000000015.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[V _ {D} (r) = \\frac {1}{r} - f \\sqrt {\\frac {N _ {c}}{2 (N _ {c} - 1)}} \\ln [ e x p (2 m r) - 1 ]\\]"
}
] | fr | |
000000016 | 00000/000000016.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\sim 14\\%\\]"
}
] | fr | |
000000017 | 00000/000000017.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[k\\]"
}
] | fr | |
000000018 | 00000/000000018.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[g\\]"
}
] | fr | |
000000019 | 00000/000000019.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\Delta^ {*}\\]"
}
] | fr | |
000000020 | 00000/000000020.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\left. \\frac {\\mathrm{d} \\Phi_ {B}}{\\mathrm{d} t} \\right| _ {t = t _ {0}} = \\left(\\int_ {\\Sigma (t _ {0})} \\left. \\frac {\\partial \\mathbf {B}}{\\partial t} \\right| _ {t = t _ {0}} \\cdot \\... | fr | |
000000021 | 00000/000000021.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[t ^ {\\prime}\\]"
}
] | fr | |
000000022 | 00000/000000022.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\bar {\\rho}\\]"
}
] | fr | |
000000023 | 00000/000000023.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[0. 3 5 \\leq y _ {2 0} \\leq 0. 4 5\\]"
}
] | fr | |
000000024 | 00000/000000024.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\overline {{\\phi}} (x) = \\phi_ {c}\\]"
}
] | fr | |
000000025 | 00000/000000025.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\theta_ {m}\\]"
}
] | fr | |
000000026 | 00000/000000026.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[i _ {\\alpha} (a \\wedge b) = (i _ {\\alpha} a) \\wedge b + (- 1) ^ {\\deg a} a \\wedge (i _ {\\alpha} b).\\]"
}
] | fr | |
000000027 | 00000/000000027.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[2 1 4. 2\\]"
}
] | fr | |
000000028 | 00000/000000028.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\Lambda > 2 \\pi / k _ {n}\\]"
}
] | fr | |
000000029 | 00000/000000029.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[P\\]"
}
] | fr | |
000000030 | 00000/000000030.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\begin{array}{c} {1, z > t h,} \\\\ {0, z \\leq t h,} \\end{array}\\]"
}
] | fr | |
000000031 | 00000/000000031.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\sigma\\]"
}
] | fr | |
000000032 | 00000/000000032.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\tilde {g} _ {m n} ^ {\\prime} (\\tau) = \\dot {\\tilde {g}} _ {m n} \\tau^ {\\prime}, \\qquad \\tilde {g} _ {m n} ^ {\\prime \\prime} (\\tau) = \\ddot {\\tilde {g}} _ {m n} + \\dot {\\tilde {g}} _ {m n... | fr | |
000000033 | 00000/000000033.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\{K _ {x}: x \\in X \\}\\]"
}
] | fr | |
000000034 | 00000/000000034.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\Phi_ {4} ^ {- 1} \\Pi_ {S ^ {\\perp}} \\partial_ {x} M _ {3} \\Phi_ {4} = \\Pi_ {S ^ {\\perp}} \\partial_ {x} O p ^ {W} \\left(\\mathtt {m} _ {\\alpha} m _ {1, \\alpha} (\\xi) + \\frac {T _ {\\alpha}}{... | fr | |
000000035 | 00000/000000035.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\int_ {0} ^ {1} p _ {g} (w, s; \\mu_ {t _ {a}}, \\mu_ {t _ {b}}, \\sigma_ {a}, \\sigma_ {b}, N) d w = \\frac {\\sqrt {\\pi} \\Gamma (\\frac {N}{2})}{2 ^ {N - 1} \\mu^ {\\frac {N - 1}{2}}} I _ {\\frac {N... | fr | |
000000036 | 00000/000000036.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\wp (z) = - \\frac {d ^ {2}}{d z ^ {2}} \\ln [ \\sigma (z) ].\\]"
}
] | fr | |
000000037 | 00000/000000037.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[V\\]"
}
] | fr | |
000000038 | 00000/000000038.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\langle N _ {D} \\rangle \\approx 1. 4 2 5 \\cdot 1 0 ^ {2 1}\\]"
}
] | fr | |
000000039 | 00000/000000039.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\alpha = 0. 2\\]"
}
] | fr | |
000000040 | 00000/000000040.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[F = R \\cdot U = {\\left[ \\begin{array}{l l l} \\cos \\theta & \\sin \\theta & 0 \\\\ - \\sin \\theta & \\cos \\theta & 0 \\\\ 0 & 0 & 1 \\end{array} \\right]} {\\left[ \\begin{array}{l l l} \\lambda_ {... | fr | |
000000041 | 00000/000000041.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[H _ {\\mathrm{eff}} ^ {0} = \\frac {G _ {\\mathrm{F}}}{\\sqrt {2}} V _ {c b} V _ {c s} ^ {*} (\\bar {c} b) _ {V - A} (\\bar {s} c) _ {V - A},\\]"
}
] | fr | |
000000042 | 00000/000000042.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[= 1\\]"
}
] | fr | |
000000043 | 00000/000000043.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\alpha\\]"
}
] | fr | |
000000044 | 00000/000000044.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[H = \\sum_ {j} E _ {j} \\left| E _ {j} \\right> \\left< E _ {j} \\right|\\]"
}
] | fr | |
000000045 | 00000/000000045.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\rightarrow\\]"
}
] | fr | |
000000046 | 00000/000000046.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[S _ {\\mathrm{c}}\\]"
}
] | fr | |
000000047 | 00000/000000047.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\phi \\in [ - \\pi / 2, \\pi / 2 ]\\]"
}
] | fr | |
000000048 | 00000/000000048.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[k = 1\\]"
}
] | fr | |
000000049 | 00000/000000049.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[U _ {\\mathrm{c}}\\]"
}
] | fr | |
000000050 | 00000/000000050.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\begin{array}{r l} \\| u - f \\| _ {C ^ {\\ell , \\alpha}} & \\leq \\| u - v \\| _ {C ^ {\\ell , \\alpha}} + \\| v - f _ {\\delta} \\| _ {C ^ {\\ell , \\alpha}} + \\| (1 - \\delta) (\\bar {w} - f) \\| _... | fr | |
000000051 | 00000/000000051.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[v _ {0} ^ {2} = v _ {r o t} ^ {2} (R _ {0}) = \\frac {G}{R _ {0}} [ M _ {v i s} + M _ {h a l o} ],\\]"
}
] | fr | |
000000052 | 00000/000000052.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\ell = 1\\]"
}
] | fr | |
000000053 | 00000/000000053.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[H _ {0}: \\theta = 0. 5\\]"
}
] | fr | |
000000054 | 00000/000000054.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[B P G L (2)\\]"
}
] | fr | |
000000055 | 00000/000000055.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[0. 8 4\\]"
}
] | fr | |
000000056 | 00000/000000056.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[= \\sum_ {j = 1} ^ {| n \\oplus m / 2 |} \\sum_ {j ^ {\\prime} = 1} ^ {| n |} c _ {2 j - 1} c _ {2 j ^ {\\prime} - 1} \\left(\\frac {1}{2} \\{\\gamma_ {2 j - 1}, \\gamma_ {2 j ^ {\\prime} - 1} \\} + \\fr... | fr | |
000000057 | 00000/000000057.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[m _ {\\nu} m _ {\\nu} ^ {\\dagger} = \\left( \\begin{array}{l l l} a ^ {2} + a ^ {2} & 0 & a ^ {\\prime} c \\\\ 0 & b ^ {2} & b b ^ {\\prime} \\\\ a ^ {\\prime} c & b b ^ {\\prime} & b ^ {2} + c ^ {2} \\... | fr | |
000000058 | 00000/000000058.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\kappa_ {n}\\]"
}
] | fr | |
000000059 | 00000/000000059.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[h _ {w m} ^ {+}\\]"
}
] | fr | |
000000060 | 00000/000000060.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[y -\\]"
}
] | fr | |
000000061 | 00000/000000061.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\begin{array}{r l r} {i \\textbf {I} _ {\\{N 2 i + \\}} \\circ \\mathbb {N} ^ {+} =} & & {i \\textbf {I} _ {\\{N 2 i + \\}} \\circ (i N _ {1 0} ^ {i +} + N _ {1 0} ^ {+}} \\\\ & & {+ i N _ {1} ^ {i +} \... | fr | |
000000062 | 00000/000000062.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\begin{array}{r l} \\nabla \\mathcal {L} (\\mathbf {x}) & = \\nabla \\mathcal {L} _ {p} (\\mathbf {x}) + \\beta \\nabla^ {2} \\mathcal {L} _ {p} (\\mathbf {x}) \\cdot \\nabla \\mathcal {L} _ {p} (\\math... | fr | |
000000063 | 00000/000000063.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[0. 0 1\\]"
}
] | fr | |
000000064 | 00000/000000064.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\int_ {t} ^ {+ \\infty} x ^ {k} e ^ {- \\tau (x)} d x \\leq \\frac {1}{a \\left(1 - \\frac {2 k + 2}{\\tau (t)}\\right)} t ^ {2 k + 2} e ^ {- \\tau (t)}.\\]"
}
] | fr | |
000000065 | 00000/000000065.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\epsilon_ {1} = \\frac {L _ {\\mathrm{B}} - L _ {\\mathrm{C}}}{2 \\overline {{L}}}, \\epsilon_ {2} = \\frac {L _ {\\mathrm{C}} + L _ {\\mathrm{B}} - 2 L _ {\\mathrm{A}}}{6 \\overline {{L}}}\\]"
}
] | fr | |
000000066 | 00000/000000066.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\mathcal {B} _ {p} ^ {(n)} = \\frac {1}{2} \\left(\\mathcal {B} _ {p} ^ {(n + \\frac {1}{2})} + \\mathcal {B} _ {p} ^ {(n - \\frac {1}{2})}\\right)\\]"
}
] | fr | |
000000067 | 00000/000000067.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\int_ {0} ^ {\\infty} \\frac {z}{\\sqrt {z ^ {3} + 1 4}} d z\\]"
}
] | fr | |
000000068 | 00000/000000068.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\nabla_ {\\mathbf {d} _ {t}} \\log q (\\mathbf {d} _ {t} | \\mathbf {d} _ {0}) = - \\frac {\\mathbf {d} _ {t} - \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {d} _ {0}}{1 - \\bar {\\alpha} _ {t}}\\]"
}
] | fr | |
000000069 | 00000/000000069.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\hat {Q} ^ {2} = i \\hbar (- 1) ^ {\\varepsilon_ {i}} L _ {m} \\sigma_ {, i \\alpha} ^ {m} \\left(\\frac {\\delta W}{\\delta J} + \\frac {\\hbar}{i} \\frac {\\delta}{\\delta J}, \\psi\\right) \\left[ \\... | fr | |
000000070 | 00000/000000070.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\pi (E): L ^ {2} (\\mu) \\to L ^ {2} (\\mu): \\psi \\mapsto \\chi_ {E} \\psi\\]"
}
] | fr | |
000000071 | 00000/000000071.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[V _ {1} / T _ {1} = V _ {2} / T _ {2}\\]"
}
] | fr | |
000000072 | 00000/000000072.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\theta_ {\\mathrm{div}}\\]"
}
] | fr | |
000000073 | 00000/000000073.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[H _ {2} ^ {(1)} (z) \\sim \\frac {2}{z ^ {2}} + \\frac {1}{2} + O (z ^ {2}, z ^ {4} \\cdot \\cdot),\\]"
}
] | fr | |
000000074 | 00000/000000074.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\begin{array}{r l} {R _ {1} (x, y)} & {= R _ {1} (\\bar {x}, y) + \\frac {\\partial R _ {1}}{\\partial x} (\\bar {x}, y) (x - \\bar {x}) + \\mathcal {O} \\big (\\| x - \\bar {x} \\| ^ {2} \\big),} \\\\ ... | fr | |
000000075 | 00000/000000075.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[w _ {j i} ^ {I}\\]"
}
] | fr | |
000000076 | 00000/000000076.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\sigma_ {y}\\]"
}
] | fr | |
000000077 | 00000/000000077.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[1 ^ {\\circ} \\mathrm{C}\\]"
}
] | fr | |
000000078 | 00000/000000078.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[= \\frac {1}{x} + \\frac {1}{z} - \\zeta (2) (z + x) + \\ldots\\]"
}
] | fr | |
000000079 | 00000/000000079.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\{v _ {\\Delta} ^ {I}, v _ {\\Delta} ^ {J}, v _ {\\Delta} ^ {K}, v _ {\\Delta} ^ {L 1}, v _ {\\Delta} ^ {L 2}, v _ {\\Delta} ^ {M 1}, v _ {\\Delta} ^ {M 2}, v _ {\\Delta} ^ {N 1}, v _ {\\Delta} ^ {N 2} ... | fr | |
000000080 | 00000/000000080.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\zeta \\equiv \\frac {g _ {1}}{g _ {8}} \\simeq - 1\\]"
}
] | fr | |
000000081 | 00000/000000081.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\widetilde {\\Phi} _ {p p} = \\frac {\\widetilde {\\omega} \\left(\\Pi^ {6 . 7 1} + (\\beta + 1) ^ {1 . 4}\\right)}{\\widetilde {\\omega} ^ {0 . 8 7} \\Delta^ {0 . 9 8} M ^ {0 . 4 4} (1 + M ^ {0 . 9 7})... | fr | |
000000082 | 00000/000000082.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\sigma_ {y} \\{[ t _ {1} \\sin (q _ {y} b) - t _ {3} \\sin (q _ {x} b) ] J _ {0} (K _ {y 1}) - t _ {2} \\sin [ (q _ {x} - q _ {y}) b ] J _ {0} (K _ {x 1}) \\}\\]"
}
] | fr | |
000000083 | 00000/000000083.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\begin{array}{r l} & {\\mathbb {E} _ {\\theta} \\ell (\\theta) \\leq \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\ell (\\theta_ {i}) + 2 \\mathcal {R} _ {N} (\\mathcal {L}) + \\sqrt {\\frac {\\log \\frac {1}{\\... | fr | |
000000084 | 00000/000000084.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[S _ {\\mathrm{~kink}} = S ^ {(-)} - S ^ {(+)}\\]"
}
] | fr | |
000000085 | 00000/000000085.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[T _ {\\mathrm{init}}\\]"
}
] | fr | |
000000086 | 00000/000000086.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\mu \\partial_ {j} (f \\mathcal {C} _ {i j}) / \\tau_ {p}\\]"
}
] | fr | |
000000087 | 00000/000000087.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\sim\\]"
}
] | fr | |
000000088 | 00000/000000088.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[F (x) = \\int f (x) d x.\\]"
}
] | fr | |
000000089 | 00000/000000089.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[f (x, y) = e ^ {x} \\sin y\\]"
}
] | fr | |
000000090 | 00000/000000090.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\sigma (E)\\]"
}
] | fr | |
000000091 | 00000/000000091.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\frac {\\partial (\\tilde {\\rho} \\overline {{u}} _ {i})}{\\partial t} + \\frac {\\partial (\\tilde {\\rho} \\overline {{u}} _ {j} \\overline {{u}} _ {i})}{\\partial x _ {j}} = - \\frac {\\partial \\ti... | fr | |
000000092 | 00000/000000092.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[^ \\circ\\]"
}
] | fr | |
000000093 | 00000/000000093.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[(z _ {+} + z _ {-}) / \\bar {a} = z _ {+} ^ {2} z _ {-} / a _ {+} + z _ {-} ^ {2} z _ {+} / a _ {-}\\]"
}
] | fr | |
000000094 | 00000/000000094.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[L = 7\\]"
}
] | fr | |
000000095 | 00000/000000095.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[\\begin{array}{r l} {X} & {= \\{1, 2, \\ldots , n \\} = \\{i \\in \\mathbb {N} \\mid 1 \\leq i \\leq n \\}} \\\\ {Y} & {= \\{a _ {1}, a _ {2}, \\ldots , a _ {n} \\}} \\\\ {F} & {= \\{(1, a _ {1}), (2, a ... | fr | |
000000096 | 00000/000000096.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[V _ {1} ^ {1 / 4} (- M _ {\\mathrm{P}}) \\geq 1 0 ^ {- 5} M _ {\\mathrm{P}}.\\]"
}
] | fr | |
000000097 | 00000/000000097.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[3 6. 8\\]"
}
] | fr | |
000000098 | 00000/000000098.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[3 0\\]"
}
] | fr | |
000000099 | 00000/000000099.png | [
{
"from": "human",
"value": "<image>\nFormula Recognition:"
},
{
"from": "gpt",
"value": "\\[1 0\\]"
}
] | fr |
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