73 lines
91 KiB
Plaintext
73 lines
91 KiB
Plaintext
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src="/images/math/1/c/0/1c00b7e0e828c0f44e484919b9e0174e.png" />";}i:145;a:2:{i:0;s:41:"\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx";i:1;s:129:"<img class="tex" alt="\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx" src="/images/math/4/0/7/40764d04d428b630657f305cba34c985.png" />";}i:146;a:2:{i:0;s:34:"\int_{1}^{3}\frac{e^3/x}{x^2}\, dx";i:1;s:122:"<img class="tex" alt="\int_{1}^{3}\frac{e^3/x}{x^2}\, dx" src="/images/math/d/5/e/d5e7d8bdc59d07349b3966578895a93f.png" />";}i:147;a:2:{i:0;s:40:"\textstyle \int\limits_{-N}^{N} e^x\, dx";i:1;s:128:"<img class="tex" alt="\textstyle \int\limits_{-N}^{N} e^x\, dx" src="/images/math/9/1/9/9194fdfb9704fa475c5ae486a56041ea.png" />";}i:148;a:2:{i:0;s:33:"\textstyle \int_{-N}^{N} e^x\, dx";i:1;s:121:"<img class="tex" alt="\textstyle \int_{-N}^{N} e^x\, dx" src="/images/math/1/7/2/1726000a5a8e3c02cea114e5b545941c.png" />";}i:149;a:2:{i:0;s:24:"\iint\limits_D \, dx\,dy";i:1;s:112:"<img class="tex" alt="\iint\limits_D \, dx\,dy" src="/images/math/4/a/b/4abac8d616c5670900504ddce25a4a4b.png" />";}i:150;a:2:{i:0;s:29:"\iiint\limits_E \, dx\,dy\,dz";i:1;s:117:"<img class="tex" alt="\iiint\limits_E \, dx\,dy\,dz" src="/images/math/6/e/9/6e9a4e709d965b32de1ab3d16aca388a.png" />";}i:151;a:2:{i:0;s:34:"\iiiint\limits_F \, dx\,dy\,dz\,dt";i:1;s:122:"<img class="tex" alt="\iiiint\limits_F \, dx\,dy\,dz\,dt" src="/images/math/4/9/0/49005f50f3ba2dfade3a265ebe363ee9.png" />";}i:152;a:2:{i:0;s:38:"\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy";i:1;s:126:"<img class="tex" alt="\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy" src="/images/math/c/f/c/cfcc65ff7c8970aac316f359a9aaf928.png" />";}i:153;a:2:{i:0;s:39:"\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy";i:1;s:127:"<img class="tex" alt="\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy" src="/images/math/d/6/c/d6c5bf8e05426a4b56804937b9ffb559.png" />";}i:154;a:2:{i:0;s:20:"\bigcap_{i=_1}^n E_i";i:1;s:108:"<img class="tex" alt="\bigcap_{i=_1}^n E_i" src="/images/math/8/3/d/83d87c98d958c7c2db86180b49230b65.png" />";}i:155;a:2:{i:0;s:20:"\bigcup_{i=_1}^n E_i";i:1;s:108:"<img class="tex" alt="\bigcup_{i=_1}^n E_i" src="/images/math/e/6/4/e6409717ec9d63567a34f9d1173ce2ae.png" />";}i:156;a:2:{i:0;s:15:"\frac{2}{4}=0.5";i:1;s:103:"<img class="tex" alt="\frac{2}{4}=0.5" src="/images/math/4/6/d/46dc0b34e0ab4e944a437720a4431d6c.png" />";}i:157;a:2:{i:0;s:18:"\tfrac{2}{4} = 0.5";i:1;s:106:"<img class="tex" alt="\tfrac{2}{4} = 0.5" src="/images/math/2/8/4/284667fc4a92790093aa59b61b3667a0.png" />";}i:158;a:2:{i:0;s:72:"\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a";i:1;s:160:"<img class="tex" alt="\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a" src="/images/math/5/a/3/5a37ae94a95c7dd603c20cd4fbe8d9e9.png" />";}i:159;a:2:{i:0;s:46:"\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a";i:1;s:134:"<img class="tex" alt="\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a" src="/images/math/6/d/0/6d099c02b3faf73f9320656217415906.png" />";}i:160;a:2:{i:0;s:60:"\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}";i:1;s:148:"<img class="tex" alt="\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}" src="/images/math/f/a/0/fa001cd2dd438152e45a44591f235148.png" />";}i:161;a:2:{i:0;s:12:"\binom{n}{k}";i:1;s:100:"<img class="tex" alt="\binom{n}{k}" src="/images/math/6/b/2/6b2be63a1b8e310465d1b538e2d7d71b.png" />";}i:162;a:2:{i:0;s:13:"\tbinom{n}{k}";i:1;s:101:"<img class="tex" alt="\tbinom{n}{k}" src="/images/math/8/4/8/8482b29cc0af31fa35ff6bf04200b265.png" />";}i:163;a:2:{i:0;s:13:"\dbinom{n}{k}";i:1;s:101:"<img class="tex" alt="\dbinom{n}{k}" src="/images/math/c/4/4/c44601a9dbb85dfb88868c14dc54c8ef.png" />";}i:164;a:2:{i:0;s:42:"\begin{matrix} x & y \\ z & v
|
|
\end{matrix}";i:1;s:142:"<img class="tex" alt="\begin{matrix} x & y \\ z & v \end{matrix}" src="/images/math/b/9/9/b99890966e1b997497211428f8e3419d.png" />";}i:165;a:2:{i:0;s:44:"\begin{vmatrix} x & y \\ z & v
|
|
\end{vmatrix}";i:1;s:144:"<img class="tex" alt="\begin{vmatrix} x & y \\ z & v \end{vmatrix}" src="/images/math/9/2/b/92b8f0e57848a80b4babd2ba93775370.png" />";}i:166;a:2:{i:0;s:44:"\begin{Vmatrix} x & y \\ z & v
|
|
\end{Vmatrix}";i:1;s:144:"<img class="tex" alt="\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}" src="/images/math/b/b/a/bba5bfd11057dbb202307584eed8f2dc.png" />";}i:167;a:2:{i:0;s:90:"\begin{bmatrix} 0 & \cdots & 0 \\ \vdots
|
|
& \ddots & \vdots \\ 0 & \cdots &
|
|
0\end{bmatrix} ";i:1;s:210:"<img class="tex" alt="\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} " src="/images/math/8/1/a/81a12a09ac84853e3d25323b8643c630.png" />";}i:168;a:2:{i:0;s:44:"\begin{Bmatrix} x & y \\ z & v
|
|
\end{Bmatrix}";i:1;s:144:"<img class="tex" alt="\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}" src="/images/math/b/f/7/bf7244e2842c8a7d55892e229560d5c1.png" />";}i:169;a:2:{i:0;s:44:"\begin{pmatrix} x & y \\ z & v
|
|
\end{pmatrix}";i:1;s:144:"<img class="tex" alt="\begin{pmatrix} x & y \\ z & v \end{pmatrix}" src="/images/math/4/4/4/444df88e616def4e275b4e920c7b872e.png" />";}i:170;a:2:{i:0;s:63:"
|
|
\bigl( \begin{smallmatrix}
|
|
a&b\\ c&d
|
|
\end{smallmatrix} \bigr)
|
|
";i:1;s:175:"<img class="tex" alt=" \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) " src="/images/math/c/d/4/cd49bbc188dce0f93fef57312af5a106.png" />";}i:171;a:2:{i:0;s:104:"f(n) =
|
|
\begin{cases}
|
|
n/2, & \text{if }n\text{ is even} \\
|
|
3n+1, & \text{if }n\text{ is odd}
|
|
\end{cases} ";i:1;s:216:"<img class="tex" alt="f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases} " src="/images/math/9/8/5/98503cc6876b22f5900297971fdd42ed.png" />";}i:172;a:2:{i:0;s:66:"
|
|
\begin{align}
|
|
f(x) & = (a+b)^2 \\
|
|
& = a^2+2ab+b^2 \\
|
|
\end{align}
|
|
";i:1;s:182:"<img class="tex" alt=" \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} " src="/images/math/2/c/5/2c50960e8bcfd9e86527a123a0c43aa2.png" />";}i:173;a:2:{i:0;s:73:"
|
|
\begin{alignat}{2}
|
|
f(x) & = (a-b)^2 \\
|
|
& = a^2-2ab+b^2 \\
|
|
\end{alignat}
|
|
";i:1;s:189:"<img class="tex" alt=" \begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} " src="/images/math/f/e/4/fe45a0df3e20bc5caf718e5333678d08.png" />";}i:174;a:2:{i:0;s:68:"\begin{array}{lcl}
|
|
z & = & a \\
|
|
f(x,y,z) & = & x + y + z
|
|
\end{array}";i:1;s:184:"<img class="tex" alt="\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}" src="/images/math/9/b/f/9bf19115bb27237fa997ca93b94ad217.png" />";}i:175;a:2:{i:0;s:68:"\begin{array}{lcr}
|
|
z & = & a \\
|
|
f(x,y,z) & = & x + y + z
|
|
\end{array}";i:1;s:184:"<img class="tex" alt="\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}" src="/images/math/0/2/a/02ae32735e1e21ba3b05984289fd2763.png" />";}i:176;a:2:{i:0;s:9:"f(x) \,\!";i:1;s:97:"<img class="tex" alt="f(x) \,\!" src="/images/math/8/d/f/8dfae20000a042d8e9047aad1d7e171e.png" />";}i:177;a:2:{i:0;s:28:"= \sum_{n=0}^\infty a_n x^n ";i:1;s:116:"<img class="tex" alt="= \sum_{n=0}^\infty a_n x^n " src="/images/math/6/6/3/6633d51d63b35281d030755a6b0aebb1.png" />";}i:178;a:2:{i:0;s:24:"= a_0+a_1x+a_2x^2+\cdots";i:1;s:112:"<img class="tex" alt="= a_0+a_1x+a_2x^2+\cdots" src="/images/math/f/e/3/fe3e268382fd486e8572daf895bd4c9d.png" />";}i:179;a:2:{i:0;s:9:"f(x) \,\!";i:1;s:97:"<img class="tex" alt="f(x) \,\!" src="/images/math/8/d/f/8dfae20000a042d8e9047aad1d7e171e.png" />";}i:180;a:2:{i:0;s:28:"= \sum_{n=0}^\infty a_n x^n ";i:1;s:116:"<img class="tex" alt="= \sum_{n=0}^\infty a_n x^n " src="/images/math/6/6/3/6633d51d63b35281d030755a6b0aebb1.png" />";}i:181;a:2:{i:0;s:25:"= a_0 +a_1x+a_2x^2+\cdots";i:1;s:113:"<img class="tex" alt="= a_0 +a_1x+a_2x^2+\cdots" src="/images/math/f/e/3/fe3e268382fd486e8572daf895bd4c9d.png" />";}i:182;a:2:{i:0;s:70:"\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}";i:1;s:158:"<img class="tex" alt="\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}" src="/images/math/6/3/4/6349be04b3562fc215c7a4e130422a96.png" />";}i:183;a:2:{i:0;s:89:"
|
|
\begin{array}{|c|c||c|} a & b & S \\
|
|
\hline
|
|
0&0&1\\
|
|
0&1&1\\
|
|
1&0&1\\
|
|
1&1&0\\
|
|
\end{array}
|
|
";i:1;s:249:"<img class="tex" alt=" \begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array} " src="/images/math/9/1/5/9151e94ef2bb52c18176dbe4c11921ed.png" />";}i:184;a:2:{i:0;s:15:"( \frac{1}{2} )";i:1;s:103:"<img class="tex" alt="( \frac{1}{2} )" src="/images/math/4/0/a/40ad9d3d1fc9a61e16d22d7e3f854fec.png" />";}i:185;a:2:{i:0;s:28:"\left ( \frac{1}{2} \right )";i:1;s:116:"<img class="tex" alt="\left ( \frac{1}{2} \right )" src="/images/math/2/8/b/28bcd5b82ce0e92b25e8a0b4bd5be215.png" />";}i:186;a:2:{i:0;s:28:"\left ( \frac{a}{b} \right )";i:1;s:116:"<img class="tex" alt="\left ( \frac{a}{b} \right )" src="/images/math/2/9/0/2905969500b40b2f2c7078206e7e0e81.png" />";}i:187;a:2:{i:0;s:75:"\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack";i:1;s:163:"<img class="tex" alt="\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack" src="/images/math/7/c/b/7cb5a74153ec87cdda6b92669ba685e1.png" />";}i:188;a:2:{i:0;s:77:"\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace";i:1;s:165:"<img class="tex" alt="\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace" src="/images/math/8/0/5/805b2e61cb380736d5366bccb844b1c7.png" />";}i:189;a:2:{i:0;s:40:"\left \langle \frac{a}{b} \right \rangle";i:1;s:128:"<img class="tex" alt="\left \langle \frac{a}{b} \right \rangle" src="/images/math/d/0/6/d06e733ce705ed26a7e048dbd2945371.png" />";}i:190;a:2:{i:0;s:72:"\left | \frac{a}{b} \right \vert \quad \left \Vert \frac{c}{d} \right \|";i:1;s:160:"<img class="tex" alt="\left | \frac{a}{b} \right \vert \quad \left \Vert \frac{c}{d} \right \|" src="/images/math/8/0/9/809fc4791f12abb16a5f9611a43469f9.png" />";}i:191;a:2:{i:0;s:85:"\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil";i:1;s:173:"<img class="tex" alt="\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil" src="/images/math/1/4/c/14c563a841b6c01dd13c5f3fa90845a1.png" />";}i:192;a:2:{i:0;s:37:"\left / \frac{a}{b} \right \backslash";i:1;s:125:"<img class="tex" alt="\left / \frac{a}{b} \right \backslash" src="/images/math/2/f/3/2f3c5907c0a4fc4fda69eb71890ce952.png" />";}i:193;a:2:{i:0;s:152:"\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow";i:1;s:240:"<img class="tex" alt="\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow" src="/images/math/d/e/7/de73c9252b269fb79408d6f791b5c3de.png" />";}i:194;a:2:{i:0;s:20:"\left [ 0,1 \right )";i:1;s:108:"<img class="tex" alt="\left [ 0,1 \right )" src="/images/math/a/3/8/a38771eae1778d0e214f6596a8dc1337.png" />";}i:195;a:2:{i:0;s:27:"\left \langle \psi \right |";i:1;s:115:"<img class="tex" alt="\left \langle \psi \right |" 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/>";}i:347;a:2:{i:0;s:59:"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots";i:1;s:147:"<img class="tex" alt="0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots" src="/images/math/4/2/f/42fbce9ee33ec5113992c9a867bfddf3.png" />";}i:348;a:2:{i:0;s:61:"{0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots}";i:1;s:149:"<img class="tex" alt="{0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots}" src="/images/math/d/3/a/d3acbcf21e8a90a92f676359b7def515.png" />";}i:349;a:2:{i:0;s:22:"\int_{-N}^{N} e^x\, dx";i:1;s:110:"<img class="tex" alt="\int_{-N}^{N} e^x\, dx" src="/images/math/4/e/0/4e053ca66cfc79a2397c40aa34c66a25.png" />";}i:350;a:2:{i:0;s:5:"\iint";i:1;s:93:"<img class="tex" alt="\iint" src="/images/math/0/e/6/0e66f8f6b272ca5db6f0b3f1c63a7560.png" />";}i:351;a:2:{i:0;s:5:"\oint";i:1;s:93:"<img class="tex" alt="\oint" src="/images/math/0/5/8/058bf10c50ba4ee074da24c60a590314.png" />";}i:352;a:2:{i:0;s:90:"\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset \mathbf D \cdot \mathrm{d}\mathbf A";i:1;s:178:"<img class="tex" alt="\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset \mathbf D \cdot \mathrm{d}\mathbf A" src="/images/math/2/e/1/2e1f7e4168ae003494bbec19102f4967.png" />";}i:353;a:2:{i:0;s:114:"\int\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\cdot\mathrm{d}\mathbf A";i:1;s:202:"<img class="tex" alt="\int\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\cdot\mathrm{d}\mathbf A" src="/images/math/4/d/0/4d0e5fd5543dece7d0ff39eff990efbb.png" />";}i:354;a:2:{i:0;s:139:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\cdot\mathrm{d}\mathbf A";i:1;s:227:"<img class="tex" alt="\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\cdot\mathrm{d}\mathbf A" src="/images/math/1/9/9/1990fe2f58972e93f7d23b3902ca925b.png" />";}i:355;a:2:{i:0;s:132:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\;\cdot\mathrm{d}\mathbf A";i:1;s:220:"<img class="tex" alt="\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\;\cdot\mathrm{d}\mathbf A" src="/images/math/d/c/5/dc59fde59ad9a9ab03d6e0eafdb6e65a.png" />";}i:356;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:104:"<img class="tex" alt="{\scriptstyle S}" src="/images/math/7/f/f/7ff140fff7dde71951767d28cb5304ac.png" />";}i:357;a:2:{i:0;s:110:"( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} ";i:1;s:198:"<img class="tex" alt="( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} " src="/images/math/f/6/d/f6d35e69f3593017cdd38fbf8e798a9f.png" />";}i:358;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:104:"<img class="tex" alt="{\scriptstyle S}" src="/images/math/7/f/f/7ff140fff7dde71951767d28cb5304ac.png" />";}i:359;a:2:{i:0;s:110:"( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} ";i:1;s:198:"<img class="tex" alt="( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} " src="/images/math/f/6/d/f6d35e69f3593017cdd38fbf8e798a9f.png" />";}i:360;a:2:{i:0;s:57:"\oint_C \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";i:1;s:145:"<img class="tex" alt="\oint_C \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 " src="/images/math/0/f/3/0f3f1a7580395190da1d7e7bba5a72e6.png" />";}i:361;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:104:"<img class="tex" alt="{\scriptstyle S}" src="/images/math/7/f/f/7ff140fff7dde71951767d28cb5304ac.png" />";}i:362;a:2:{i:0;s:96:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";i:1;s:184:"<img class="tex" alt="\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}" src="/images/math/3/9/a/39a571d0f6a01877c10d8790a5943eab.png" />";}i:363;a:2:{i:0;s:68:"\oint_{\partial S} \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";i:1;s:156:"<img class="tex" alt="\oint_{\partial S} \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 " src="/images/math/2/2/9/229ef1d17720ecf0b771d0783ce81c24.png" />";}i:364;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:104:"<img class="tex" alt="{\scriptstyle S}" src="/images/math/7/f/f/7ff140fff7dde71951767d28cb5304ac.png" />";}i:365;a:2:{i:0;s:96:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";i:1;s:184:"<img class="tex" alt="\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}" src="/images/math/3/9/a/39a571d0f6a01877c10d8790a5943eab.png" />";}i:366;a:2:{i:0;s:11:"\bold{P} = ";i:1;s:99:"<img class="tex" alt="\bold{P} = " src="/images/math/5/b/2/5b2cfaf066bee44f213c6c2882e172c7.png" />";}i:367;a:2:{i:0;s:30:"{\scriptstyle \partial \Omega}";i:1;s:118:"<img class="tex" alt="{\scriptstyle \partial \Omega}" src="/images/math/3/0/c/30c24016df2b868da4e3a8ec58e45ce7.png" />";}i:368;a:2:{i:0;s:47:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";i:1;s:135:"<img class="tex" alt="\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0" src="/images/math/7/3/5/7357641bffa0e625f2d806b7357b7ee5.png" />";}i:369;a:2:{i:0;s:11:"\bold{P} = ";i:1;s:99:"<img class="tex" alt="\bold{P} = " src="/images/math/5/b/2/5b2cfaf066bee44f213c6c2882e172c7.png" />";}i:370;a:2:{i:0;s:30:"{\scriptstyle \partial \Omega}";i:1;s:118:"<img class="tex" alt="{\scriptstyle \partial \Omega}" src="/images/math/3/0/c/30c24016df2b868da4e3a8ec58e45ce7.png" />";}i:371;a:2:{i:0;s:47:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";i:1;s:135:"<img class="tex" alt="\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0" src="/images/math/7/3/5/7357641bffa0e625f2d806b7357b7ee5.png" />";}i:372;a:2:{i:0;s:20:"\overset{\frown}{AB}";i:1;s:108:"<img class="tex" alt="\overset{\frown}{AB}" src="/images/math/8/7/4/8748475980cbfc9c9028b4b298d2f438.png" />";}i:373;a:2:{i:0;s:17:"ax^2 + bx + c = 0";i:1;s:105:"<img class="tex" alt="ax^2 + bx + c = 0" src="/images/math/0/c/4/0c4913db725b72609d4825124dda12aa.png" />";}i:374;a:2:{i:0;s:17:"ax^2 + bx + c = 0";i:1;s:105:"<img class="tex" alt="ax^2 + bx + c = 0" src="/images/math/0/c/4/0c4913db725b72609d4825124dda12aa.png" />";}i:375;a:2:{i:0;s:32:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";i:1;s:120:"<img class="tex" alt="x={-b\pm\sqrt{b^2-4ac} \over 2a}" src="/images/math/a/1/f/a1f76f347b763aa6fc880cbc641fc29f.png" />";}i:376;a:2:{i:0;s:32:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";i:1;s:120:"<img class="tex" alt="x={-b\pm\sqrt{b^2-4ac} \over 2a}" src="/images/math/a/1/f/a1f76f347b763aa6fc880cbc641fc29f.png" />";}i:377;a:2:{i:0;s:56:"2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)";i:1;s:144:"<img class="tex" alt="2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)" src="/images/math/8/9/4/894f312e78ebc09a4e78c11b79cf4a8c.png" />";}i:378;a:2:{i:0;s:56:"2 = \left(
|
|
\frac{\left(3-x\right) \times 2}{3-x}
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|
\right)";i:1;s:152:"<img class="tex" alt="2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)" src="/images/math/8/9/4/894f312e78ebc09a4e78c11b79cf4a8c.png" />";}i:379;a:2:{i:0;s:67:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";i:1;s:155:"<img class="tex" alt="S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}" src="/images/math/a/a/0/aa0dc58e7114c5b91f6113130dcbc1d5.png" />";}i:380;a:2:{i:0;s:67:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";i:1;s:155:"<img class="tex" alt="S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}" src="/images/math/a/a/0/aa0dc58e7114c5b91f6113130dcbc1d5.png" />";}i:381;a:2:{i:0;s:61:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy";i:1;s:149:"<img class="tex" alt="\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy" src="/images/math/4/4/6/4465ba032469b775777205effe6cdc0f.png" />";}i:382;a:2:{i:0;s:61:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds
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|
= \int_a^x f(y)(x-y)\,dy";i:1;s:153:"<img class="tex" alt="\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy" src="/images/math/4/4/6/4465ba032469b775777205effe6cdc0f.png" />";}i:383;a:2:{i:0;s:38:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";i:1;s:126:"<img class="tex" alt="\det(\mathsf{A}-\lambda\mathsf{I}) = 0" src="/images/math/6/9/1/691187249f1e86a2e459362d66b5a743.png" />";}i:384;a:2:{i:0;s:38:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";i:1;s:126:"<img class="tex" alt="\det(\mathsf{A}-\lambda\mathsf{I}) = 0" src="/images/math/6/9/1/691187249f1e86a2e459362d66b5a743.png" />";}i:385;a:2:{i:0;s:18:"\sum_{i=0}^{n-1} i";i:1;s:106:"<img class="tex" alt="\sum_{i=0}^{n-1} i" src="/images/math/9/c/3/9c3090bae1d9eccd9e1747ecc51eaece.png" />";}i:386;a:2:{i:0;s:18:"\sum_{i=0}^{n-1} i";i:1;s:106:"<img class="tex" alt="\sum_{i=0}^{n-1} i" src="/images/math/9/c/3/9c3090bae1d9eccd9e1747ecc51eaece.png" />";}i:387;a:2:{i:0;s:78:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}";i:1;s:166:"<img class="tex" alt="\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}" src="/images/math/5/c/d/5cd6041b50d619f041f121baea301898.png" />";}i:388;a:2:{i:0;s:79:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
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{3^m\left(m\,3^n+n\,3^m\right)}";i:1;s:171:"<img class="tex" alt="\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} {3^m\left(m\,3^n+n\,3^m\right)}" src="/images/math/5/c/d/5cd6041b50d619f041f121baea301898.png" />";}i:389;a:2:{i:0;s:35:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";i:1;s:141:"<img class="tex" alt="u'' + p(x)u' + q(x)u=f(x),\quad x>a" src="/images/math/d/7/b/d7b3799aedae667fcc79b43ba678b94a.png" />";}i:390;a:2:{i:0;s:35:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";i:1;s:141:"<img class="tex" alt="u'' + p(x)u' + q(x)u=f(x),\quad x>a" src="/images/math/d/7/b/d7b3799aedae667fcc79b43ba678b94a.png" />";}i:391;a:2:{i:0;s:61:"|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)";i:1;s:149:"<img class="tex" alt="|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)" src="/images/math/2/e/a/2eac34dbc8ebbccb22ce8dfe9d5c1a86.png" />";}i:392;a:2:{i:0;s:61:"|\bar{z}| = |z|,
|
|
|(\bar{z})^n| = |z|^n,
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\arg(z^n) = n \arg(z)";i:1;s:157:"<img class="tex" alt="|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)" src="/images/math/2/e/a/2eac34dbc8ebbccb22ce8dfe9d5c1a86.png" />";}i:393;a:2:{i:0;s:35:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";i:1;s:123:"<img class="tex" alt="\lim_{z\rightarrow z_0} f(z)=f(z_0)" src="/images/math/0/2/1/02122c7e5ff915c4616fb457747c8bf4.png" />";}i:394;a:2:{i:0;s:35:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";i:1;s:123:"<img class="tex" alt="\lim_{z\rightarrow z_0} f(z)=f(z_0)" src="/images/math/0/2/1/02122c7e5ff915c4616fb457747c8bf4.png" />";}i:395;a:2:{i:0;s:170:"\phi_n(\kappa)
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|
= \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";i:1;s:262:"<img class="tex" alt="\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR" src="/images/math/7/f/b/7fb11db1e8b5890998b2f0f59f0e3d60.png" />";}i:396;a:2:{i:0;s:170:"\phi_n(\kappa) =
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\frac{1}{4\pi^2\kappa^2} \int_0^\infty
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|
\frac{\sin(\kappa R)}{\kappa R}
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\frac{\partial}{\partial R}
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\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";i:1;s:274:"<img class="tex" alt="\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR" src="/images/math/7/f/b/7fb11db1e8b5890998b2f0f59f0e3d60.png" />";}i:397;a:2:{i:0;s:86:"\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";i:1;s:174:"<img class="tex" alt="\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}" src="/images/math/8/f/7/8f72d606f5f91bd51583a0a08b36eed9.png" />";}i:398;a:2:{i:0;s:86:"\phi_n(\kappa) =
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0.033C_n^2\kappa^{-11/3},\quad
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\frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";i:1;s:182:"<img class="tex" alt="\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}" src="/images/math/8/f/7/8f72d606f5f91bd51583a0a08b36eed9.png" />";}i:399;a:2:{i:0;s:100:"f(x) = \begin{cases}1 & -1 \le x < 0 \\
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\frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise}\end{cases}";i:1;s:207:"<img class="tex" alt="f(x) = \begin{cases}1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise}\end{cases}" src="/images/math/3/e/3/3e3579f4c1c6a95f181f227fd3ede7de.png" />";}i:400;a:2:{i:0;s:104:"
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f(x) =
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\begin{cases}
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1 & -1 \le x < 0 \\
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\frac{1}{2} & x = 0 \\
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1 - x^2 & \text{otherwise}
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\end{cases}
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";i:1;s:235:"<img class="tex" alt=" f(x) = \begin{cases} 1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise} \end{cases} " src="/images/math/3/e/3/3e3579f4c1c6a95f181f227fd3ede7de.png" />";}i:401;a:2:{i:0;s:122:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}\frac{z^n}{n!}";i:1;s:210:"<img class="tex" alt="{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}\frac{z^n}{n!}" src="/images/math/c/0/2/c02cbc6ec9c57aca74ebc3a0314dea79.png" />";}i:402;a:2:{i:0;s:123:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
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= \sum_{n=0}^\infty
|
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\frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}
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\frac{z^n}{n!}";i:1;s:223:"<img class="tex" alt="{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n} \frac{z^n}{n!}" src="/images/math/c/0/2/c02cbc6ec9c57aca74ebc3a0314dea79.png" />";}i:403;a:2:{i:0;s:25:"\frac{a}{b}\ \tfrac{a}{b}";i:1;s:113:"<img class="tex" alt="\frac{a}{b}\ \tfrac{a}{b}" src="/images/math/5/4/e/54e172be623599fef29e40733c94895e.png" />";}i:404;a:2:{i:0;s:25:"\frac{a}{b}\ \tfrac{a}{b}";i:1;s:113:"<img class="tex" alt="\frac{a}{b}\ \tfrac{a}{b}" src="/images/math/5/4/e/54e172be623599fef29e40733c94895e.png" />";}i:405;a:2:{i:0;s:18:"S=dD\,\sin\alpha\!";i:1;s:106:"<img class="tex" alt="S=dD\,\sin\alpha\!" src="/images/math/3/8/5/385776efb87d3eb7fe18587efd484ef5.png" />";}i:406;a:2:{i:0;s:18:"S=dD\,\sin\alpha\!";i:1;s:106:"<img class="tex" alt="S=dD\,\sin\alpha\!" src="/images/math/3/8/5/385776efb87d3eb7fe18587efd484ef5.png" />";}i:407;a:2:{i:0;s:56:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";i:1;s:144:"<img class="tex" alt="V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]" src="/images/math/6/2/4/624bfa733e479dff276edfdc7b1b8f6a.png" />";}i:408;a:2:{i:0;s:56:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";i:1;s:144:"<img class="tex" alt="V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]" src="/images/math/6/2/4/624bfa733e479dff276edfdc7b1b8f6a.png" />";}i:409;a:2:{i:0;s:167:"\begin{align}
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u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v)\\
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v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v)
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\end{align}";i:1;s:291:"<img class="tex" alt="\begin{align} u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v)\\ v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v) \end{align}" src="/images/math/7/8/7/787eb92e00313cb866a89579fde92108.png" />";}i:410;a:2:{i:0;s:168:"\begin{align}
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u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v) \\
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v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v)
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\end{align}";i:1;s:292:"<img class="tex" alt="\begin{align} u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v) \\ v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v) \end{align}" src="/images/math/7/8/7/787eb92e00313cb866a89579fde92108.png" />";}i:411;a:2:{i:0;s:172:" with a thumbnail- we don't render math in the parsertests by default, so math is not stripped and turns up as escaped <math> tags. [[Image:foobar.jpg|thumb|<math>2+2";i:1;s:259:"<strong class='error texerror'>Failed to parse (syntax error): with a thumbnail- we don't render math in the parsertests by default, so math is not stripped and turns up as escaped &lt;math&gt; tags. [[Image:foobar.jpg|thumb|<math>2+2</strong>
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";}i:412;a:2:{i:0;s:66:" with a thumbnail- math enabled [[Image:foobar.jpg|thumb|<math>2+2";i:1;s:160:"<img class="tex" alt=" with a thumbnail- math enabled [[Image:foobar.jpg|thumb|<math>2+2" src="/images/math/4/b/1/4b1d6eacd0bcc60a0aadf0d34626ee74.png" />";}i:413;a:2:{i:0;s:41:"<script>alert(document.cookies);</script>";i:1;s:141:"<img class="tex" alt="<script>alert(document.cookies);</script>" src="/images/math/5/9/f/59f1117d63b4ce95a694d44b588f0840.png" />";}i:414;a:2:{i:0;s:11:"\widehat{x}";i:1;s:99:"<img class="tex" alt="\widehat{x}" src="/images/math/9/9/8/998309e831dfb051f233c92b4b8a825b.png" />";}i:415;a:2:{i:0;s:13:"\widetilde{x}";i:1;s:101:"<img class="tex" alt="\widetilde{x}" src="/images/math/e/9/e/e9e91996778a6d6f5cdf4cc951955206.png" />";}i:416;a:2:{i:0;s:9:"\euro 200";i:1;s:97:"<img class="tex" alt="\euro 200" src="/images/math/1/8/8/18867d4c568a19ae7b2388346e504ec3.png" />";}i:417;a:2:{i:0;s:8:"\geneuro";i:1;s:96:"<img class="tex" alt="\geneuro" 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class="tex" alt="\tilde \mathcal{M}" src="/images/math/5/5/0/55072ce6ef8c840c4b7687bd8a028bde.png" />";}i:445;a:2:{i:0;s:0:"";i:1;s:160:"<strong class='error texerror'>Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): </strong>
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";}i:446;a:2:{i:0;s:1:" ";i:1;s:161:"<strong class='error texerror'>Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): </strong>
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";}} |