mediawiki-extensions-Math/tests/ParserTest.data
Moritz Schubotz (Physikerwelt) c5b0b15d8f Fix MathJax centers equations
* Removes the MathJax heuristics that decides
  if equations are centered or left-aligned.
* Introduces the attribute display to specify
  if the math element is rendered in inline,
  display, or inline-displaystyle.
* add css rules for display / inline math images

Bug: 61051
Change-Id: Iba69903f781f0cb1606b8ddcffb90fb86c9b229b
2014-04-06 21:58:30 +00:00

73 lines
104 KiB
Plaintext

a:449:{i:0;a:2:{i:0;s:21:"e^{i \pi} + 1 = 0\,\!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="e^{i \pi} + 1 = 0\,\!" src="/images/math/9/e/9/9e9a547076c6820b95e439dd1a5d6a32.png" />";}i:1;a:2:{i:0;s:21:"e^{i \pi} + 1 = 0\,\!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="e^{i \pi} + 1 = 0\,\!" src="/images/math/9/e/9/9e9a547076c6820b95e439dd1a5d6a32.png" />";}i:2;a:2:{i:0;s:67:"\definecolor{red}{RGB}{255,0,0}\pagecolor{red}e^{i \pi} + 1 = 0\,\!";i:1;s:184:"<img class="mwe-math-fallback-png-inline tex" alt="\definecolor{red}{RGB}{255,0,0}\pagecolor{red}e^{i \pi} + 1 = 0\,\!" src="/images/math/6/7/a/67aca9e0de80ac6ab651ed1097b49fe2.png" />";}i:3;a:2:{i:0;s:10:"\text{abc}";i:1;s:127:"<img class="mwe-math-fallback-png-inline tex" alt="\text{abc}" src="/images/math/4/6/0/46045b1f6fa9dc10a3112ba360d4d9d7.png" />";}i:4;a:2:{i:0;s:10:"\alpha\,\!";i:1;s:127:"<img class="mwe-math-fallback-png-inline tex" alt="\alpha\,\!" src="/images/math/4/b/c/4bc6c42bbabe567d1f2516326e52b775.png" />";}i:5;a:2:{i:0;s:15:" f(x) = x^2\,\!";i:1;s:132:"<img class="mwe-math-fallback-png-inline tex" alt=" f(x) = x^2\,\!" src="/images/math/3/a/5/3a5f0f03603148035120a3cba993e54f.png" />";}i:6;a:2:{i:0;s:8:"\sqrt{2}";i:1;s:125:"<img class="mwe-math-fallback-png-inline tex" alt="\sqrt{2}" src="/images/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" />";}i:7;a:2:{i:0;s:14:"\sqrt{1-e^2}\!";i:1;s:131:"<img class="mwe-math-fallback-png-inline tex" alt="\sqrt{1-e^2}\!" src="/images/math/0/4/c/04c93cf9f0a7cf697add9a2d4173a9e9.png" />";}i:8;a:2:{i:0;s:14:"\sqrt{1-z^3}\!";i:1;s:131:"<img class="mwe-math-fallback-png-inline tex" alt="\sqrt{1-z^3}\!" src="/images/math/1/0/8/108d6aa70c84fddabbbd3ec97f3d3ff8.png" />";}i:9;a:2:{i:0;s:1:"x";i:1;s:118:"<img class="mwe-math-fallback-png-inline tex" alt="x" src="/images/math/9/d/d/9dd4e461268c8034f5c8564e155c67a6.png" />";}i:10;a:2:{i:0;s:42:"\dot{a}, \ddot{a}, \acute{a}, \grave{a} \!";i:1;s:159:"<img class="mwe-math-fallback-png-inline tex" alt="\dot{a}, \ddot{a}, \acute{a}, \grave{a} \!" src="/images/math/c/0/9/c096beaae99e2d37b4050c4ccf30fbf8.png" />";}i:11;a:2:{i:0;s:43:"\check{a}, \breve{a}, \tilde{a}, \bar{a} \!";i:1;s:160:"<img class="mwe-math-fallback-png-inline tex" alt="\check{a}, \breve{a}, \tilde{a}, \bar{a} \!" src="/images/math/e/f/3/ef387ac79f18651dd3105d2c584b3c95.png" />";}i:12;a:2:{i:0;s:32:"\hat{a}, \widehat{a}, \vec{a} \!";i:1;s:149:"<img class="mwe-math-fallback-png-inline tex" alt="\hat{a}, \widehat{a}, \vec{a} \!" src="/images/math/e/a/e/eaededf26bb201c699ef1597902383c3.png" />";}i:13;a:2:{i:0;s:37:"\exp_a b = a^b, \exp b = e^b, 10^m \!";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\exp_a b = a^b, \exp b = e^b, 10^m \!" src="/images/math/1/9/9/199ac36bc19f7951df5041aedc1e2525.png" />";}i:14;a:2:{i:0;s:37:"\ln c, \lg d = \log e, \log_{10} f \!";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\ln c, \lg d = \log e, \log_{10} f \!" src="/images/math/d/5/8/d58edc12e2750302cfcdfd47f7674607.png" />";}i:15;a:2:{i:0;s:48:"\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\!";i:1;s:165:"<img class="mwe-math-fallback-png-inline tex" alt="\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\!" src="/images/math/0/d/e/0de90ca439db043c53360a81e56e2543.png" />";}i:16;a:2:{i:0;s:34:"\arcsin h, \arccos i, \arctan j \!";i:1;s:151:"<img class="mwe-math-fallback-png-inline tex" alt="\arcsin h, \arccos i, \arctan j \!" src="/images/math/d/4/f/d4f41532d2a06150554f27d52b3c9479.png" />";}i:17;a:2:{i:0;s:37:"\sinh k, \cosh l, \tanh m, \coth n \!";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\sinh k, \cosh l, \tanh m, \coth n \!" src="/images/math/2/d/4/2d460f19d2addae865a78806e3a3afd8.png" />";}i:18;a:2:{i:0;s:91:"\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m, \operatorname{coth}\,n \!";i:1;s:208:"<img class="mwe-math-fallback-png-inline tex" alt="\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m, \operatorname{coth}\,n \!" src="/images/math/7/f/3/7f37a94f008e914726d78b52bf7e3ff4.png" />";}i:19;a:2:{i:0;s:76:"\operatorname{argsh}\,o, \operatorname{argch}\,p, \operatorname{argth}\,q \!";i:1;s:193:"<img class="mwe-math-fallback-png-inline tex" alt="\operatorname{argsh}\,o, \operatorname{argch}\,p, \operatorname{argth}\,q \!" src="/images/math/4/e/7/4e797e4c1988d0f75df043f9347214c0.png" />";}i:20;a:2:{i:0;s:35:"\sgn r, \left\vert s \right\vert \!";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="\sgn r, \left\vert s \right\vert \!" src="/images/math/c/f/2/cf2302a36d9f76e484ea9833b583bc73.png" />";}i:21;a:2:{i:0;s:23:"\min(x,y), \max(x,y) \!";i:1;s:140:"<img class="mwe-math-fallback-png-inline tex" alt="\min(x,y), \max(x,y) \!" src="/images/math/6/6/8/6685fb9850f120547152b9e8f89e127d.png" />";}i:22;a:2:{i:0;s:33:"\min x, \max y, \inf s, \sup t \!";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\min x, \max y, \inf s, \sup t \!" src="/images/math/8/c/b/8cb6afbfa7011932573dc4fe62a6326f.png" />";}i:23;a:2:{i:0;s:31:"\lim u, \liminf v, \limsup w \!";i:1;s:148:"<img class="mwe-math-fallback-png-inline tex" alt="\lim u, \liminf v, \limsup w \!" src="/images/math/1/5/e/15e23ef762c80f28daef47e565900b89.png" />";}i:24;a:2:{i:0;s:35:"\dim p, \deg q, \det m, \ker\phi \!";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="\dim p, \deg q, \det m, \ker\phi \!" src="/images/math/f/f/b/ffbfa151b5260ecb5ef79f0c87514688.png" />";}i:25;a:2:{i:0;s:41:"\Pr j, \hom l, \lVert z \rVert, \arg z \!";i:1;s:158:"<img class="mwe-math-fallback-png-inline tex" alt="\Pr j, \hom l, \lVert z \rVert, \arg z \!" src="/images/math/d/d/e/dde6ad7a50f2079b6e085bccfcbe49e0.png" />";}i:26;a:2:{i:0;s:49:"dt, \operatorname{d}\!t, \partial t, \nabla\psi\!";i:1;s:166:"<img class="mwe-math-fallback-png-inline tex" alt="dt, \operatorname{d}\!t, \partial t, \nabla\psi\!" src="/images/math/b/3/2/b32346afbfaabbd8e7e3eee827952c44.png" />";}i:27;a:2:{i:0;s:155:"dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y \!";i:1;s:272:"<img class="mwe-math-fallback-png-inline tex" alt="dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y \!" src="/images/math/8/8/5/8854ea48cc731b20acb7e31b7676ab14.png" />";}i:28;a:2:{i:0;s:66:"\prime, \backprime, f^\prime, f', f'', f^{(3)} \!, \dot y, \ddot y";i:1;s:198:"<img class="mwe-math-fallback-png-inline tex" alt="\prime, \backprime, f^\prime, f&#039;, f&#039;&#039;, f^{(3)} \!, \dot y, \ddot y" src="/images/math/9/9/4/99434cfc81c7e2121520b25248f49eab.png" />";}i:29;a:2:{i:0;s:64:"\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar \!";i:1;s:181:"<img class="mwe-math-fallback-png-inline tex" alt="\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar \!" src="/images/math/5/a/4/5a419cad96da19939591abb89e952110.png" />";}i:30;a:2:{i:0;s:62:"\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS \!";i:1;s:179:"<img class="mwe-math-fallback-png-inline tex" alt="\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS \!" src="/images/math/c/3/9/c390bebffad60aca74b245dcc59a25ef.png" />";}i:31;a:2:{i:0;s:24:"s_k \equiv 0 \pmod{m} \!";i:1;s:141:"<img class="mwe-math-fallback-png-inline tex" alt="s_k \equiv 0 \pmod{m} \!" src="/images/math/3/5/3/353ab52b3f2c5f26ee74c81d31f2a36c.png" />";}i:32;a:2:{i:0;s:14:"a\,\bmod\,b \!";i:1;s:131:"<img class="mwe-math-fallback-png-inline tex" alt="a\,\bmod\,b \!" src="/images/math/e/e/6/ee6494b1a13934593f79f5874592a117.png" />";}i:33;a:2:{i:0;s:36:"\gcd(m, n), \operatorname{lcm}(m, n)";i:1;s:153:"<img class="mwe-math-fallback-png-inline tex" alt="\gcd(m, n), \operatorname{lcm}(m, n)" src="/images/math/6/d/9/6d966ef8f78b4ae70f97c9d14f873cfa.png" />";}i:34;a:2:{i:0;s:37:"\mid, \nmid, \shortmid, \nshortmid \!";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\mid, \nmid, \shortmid, \nshortmid \!" src="/images/math/3/9/e/39e442097c139a70392ae8a043a9297a.png" />";}i:35;a:2:{i:0;s:57:"\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{x^3+y^3 \over 2} \!";i:1;s:174:"<img class="mwe-math-fallback-png-inline tex" alt="\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{x^3+y^3 \over 2} \!" src="/images/math/2/a/b/2ab6022932b3bf67498985081a9a0546.png" />";}i:36;a:2:{i:0;s:27:"+, -, \pm, \mp, \dotplus \!";i:1;s:144:"<img class="mwe-math-fallback-png-inline tex" alt="+, -, \pm, \mp, \dotplus \!" src="/images/math/5/c/6/5c60a256506efc42047c06ea4cba9cf3.png" />";}i:37;a:2:{i:0;s:46:"\times, \div, \divideontimes, /, \backslash \!";i:1;s:163:"<img class="mwe-math-fallback-png-inline tex" alt="\times, \div, \divideontimes, /, \backslash \!" src="/images/math/b/3/8/b386c20a84be6bea1495f8f4d34aaf9d.png" />";}i:38;a:2:{i:0;s:39:"\cdot, * \ast, \star, \circ, \bullet \!";i:1;s:156:"<img class="mwe-math-fallback-png-inline tex" alt="\cdot, * \ast, \star, \circ, \bullet \!" src="/images/math/1/5/3/1538e6e687ddbc430d2edba1dd4c57f3.png" />";}i:39;a:2:{i:0;s:42:"\boxplus, \boxminus, \boxtimes, \boxdot \!";i:1;s:159:"<img class="mwe-math-fallback-png-inline tex" alt="\boxplus, \boxminus, \boxtimes, \boxdot \!" src="/images/math/a/7/d/a7d67089f319edbd2c6ceda550ae97fc.png" />";}i:40;a:2:{i:0;s:42:"\oplus, \ominus, \otimes, \oslash, \odot\!";i:1;s:159:"<img class="mwe-math-fallback-png-inline tex" alt="\oplus, \ominus, \otimes, \oslash, \odot\!" src="/images/math/e/f/a/efa177feefc3df54b529112042dd4862.png" />";}i:41;a:2:{i:0;s:42:"\circleddash, \circledcirc, \circledast \!";i:1;s:159:"<img class="mwe-math-fallback-png-inline tex" alt="\circleddash, \circledcirc, \circledast \!" src="/images/math/e/3/3/e33c682e034881ea51ca94419fe6534f.png" />";}i:42;a:2:{i:0;s:34:"\bigoplus, \bigotimes, \bigodot \!";i:1;s:151:"<img class="mwe-math-fallback-png-inline tex" alt="\bigoplus, \bigotimes, \bigodot \!" src="/images/math/9/0/1/901f6c26646a95b68684a88c3dd7ba23.png" />";}i:43;a:2:{i:0;s:42:"\{ \}, \O \empty \emptyset, \varnothing \!";i:1;s:159:"<img class="mwe-math-fallback-png-inline tex" alt="\{ \}, \O \empty \emptyset, \varnothing \!" src="/images/math/6/6/f/66f1c50302d04ec150b9791a0ed9dd72.png" />";}i:44;a:2:{i:0;s:36:"\in, \notin \not\in, \ni, \not\ni \!";i:1;s:153:"<img class="mwe-math-fallback-png-inline tex" alt="\in, \notin \not\in, \ni, \not\ni \!" src="/images/math/e/3/c/e3ccfeab48f96e390879beae43fef5f6.png" />";}i:45;a:2:{i:0;s:30:"\cap, \Cap, \sqcap, \bigcap \!";i:1;s:147:"<img class="mwe-math-fallback-png-inline tex" alt="\cap, \Cap, \sqcap, \bigcap \!" src="/images/math/f/c/e/fce1ad3d3efa856b424905062f483e19.png" />";}i:46;a:2:{i:0;s:60:"\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus \!";i:1;s:177:"<img class="mwe-math-fallback-png-inline tex" alt="\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus \!" src="/images/math/b/8/6/b8621006bb69395016e695a8f866c004.png" />";}i:47;a:2:{i:0;s:36:"\setminus, \smallsetminus, \times \!";i:1;s:153:"<img class="mwe-math-fallback-png-inline tex" alt="\setminus, \smallsetminus, \times \!" src="/images/math/e/1/7/e17420f59b39e697a8f0cbd94dd53ad5.png" />";}i:48;a:2:{i:0;s:30:"\subset, \Subset, \sqsubset \!";i:1;s:147:"<img class="mwe-math-fallback-png-inline tex" alt="\subset, \Subset, \sqsubset \!" src="/images/math/b/4/9/b4900dc0901ce8489cff150076d16088.png" />";}i:49;a:2:{i:0;s:30:"\supset, \Supset, \sqsupset \!";i:1;s:147:"<img class="mwe-math-fallback-png-inline tex" alt="\supset, \Supset, \sqsupset \!" src="/images/math/c/b/5/cb5fa1a8597041a2eb565361a1401079.png" />";}i:50;a:2:{i:0;s:64:"\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq \!";i:1;s:181:"<img class="mwe-math-fallback-png-inline tex" alt="\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq \!" src="/images/math/5/4/b/54b164cefa6faadfce92a97d239f2f80.png" />";}i:51;a:2:{i:0;s:64:"\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq \!";i:1;s:181:"<img class="mwe-math-fallback-png-inline tex" alt="\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq \!" src="/images/math/4/e/9/4e928a53227784971555d98d1ef5c7be.png" />";}i:52;a:2:{i:0;s:55:"\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq \!";i:1;s:172:"<img class="mwe-math-fallback-png-inline tex" alt="\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq \!" src="/images/math/0/1/6/0162e51aac9e459011206dd370890444.png" />";}i:53;a:2:{i:0;s:55:"\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq \!";i:1;s:172:"<img class="mwe-math-fallback-png-inline tex" alt="\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq \!" src="/images/math/3/a/0/3a07c3fb9a0f14534117951fc276d2e0.png" />";}i:54;a:2:{i:0;s:35:"=, \ne, \neq, \equiv, \not\equiv \!";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="=, \ne, \neq, \equiv, \not\equiv \!" src="/images/math/7/1/b/71bb47c2145fabb0a1692fe545a019c8.png" />";}i:55;a:2:{i:0;s:64:"\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, := \!";i:1;s:181:"<img class="mwe-math-fallback-png-inline tex" alt="\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, := \!" src="/images/math/6/4/2/6426a1cb9fe7d87280f4d1b7137abc07.png" />";}i:56;a:2:{i:0;s:78:"\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong \!";i:1;s:195:"<img class="mwe-math-fallback-png-inline tex" alt="\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong \!" src="/images/math/3/0/7/30784f1f1b325970cfacabacb47b192e.png" />";}i:57;a:2:{i:0;s:64:"\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto \!";i:1;s:181:"<img class="mwe-math-fallback-png-inline tex" alt="\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto \!" src="/images/math/8/c/5/8c58c414b8003f68301141b50ceadc02.png" />";}i:58;a:2:{i:0;s:52:"<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot \!";i:1;s:172:"<img class="mwe-math-fallback-png-inline tex" alt="&lt;, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot \!" src="/images/math/3/4/6/346b8a9e0891b24a7433041f233be228.png" />";}i:59;a:2:{i:0;s:50:">, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot \!";i:1;s:170:"<img class="mwe-math-fallback-png-inline tex" alt="&gt;, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot \!" src="/images/math/8/b/8/8b8f7a0e7ad46e494dc5b032c5558068.png" />";}i:60;a:2:{i:0;s:53:"\le \leq, \lneq, \leqq, \nleqq, \lneqq, \lvertneqq \!";i:1;s:170:"<img class="mwe-math-fallback-png-inline tex" alt="\le \leq, \lneq, \leqq, \nleqq, \lneqq, \lvertneqq \!" src="/images/math/2/a/0/2a0fc5dad4cb369221b29e8a49c0e769.png" />";}i:61;a:2:{i:0;s:53:"\ge \geq, \gneq, \geqq, \ngeqq, \gneqq, \gvertneqq \!";i:1;s:170:"<img class="mwe-math-fallback-png-inline tex" alt="\ge \geq, \gneq, \geqq, \ngeqq, \gneqq, \gvertneqq \!" src="/images/math/a/b/7/ab7369a11c4f4e0db4d838b4303a673c.png" />";}i:62;a:2:{i:0;s:66:"\lessgtr \lesseqgtr \lesseqqgtr \gtrless \gtreqless \gtreqqless \!";i:1;s:183:"<img class="mwe-math-fallback-png-inline tex" alt="\lessgtr \lesseqgtr \lesseqqgtr \gtrless \gtreqless \gtreqqless \!" src="/images/math/8/4/9/849c96983e134159f2d7da012e2fef32.png" />";}i:63;a:2:{i:0;s:38:"\leqslant, \nleqslant, \eqslantless \!";i:1;s:155:"<img class="mwe-math-fallback-png-inline tex" alt="\leqslant, \nleqslant, \eqslantless \!" src="/images/math/6/9/b/69bafd8e6dd7f1e6c45449a7eb0bbd72.png" />";}i:64;a:2:{i:0;s:37:"\geqslant, \ngeqslant, \eqslantgtr \!";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\geqslant, \ngeqslant, \eqslantgtr \!" src="/images/math/d/f/b/dfba791fb6522dc8d44b3c8d751d8bf5.png" />";}i:65;a:2:{i:0;s:43:"\lesssim, \lnsim, \lessapprox, \lnapprox \!";i:1;s:160:"<img class="mwe-math-fallback-png-inline tex" alt="\lesssim, \lnsim, \lessapprox, \lnapprox \!" src="/images/math/1/3/f/13fd2ed1c2d478c14cece389bb5c64a1.png" />";}i:66;a:2:{i:0;s:42:" \gtrsim, \gnsim, \gtrapprox, \gnapprox \,";i:1;s:159:"<img class="mwe-math-fallback-png-inline tex" alt=" \gtrsim, \gnsim, \gtrapprox, \gnapprox \," src="/images/math/d/7/4/d74fd13928904c2d1b8f494a026e58b1.png" />";}i:67;a:2:{i:0;s:46:"\prec, \nprec, \preceq, \npreceq, \precneqq \!";i:1;s:163:"<img class="mwe-math-fallback-png-inline tex" alt="\prec, \nprec, \preceq, \npreceq, \precneqq \!" src="/images/math/e/f/d/efd1161f1c5933353120560a5706009b.png" />";}i:68;a:2:{i:0;s:46:"\succ, \nsucc, \succeq, \nsucceq, \succneqq \!";i:1;s:163:"<img class="mwe-math-fallback-png-inline tex" alt="\succ, \nsucc, \succeq, \nsucceq, \succneqq \!" src="/images/math/f/b/f/fbf129d72470a83b6f94671d3f3c3736.png" />";}i:69;a:2:{i:0;s:29:"\preccurlyeq, \curlyeqprec \,";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\preccurlyeq, \curlyeqprec \," src="/images/math/6/1/8/618877a0da3b42786403dd6f89f23cd4.png" />";}i:70;a:2:{i:0;s:29:"\succcurlyeq, \curlyeqsucc \,";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\succcurlyeq, \curlyeqsucc \," src="/images/math/c/6/2/c62e39463302a563b562ca55a05b427b.png" />";}i:71;a:2:{i:0;s:49:"\precsim, \precnsim, \precapprox, \precnapprox \,";i:1;s:166:"<img class="mwe-math-fallback-png-inline tex" alt="\precsim, \precnsim, \precapprox, \precnapprox \," src="/images/math/9/4/d/94defc1756f8294cc2126346b99a61a6.png" />";}i:72;a:2:{i:0;s:49:"\succsim, \succnsim, \succapprox, \succnapprox \,";i:1;s:166:"<img class="mwe-math-fallback-png-inline tex" alt="\succsim, \succnsim, \succapprox, \succnapprox \," src="/images/math/c/7/d/c7d48d910d1de01a804bcf1e0ef65e1d.png" />";}i:73;a:2:{i:0;s:57:"\parallel, \nparallel, \shortparallel, \nshortparallel \!";i:1;s:174:"<img class="mwe-math-fallback-png-inline tex" alt="\parallel, \nparallel, \shortparallel, \nshortparallel \!" src="/images/math/5/b/0/5b09ecb8b14b1df562a4caf1180c7d29.png" />";}i:74;a:2:{i:0;s:59:"\perp, \angle, \sphericalangle, \measuredangle, 45^\circ \!";i:1;s:176:"<img class="mwe-math-fallback-png-inline tex" alt="\perp, \angle, \sphericalangle, \measuredangle, 45^\circ \!" src="/images/math/d/d/c/ddc31bfbbe9c00652ee9dfa869cdbd73.png" />";}i:75;a:2:{i:0;s:75:"\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar \!";i:1;s:192:"<img class="mwe-math-fallback-png-inline tex" alt="\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar \!" src="/images/math/b/d/f/bdf723cee9fa064c46b56a76fc90f40f.png" />";}i:76;a:2:{i:0;s:55:"\bigcirc, \triangle \bigtriangleup, \bigtriangledown \!";i:1;s:172:"<img class="mwe-math-fallback-png-inline tex" alt="\bigcirc, \triangle \bigtriangleup, \bigtriangledown \!" src="/images/math/a/a/8/aa8038ff0b44c400b3ce49f30bd8640a.png" />";}i:77;a:2:{i:0;s:29:"\vartriangle, \triangledown\!";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\vartriangle, \triangledown\!" src="/images/math/a/0/c/a0ce77d5ff2eee65687c195a386e2a57.png" />";}i:78;a:2:{i:0;s:78:"\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright \!";i:1;s:195:"<img class="mwe-math-fallback-png-inline tex" alt="\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright \!" src="/images/math/f/b/2/fb28c5e57867c70b72ee3ec7767725a2.png" />";}i:79;a:2:{i:0;s:29:"\forall, \exists, \nexists \!";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\forall, \exists, \nexists \!" src="/images/math/6/8/6/686b55bf8ded08acf37721fa9e289505.png" />";}i:80;a:2:{i:0;s:29:"\therefore, \because, \And \!";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\therefore, \because, \And \!" src="/images/math/e/1/5/e152ae479d89f44ffcb05f5c0010f977.png" />";}i:81;a:2:{i:0;s:36:"\or \lor \vee, \curlyvee, \bigvee \!";i:1;s:153:"<img class="mwe-math-fallback-png-inline tex" alt="\or \lor \vee, \curlyvee, \bigvee \!" src="/images/math/7/3/c/73cb2ef925b7885181d33363b6dc562a.png" />";}i:82;a:2:{i:0;s:44:"\and \land \wedge, \curlywedge, \bigwedge \!";i:1;s:161:"<img class="mwe-math-fallback-png-inline tex" alt="\and \land \wedge, \curlywedge, \bigwedge \!" src="/images/math/6/b/5/6b5e9b7373ce2c57602dc9dae4c84adb.png" />";}i:83;a:2:{i:0;s:52:"\bar{q}, \bar{abc}, \overline{q}, \overline{abc}, \!";i:1;s:169:"<img class="mwe-math-fallback-png-inline tex" alt="\bar{q}, \bar{abc}, \overline{q}, \overline{abc}, \!" src="/images/math/d/c/b/dcb1a2881216fe505b14faa2f5dd4f0e.png" />";}i:84;a:2:{i:0;s:47:"\lnot \neg, \not\operatorname{R}, \bot, \top \!";i:1;s:164:"<img class="mwe-math-fallback-png-inline tex" alt="\lnot \neg, \not\operatorname{R}, \bot, \top \!" src="/images/math/9/9/f/99f7d273b7b0b3509afedb5c7f6738a0.png" />";}i:85;a:2:{i:0;s:41:"\vdash \dashv, \vDash, \Vdash, \models \!";i:1;s:158:"<img class="mwe-math-fallback-png-inline tex" alt="\vdash \dashv, \vDash, \Vdash, \models \!" src="/images/math/c/1/e/c1eec4d326b28c81681be40303f53029.png" />";}i:86;a:2:{i:0;s:42:"\Vvdash \nvdash \nVdash \nvDash \nVDash \!";i:1;s:159:"<img class="mwe-math-fallback-png-inline tex" alt="\Vvdash \nvdash \nVdash \nvDash \nVDash \!" src="/images/math/8/9/b/89b4b08896b7110ddb06bf486b6791ec.png" />";}i:87;a:2:{i:0;s:42:"\ulcorner \urcorner \llcorner \lrcorner \,";i:1;s:159:"<img class="mwe-math-fallback-png-inline tex" alt="\ulcorner \urcorner \llcorner \lrcorner \," src="/images/math/a/2/1/a21720642028f8a9fe4157c6800f3ba3.png" />";}i:88;a:2:{i:0;s:28:"\Rrightarrow, \Lleftarrow \!";i:1;s:145:"<img class="mwe-math-fallback-png-inline tex" alt="\Rrightarrow, \Lleftarrow \!" src="/images/math/c/9/6/c960b376ea9224b684e54d964af456dd.png" />";}i:89;a:2:{i:0;s:53:"\Rightarrow, \nRightarrow, \Longrightarrow \implies\!";i:1;s:170:"<img class="mwe-math-fallback-png-inline tex" alt="\Rightarrow, \nRightarrow, \Longrightarrow \implies\!" src="/images/math/3/1/c/31c1448fab538846ac5f11bc2022c176.png" />";}i:90;a:2:{i:0;s:42:"\Leftarrow, \nLeftarrow, \Longleftarrow \!";i:1;s:159:"<img class="mwe-math-fallback-png-inline tex" alt="\Leftarrow, \nLeftarrow, \Longleftarrow \!" src="/images/math/8/4/b/84b1cba7e578ad0ff11d4bf2f22ce2e7.png" />";}i:91;a:2:{i:0;s:62:"\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff \!";i:1;s:179:"<img class="mwe-math-fallback-png-inline tex" alt="\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff \!" src="/images/math/7/e/b/7eb8b8e5483e32ff80c2cfcc8255091d.png" />";}i:92;a:2:{i:0;s:37:"\Uparrow, \Downarrow, \Updownarrow \!";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\Uparrow, \Downarrow, \Updownarrow \!" src="/images/math/7/e/f/7efd0476ba546822fa6059aea7adfec6.png" />";}i:93;a:2:{i:0;s:48:"\rightarrow \to, \nrightarrow, \longrightarrow\!";i:1;s:165:"<img class="mwe-math-fallback-png-inline tex" alt="\rightarrow \to, \nrightarrow, \longrightarrow\!" src="/images/math/f/1/2/f1274eb98e3631ddde35ce79a1371ccc.png" />";}i:94;a:2:{i:0;s:47:"\leftarrow \gets, \nleftarrow, \longleftarrow\!";i:1;s:164:"<img class="mwe-math-fallback-png-inline tex" alt="\leftarrow \gets, \nleftarrow, \longleftarrow\!" src="/images/math/4/1/6/416c117d1c7b30d1f655eff0dd223aa7.png" />";}i:95;a:2:{i:0;s:57:"\leftrightarrow, \nleftrightarrow, \longleftrightarrow \!";i:1;s:174:"<img class="mwe-math-fallback-png-inline tex" alt="\leftrightarrow, \nleftrightarrow, \longleftrightarrow \!" src="/images/math/4/c/5/4c589175a17c959876c7843656839055.png" />";}i:96;a:2:{i:0;s:37:"\uparrow, \downarrow, \updownarrow \!";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\uparrow, \downarrow, \updownarrow \!" src="/images/math/9/2/d/92df6c1de62cb4c990943f697dc9d5e9.png" />";}i:97;a:2:{i:0;s:41:"\nearrow, \swarrow, \nwarrow, \searrow \!";i:1;s:158:"<img class="mwe-math-fallback-png-inline tex" alt="\nearrow, \swarrow, \nwarrow, \searrow \!" src="/images/math/c/0/5/c050f2c2ab90cedc7b277ca59954d607.png" />";}i:98;a:2:{i:0;s:23:"\mapsto, \longmapsto \!";i:1;s:140:"<img class="mwe-math-fallback-png-inline tex" alt="\mapsto, \longmapsto \!" src="/images/math/f/b/d/fbd64bf3496731549c3adf48abcb6726.png" />";}i:99;a:2:{i:0;s:174:"\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,\!";i:1;s:291:"<img class="mwe-math-fallback-png-inline tex" alt="\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,\!" src="/images/math/4/2/2/422d605ad5b47e52b7275a53d9d87499.png" />";}i:100;a:2:{i:0;s:121:"\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright \,\!";i:1;s:238:"<img class="mwe-math-fallback-png-inline tex" alt="\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright \,\!" src="/images/math/4/9/b/49b807f451f07bd074ece7e0dd1030c0.png" />";}i:101;a:2:{i:0;s:123:"\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft \,\!";i:1;s:240:"<img class="mwe-math-fallback-png-inline tex" alt="\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft \,\!" src="/images/math/4/b/d/4bd4fbd2e32aabba593a093331aa5e7a.png" />";}i:102;a:2:{i:0;s:118:"\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow \!";i:1;s:235:"<img class="mwe-math-fallback-png-inline tex" alt="\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow \!" src="/images/math/a/d/1/ad1b5e897e1e42b0541f628ba2373316.png" />";}i:103;a:2:{i:0;s:49:"\amalg \P \S \% \dagger \ddagger \ldots \cdots \!";i:1;s:166:"<img class="mwe-math-fallback-png-inline tex" alt="\amalg \P \S \% \dagger \ddagger \ldots \cdots \!" src="/images/math/c/e/e/cee34c650af3f8f9d2509ff6a532d72b.png" />";}i:104;a:2:{i:0;s:48:"\smile \frown \wr \triangleleft \triangleright\!";i:1;s:165:"<img class="mwe-math-fallback-png-inline tex" alt="\smile \frown \wr \triangleleft \triangleright\!" src="/images/math/2/1/a/21ac72c7b055e08569958c900c80fc2c.png" />";}i:105;a:2:{i:0;s:82:"\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp \!";i:1;s:199:"<img class="mwe-math-fallback-png-inline tex" alt="\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp \!" src="/images/math/0/c/2/0c2b0cc6b1aec3eef3dd4ea2a2577cfd.png" />";}i:106;a:2:{i:0;s:80:"\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes \!";i:1;s:197:"<img class="mwe-math-fallback-png-inline tex" alt="\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes \!" src="/images/math/d/b/4/db4e3633a6cb328d58e994d8902e214c.png" />";}i:107;a:2:{i:0;s:84:"\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq \!";i:1;s:201:"<img class="mwe-math-fallback-png-inline tex" alt="\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq \!" src="/images/math/6/2/1/62167659ee6ffb21c81d130f9444aaeb.png" />";}i:108;a:2:{i:0;s:66:"\intercal \barwedge \veebar \doublebarwedge \between \pitchfork \!";i:1;s:183:"<img class="mwe-math-fallback-png-inline tex" alt="\intercal \barwedge \veebar \doublebarwedge \between \pitchfork \!" src="/images/math/7/7/c/77c1d9d38e2af63f15deb3bfab0a75e8.png" />";}i:109;a:2:{i:0;s:68:"\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright \!";i:1;s:185:"<img class="mwe-math-fallback-png-inline tex" alt="\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright \!" src="/images/math/2/2/9/22942360063a4b9991511ce68a0461b8.png" />";}i:110;a:2:{i:0;s:70:"\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq \!";i:1;s:187:"<img class="mwe-math-fallback-png-inline tex" alt="\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq \!" src="/images/math/3/1/4/314bd37d48aa31ee670ae3c5c94e4663.png" />";}i:111;a:2:{i:0;s:3:"a^2";i:1;s:120:"<img class="mwe-math-fallback-png-inline tex" alt="a^2" src="/images/math/a/4/7/a4791fd2e334993453b00d036ab792af.png" />";}i:112;a:2:{i:0;s:3:"a_2";i:1;s:120:"<img class="mwe-math-fallback-png-inline tex" alt="a_2" src="/images/math/0/f/7/0f768ac5d5dea8d93716a27da05871de.png" />";}i:113;a:2:{i:0;s:15:"10^{30} a^{2+2}";i:1;s:132:"<img class="mwe-math-fallback-png-inline tex" alt="10^{30} a^{2+2}" src="/images/math/3/2/c/32ca3769f0845a739d1905190921cfbf.png" />";}i:114;a:2:{i:0;s:14:"a_{i,j} b_{f'}";i:1;s:136:"<img class="mwe-math-fallback-png-inline tex" alt="a_{i,j} b_{f&#039;}" src="/images/math/0/f/4/0f4147d22d4fd86b0b1ae03159179f75.png" />";}i:115;a:2:{i:0;s:5:"x_2^3";i:1;s:122:"<img class="mwe-math-fallback-png-inline tex" alt="x_2^3" src="/images/math/1/d/3/1d368948190fdda83d5a2a398b1c1927.png" />";}i:116;a:2:{i:0;s:12:"{x_2}^3 \,\!";i:1;s:129:"<img class="mwe-math-fallback-png-inline tex" alt="{x_2}^3 \,\!" src="/images/math/a/1/6/a168479afc14eaf30f911f14100be89d.png" />";}i:117;a:2:{i:0;s:11:"10^{10^{8}}";i:1;s:128:"<img class="mwe-math-fallback-png-inline tex" alt="10^{10^{8}}" src="/images/math/9/c/6/9c6e0dad7a12f5eb70209bc235df2e3a.png" />";}i:118;a:2:{i:0;s:29:"\sideset{_1^2}{_3^4}\prod_a^b";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\sideset{_1^2}{_3^4}\prod_a^b" src="/images/math/b/d/0/bd00243bd391e7d7401aa59203f59981.png" />";}i:119;a:2:{i:0;s:18:"{}_1^2\!\Omega_3^4";i:1;s:135:"<img class="mwe-math-fallback-png-inline tex" alt="{}_1^2\!\Omega_3^4" src="/images/math/1/5/b/15ba0b09e81e31854db164051a52502e.png" />";}i:120;a:2:{i:0;s:24:"\overset{\alpha}{\omega}";i:1;s:141:"<img class="mwe-math-fallback-png-inline tex" alt="\overset{\alpha}{\omega}" src="/images/math/f/d/9/fd91a9665d330097d6f847e140a0bf09.png" />";}i:121;a:2:{i:0;s:25:"\underset{\alpha}{\omega}";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\underset{\alpha}{\omega}" src="/images/math/d/7/5/d75cfe5f3b21632bdc8c274d9690a4a6.png" />";}i:122;a:2:{i:0;s:43:"\overset{\alpha}{\underset{\gamma}{\omega}}";i:1;s:160:"<img class="mwe-math-fallback-png-inline tex" alt="\overset{\alpha}{\underset{\gamma}{\omega}}" src="/images/math/a/d/6/ad6263e136435be19ea5761d672622e9.png" />";}i:123;a:2:{i:0;s:25:"\stackrel{\alpha}{\omega}";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\stackrel{\alpha}{\omega}" src="/images/math/d/e/5/de51915eed5826ec13b061539f249359.png" />";}i:124;a:2:{i:0;s:16:"x', y'', f', f''";i:1;s:163:"<img class="mwe-math-fallback-png-inline tex" alt="x&#039;, y&#039;&#039;, f&#039;, f&#039;&#039;" src="/images/math/3/8/1/38198fd7fa831b8cca706fe92505c726.png" />";}i:125;a:2:{i:0;s:26:"x^\prime, y^{\prime\prime}";i:1;s:143:"<img class="mwe-math-fallback-png-inline tex" alt="x^\prime, y^{\prime\prime}" src="/images/math/3/f/8/3f8892c43f66700333f11c45029e30ac.png" />";}i:126;a:2:{i:0;s:17:"\dot{x}, \ddot{x}";i:1;s:134:"<img class="mwe-math-fallback-png-inline tex" alt="\dot{x}, \ddot{x}" src="/images/math/2/8/c/28c4f624dc02d1e01adde0928c45ff07.png" />";}i:127;a:2:{i:0;s:25:" \hat a \ \bar b \ \vec c";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt=" \hat a \ \bar b \ \vec c" src="/images/math/9/3/f/93f5427e14ad2339f6905e1141f52d38.png" />";}i:128;a:2:{i:0;s:61:" \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}";i:1;s:178:"<img class="mwe-math-fallback-png-inline tex" alt=" \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}" src="/images/math/1/2/e/12e159cc1c8699d116a85ef715af3951.png" />";}i:129;a:2:{i:0;s:37:" \overline{g h i} \ \underline{j k l}";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt=" \overline{g h i} \ \underline{j k l}" src="/images/math/2/d/c/2dc44edf7a2bdedf2e01e6622e15d695.png" />";}i:130;a:2:{i:0;s:21:"\overset{\frown} {AB}";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\overset{\frown} {AB}" src="/images/math/8/7/4/8748475980cbfc9c9028b4b298d2f438.png" />";}i:131;a:2:{i:0;s:53:" A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C";i:1;s:170:"<img class="mwe-math-fallback-png-inline tex" alt=" A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C" src="/images/math/c/e/5/ce50e9216ca80ae92251cbdeea7ce134.png" />";}i:132;a:2:{i:0;s:35:"\overbrace{ 1+2+\cdots+100 }^{5050}";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="\overbrace{ 1+2+\cdots+100 }^{5050}" src="/images/math/8/1/3/813e812891b31b2b02178327fd69fdb9.png" />";}i:133;a:2:{i:0;s:32:"\underbrace{ a+b+\cdots+z }_{26}";i:1;s:149:"<img class="mwe-math-fallback-png-inline tex" alt="\underbrace{ a+b+\cdots+z }_{26}" src="/images/math/f/1/d/f1da0064e0dba6c5951d44e07e191c5a.png" />";}i:134;a:2:{i:0;s:16:"\sum_{k=1}^N k^2";i:1;s:133:"<img class="mwe-math-fallback-png-inline tex" alt="\sum_{k=1}^N k^2" src="/images/math/3/1/8/3187b0dd4e53e474d81e26f775c1cdfa.png" />";}i:135;a:2:{i:0;s:27:"\textstyle \sum_{k=1}^N k^2";i:1;s:144:"<img class="mwe-math-fallback-png-inline tex" alt="\textstyle \sum_{k=1}^N k^2" src="/images/math/e/e/6/ee6fd1bafe0faa5913e5cf53d90096fa.png" />";}i:136;a:2:{i:0;s:26:"\frac{\sum_{k=1}^N k^2}{a}";i:1;s:143:"<img class="mwe-math-fallback-png-inline tex" alt="\frac{\sum_{k=1}^N k^2}{a}" src="/images/math/e/4/b/e4b2e0205d7b4bc8dfdd8bfb4fa6986e.png" />";}i:137;a:2:{i:0;s:40:"\frac{\displaystyle \sum_{k=1}^N k^2}{a}";i:1;s:157:"<img class="mwe-math-fallback-png-inline tex" alt="\frac{\displaystyle \sum_{k=1}^N k^2}{a}" src="/images/math/8/c/1/8c1e37db35417fd592a89614b954327d.png" />";}i:138;a:2:{i:0;s:36:"\frac{\sum\limits^{^N}_{k=1} k^2}{a}";i:1;s:153:"<img class="mwe-math-fallback-png-inline tex" alt="\frac{\sum\limits^{^N}_{k=1} k^2}{a}" src="/images/math/f/6/e/f6e3e304b3ee1d87ebb949075e8839e4.png" />";}i:139;a:2:{i:0;s:17:"\prod_{i=1}^N x_i";i:1;s:134:"<img class="mwe-math-fallback-png-inline tex" alt="\prod_{i=1}^N x_i" src="/images/math/f/2/b/f2be40a3bca3b9cc59559468999c5a9d.png" />";}i:140;a:2:{i:0;s:28:"\textstyle \prod_{i=1}^N x_i";i:1;s:145:"<img class="mwe-math-fallback-png-inline tex" alt="\textstyle \prod_{i=1}^N x_i" src="/images/math/6/5/b/65b9b87b09704b4e4301e774de4c57ae.png" />";}i:141;a:2:{i:0;s:19:"\coprod_{i=1}^N x_i";i:1;s:136:"<img class="mwe-math-fallback-png-inline tex" alt="\coprod_{i=1}^N x_i" src="/images/math/d/6/8/d684b776e6e99aaa14db27115904c5bf.png" />";}i:142;a:2:{i:0;s:30:"\textstyle \coprod_{i=1}^N x_i";i:1;s:147:"<img class="mwe-math-fallback-png-inline tex" alt="\textstyle \coprod_{i=1}^N x_i" src="/images/math/1/4/a/14a11d376f41516ee499e2830f056523.png" />";}i:143;a:2:{i:0;s:22:"\lim_{n \to \infty}x_n";i:1;s:139:"<img class="mwe-math-fallback-png-inline tex" alt="\lim_{n \to \infty}x_n" src="/images/math/f/6/4/f64f3526ec6d389a67c3e13dbf609dc9.png" />";}i:144;a:2:{i:0;s:33:"\textstyle \lim_{n \to \infty}x_n";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\textstyle \lim_{n \to \infty}x_n" 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:158:"<img class="mwe-math-fallback-png-inline 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:151:"<img class="mwe-math-fallback-png-inline 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:157:"<img class="mwe-math-fallback-png-inline 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:150:"<img class="mwe-math-fallback-png-inline 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:141:"<img class="mwe-math-fallback-png-inline 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:146:"<img class="mwe-math-fallback-png-inline 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:151:"<img class="mwe-math-fallback-png-inline 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:155:"<img class="mwe-math-fallback-png-inline 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:156:"<img class="mwe-math-fallback-png-inline 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:137:"<img class="mwe-math-fallback-png-inline 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:137:"<img class="mwe-math-fallback-png-inline 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:132:"<img class="mwe-math-fallback-png-inline 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:135:"<img class="mwe-math-fallback-png-inline 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:189:"<img class="mwe-math-fallback-png-inline 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:163:"<img class="mwe-math-fallback-png-inline 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:177:"<img class="mwe-math-fallback-png-inline 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:129:"<img class="mwe-math-fallback-png-inline 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:130:"<img class="mwe-math-fallback-png-inline 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:130:"<img class="mwe-math-fallback-png-inline 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:171:"<img class="mwe-math-fallback-png-inline tex" alt="\begin{matrix} x &amp; y \\ z &amp; v&#10;\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:173:"<img class="mwe-math-fallback-png-inline tex" alt="\begin{vmatrix} x &amp; y \\ z &amp; v&#10;\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:173:"<img class="mwe-math-fallback-png-inline tex" alt="\begin{Vmatrix} x &amp; y \\ z &amp; v&#10;\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:239:"<img class="mwe-math-fallback-png-inline tex" alt="\begin{bmatrix} 0 &amp; \cdots &amp; 0 \\ \vdots&#10;&amp; \ddots &amp; \vdots \\ 0 &amp; \cdots &amp;&#10;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:173:"<img class="mwe-math-fallback-png-inline tex" alt="\begin{Bmatrix} x &amp; y \\ z &amp; v&#10;\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:173:"<img class="mwe-math-fallback-png-inline tex" alt="\begin{pmatrix} x &amp; y \\ z &amp; v&#10;\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:204:"<img class="mwe-math-fallback-png-inline tex" alt="&#10;\bigl( \begin{smallmatrix}&#10;a&amp;b\\ c&amp;d&#10;\end{smallmatrix} \bigr)&#10;" 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:245:"<img class="mwe-math-fallback-png-inline tex" alt="f(n) =&#10;\begin{cases}&#10;n/2, &amp; \text{if }n\text{ is even} \\&#10;3n+1, &amp; \text{if }n\text{ is odd}&#10;\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:211:"<img class="mwe-math-fallback-png-inline tex" alt="&#10;\begin{align}&#10;f(x) &amp; = (a+b)^2 \\&#10;&amp; = a^2+2ab+b^2 \\&#10;\end{align}&#10;" 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:218:"<img class="mwe-math-fallback-png-inline tex" alt="&#10;\begin{alignat}{2}&#10;f(x) &amp; = (a-b)^2 \\&#10;&amp; = a^2-2ab+b^2 \\&#10;\end{alignat}&#10;" 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:213:"<img class="mwe-math-fallback-png-inline tex" alt="\begin{array}{lcl}&#10;z &amp; = &amp; a \\&#10;f(x,y,z) &amp; = &amp; x + y + z&#10;\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:213:"<img class="mwe-math-fallback-png-inline tex" alt="\begin{array}{lcr}&#10;z &amp; = &amp; a \\&#10;f(x,y,z) &amp; = &amp; x + y + z&#10;\end{array}" src="/images/math/0/2/a/02ae32735e1e21ba3b05984289fd2763.png" />";}i:176;a:2:{i:0;s:9:"f(x) \,\!";i:1;s:126:"<img class="mwe-math-fallback-png-inline 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:145:"<img class="mwe-math-fallback-png-inline 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:141:"<img class="mwe-math-fallback-png-inline 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:126:"<img class="mwe-math-fallback-png-inline 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:145:"<img class="mwe-math-fallback-png-inline 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:142:"<img class="mwe-math-fallback-png-inline 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:187:"<img class="mwe-math-fallback-png-inline 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:278:"<img class="mwe-math-fallback-png-inline tex" alt="&#10;\begin{array}{|c|c||c|} a &amp; b &amp; S \\&#10;\hline&#10;0&amp;0&amp;1\\&#10;0&amp;1&amp;1\\&#10;1&amp;0&amp;1\\&#10;1&amp;1&amp;0\\&#10;\end{array}&#10;" src="/images/math/9/1/5/9151e94ef2bb52c18176dbe4c11921ed.png" />";}i:184;a:2:{i:0;s:15:"( \frac{1}{2} )";i:1;s:132:"<img class="mwe-math-fallback-png-inline 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:145:"<img class="mwe-math-fallback-png-inline 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:145:"<img class="mwe-math-fallback-png-inline 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:192:"<img class="mwe-math-fallback-png-inline 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:194:"<img class="mwe-math-fallback-png-inline 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:157:"<img class="mwe-math-fallback-png-inline 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:189:"<img class="mwe-math-fallback-png-inline 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:202:"<img class="mwe-math-fallback-png-inline 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:154:"<img class="mwe-math-fallback-png-inline 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:269:"<img class="mwe-math-fallback-png-inline 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:137:"<img class="mwe-math-fallback-png-inline 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:144:"<img class="mwe-math-fallback-png-inline tex" alt="\left \langle \psi \right |" src="/images/math/d/a/2/da25fc177fd4c53a2c3399c25685dd4c.png" />";}i:196;a:2:{i:0;s:35:"\left . \frac{A}{B} \right \} \to X";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="\left . \frac{A}{B} \right \} \to X" src="/images/math/b/7/1/b71d82a3ed5c1a72ded46efc19ecc582.png" />";}i:197;a:2:{i:0;s:57:"\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]";i:1;s:174:"<img class="mwe-math-fallback-png-inline tex" alt="\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]" src="/images/math/6/4/2/642a7988a93248dd92f1a53804cd40aa.png" />";}i:198;a:2:{i:0;s:85:"\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle";i:1;s:202:"<img class="mwe-math-fallback-png-inline tex" alt="\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle" src="/images/math/a/3/c/a3c9de0fb4f73e62e457cc7c91c5f6f0.png" />";}i:199;a:2:{i:0;s:61:"\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|";i:1;s:178:"<img class="mwe-math-fallback-png-inline tex" alt="\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|" src="/images/math/0/4/4/0445cc925a6ea0bd478a8f5fefc3633c.png" />";}i:200;a:2:{i:0;s:101:"\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil";i:1;s:218:"<img class="mwe-math-fallback-png-inline tex" alt="\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil" src="/images/math/9/4/c/94c286b66620b6e5cd43c5cc20fe1a22.png" />";}i:201;a:2:{i:0;s:121:"\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow";i:1;s:238:"<img class="mwe-math-fallback-png-inline tex" alt="\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow" src="/images/math/e/1/6/e16f28e8e168f07f25b7a0162ccc2866.png" />";}i:202;a:2:{i:0;s:145:"\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow";i:1;s:262:"<img class="mwe-math-fallback-png-inline tex" alt="\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow" src="/images/math/d/3/0/d30b4b79fa453480ad0a50be8dfd8911.png" />";}i:203;a:2:{i:0;s:97:"\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash";i:1;s:214:"<img class="mwe-math-fallback-png-inline tex" alt="\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash" src="/images/math/f/0/1/f01a0b3277fdff89f7dee39c2d6f7928.png" />";}i:204;a:2:{i:0;s:22:"x^2 + y^2 + z^2 = 1 \,";i:1;s:139:"<img class="mwe-math-fallback-png-inline tex" alt="x^2 + y^2 + z^2 = 1 \," src="/images/math/6/5/f/65f59a1d3fcd866ff10d5e3ac57f991e.png" />";}i:205;a:2:{i:0;s:56:"\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta \!";i:1;s:173:"<img class="mwe-math-fallback-png-inline tex" alt="\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta \!" src="/images/math/a/7/a/a7a8e6bbde24e99f9dab00c840f9483d.png" />";}i:206;a:2:{i:0;s:44:"\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho \!";i:1;s:161:"<img class="mwe-math-fallback-png-inline tex" alt="\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho \!" src="/images/math/5/0/5/5052faf817c1a445941f4005983fdc63.png" />";}i:207;a:2:{i:0;s:45:"\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega \!";i:1;s:162:"<img class="mwe-math-fallback-png-inline tex" alt="\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega \!" src="/images/math/9/d/9/9d97dae2e9b62c1c9b6c104ef5eac475.png" />";}i:208;a:2:{i:0;s:56:"\alpha \beta \gamma \delta \epsilon \zeta \eta \theta \!";i:1;s:173:"<img class="mwe-math-fallback-png-inline tex" alt="\alpha \beta \gamma \delta \epsilon \zeta \eta \theta \!" src="/images/math/9/f/e/9fef94989f0aefed4c953823bd945e89.png" />";}i:209;a:2:{i:0;s:44:"\iota \kappa \lambda \mu \nu \xi \pi \rho \!";i:1;s:161:"<img class="mwe-math-fallback-png-inline tex" alt="\iota \kappa \lambda \mu \nu \xi \pi \rho \!" src="/images/math/d/d/4/dd438c310fdd611181d2d78eeca09d6f.png" />";}i:210;a:2:{i:0;s:45:"\sigma \tau \upsilon \phi \chi \psi \omega \!";i:1;s:162:"<img class="mwe-math-fallback-png-inline tex" alt="\sigma \tau \upsilon \phi \chi \psi \omega \!" src="/images/math/c/5/a/c5a0f66abb41232d4d6e6e79954e3ee2.png" />";}i:211;a:2:{i:0;s:40:"\varepsilon \digamma \varkappa \varpi \!";i:1;s:157:"<img class="mwe-math-fallback-png-inline tex" alt="\varepsilon \digamma \varkappa \varpi \!" src="/images/math/d/3/9/d393ba319387b0c29b54c3488101e21b.png" />";}i:212;a:2:{i:0;s:38:"\varrho \varsigma \vartheta \varphi \!";i:1;s:155:"<img class="mwe-math-fallback-png-inline tex" alt="\varrho \varsigma \vartheta \varphi \!" src="/images/math/4/0/7/40714b7031faeacd49b6f8e23a529b7f.png" />";}i:213;a:2:{i:0;s:30:"\aleph \beth \gimel \daleth \!";i:1;s:147:"<img class="mwe-math-fallback-png-inline tex" alt="\aleph \beth \gimel \daleth \!" src="/images/math/d/0/2/d02fa3b52ced52aa798b674ea5710116.png" />";}i:214;a:2:{i:0;s:21:"\mathbb{ABCDEFGHI} \!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\mathbb{ABCDEFGHI} \!" src="/images/math/1/6/b/16b49d7cbcbe69f78f5b039e1082eb21.png" />";}i:215;a:2:{i:0;s:21:"\mathbb{JKLMNOPQR} \!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\mathbb{JKLMNOPQR} \!" src="/images/math/5/9/8/59834bc6366bc6bd065b46c9da28b81f.png" />";}i:216;a:2:{i:0;s:20:"\mathbb{STUVWXYZ} \!";i:1;s:137:"<img class="mwe-math-fallback-png-inline tex" alt="\mathbb{STUVWXYZ} \!" src="/images/math/f/8/c/f8cecba104ecf7248d1e8624ea4f97ad.png" />";}i:217;a:2:{i:0;s:21:"\mathbf{ABCDEFGHI} \!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\mathbf{ABCDEFGHI} \!" src="/images/math/a/0/0/a007c39fe7cdcaac5787780cd59f9863.png" />";}i:218;a:2:{i:0;s:21:"\mathbf{JKLMNOPQR} \!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\mathbf{JKLMNOPQR} \!" src="/images/math/d/5/7/d576d3e20c41ffb373b3aa2666f84631.png" />";}i:219;a:2:{i:0;s:20:"\mathbf{STUVWXYZ} \!";i:1;s:137:"<img class="mwe-math-fallback-png-inline tex" alt="\mathbf{STUVWXYZ} \!" src="/images/math/d/6/3/d63658e6be16cb35c5eeddd9af0d0456.png" />";}i:220;a:2:{i:0;s:25:"\mathbf{abcdefghijklm} \!";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\mathbf{abcdefghijklm} \!" src="/images/math/7/4/6/746a58465658c7ce27865b5874b866de.png" />";}i:221;a:2:{i:0;s:25:"\mathbf{nopqrstuvwxyz} \!";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\mathbf{nopqrstuvwxyz} \!" src="/images/math/7/a/2/7a2d9be40a985f3f4062e810aa82850f.png" />";}i:222;a:2:{i:0;s:22:"\mathbf{0123456789} \!";i:1;s:139:"<img class="mwe-math-fallback-png-inline tex" alt="\mathbf{0123456789} \!" src="/images/math/b/5/8/b58f56dec00a8c4058e96f4868dfaf38.png" />";}i:223;a:2:{i:0;s:62:"\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!";i:1;s:179:"<img class="mwe-math-fallback-png-inline tex" alt="\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!" src="/images/math/5/3/c/53c4c980272d709263a0ec407ce9f000.png" />";}i:224;a:2:{i:0;s:50:"\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!";i:1;s:167:"<img class="mwe-math-fallback-png-inline tex" alt="\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!" src="/images/math/e/6/8/e68389a7314c09b14444e535f71e853c.png" />";}i:225;a:2:{i:0;s:52:"\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!";i:1;s:169:"<img class="mwe-math-fallback-png-inline tex" alt="\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!" src="/images/math/7/2/f/72f30cfb281ddfdbd437f17eab32dfde.png" />";}i:226;a:2:{i:0;s:62:"\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta} \!";i:1;s:179:"<img class="mwe-math-fallback-png-inline tex" alt="\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta} \!" src="/images/math/c/3/d/c3d73d4055fbe3c3631848bc0317a0c5.png" />";}i:227;a:2:{i:0;s:50:"\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho} \!";i:1;s:167:"<img class="mwe-math-fallback-png-inline tex" alt="\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho} \!" src="/images/math/d/8/b/d8bf62dcf94457cebec14434b72e3f62.png" />";}i:228;a:2:{i:0;s:52:"\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega} \!";i:1;s:169:"<img class="mwe-math-fallback-png-inline tex" alt="\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega} \!" src="/images/math/3/8/0/3801c81d051bce44677f49e7d9069dd5.png" />";}i:229;a:2:{i:0;s:50:"\boldsymbol{\varepsilon\digamma\varkappa\varpi} \!";i:1;s:167:"<img class="mwe-math-fallback-png-inline tex" alt="\boldsymbol{\varepsilon\digamma\varkappa\varpi} \!" src="/images/math/2/7/b/27b172a5d4d90f193347807c2828a142.png" />";}i:230;a:2:{i:0;s:48:"\boldsymbol{\varrho\varsigma\vartheta\varphi} \!";i:1;s:165:"<img class="mwe-math-fallback-png-inline tex" alt="\boldsymbol{\varrho\varsigma\vartheta\varphi} \!" src="/images/math/9/d/c/9dc6a867e48fba8d25fdd599b6330f4f.png" />";}i:231;a:2:{i:0;s:22:"\mathit{0123456789} \!";i:1;s:139:"<img class="mwe-math-fallback-png-inline tex" alt="\mathit{0123456789} \!" src="/images/math/9/6/8/96846c8042557a593245c9adbfadcf67.png" />";}i:232;a:2:{i:0;s:58:"\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!";i:1;s:175:"<img class="mwe-math-fallback-png-inline tex" alt="\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!" src="/images/math/c/a/1/ca124a231c239009f51303d8ac514eff.png" />";}i:233;a:2:{i:0;s:46:"\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!";i:1;s:163:"<img class="mwe-math-fallback-png-inline tex" alt="\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!" src="/images/math/b/f/a/bfa30e6555a2803a938815fbee4a2c0a.png" />";}i:234;a:2:{i:0;s:48:"\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!";i:1;s:165:"<img class="mwe-math-fallback-png-inline tex" alt="\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!" src="/images/math/b/2/d/b2ddf1062667a4ba071276d7368fe453.png" />";}i:235;a:2:{i:0;s:21:"\mathrm{ABCDEFGHI} \!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\mathrm{ABCDEFGHI} \!" src="/images/math/3/d/3/3d36032a7983b4c8da9148beaf789055.png" />";}i:236;a:2:{i:0;s:21:"\mathrm{JKLMNOPQR} \!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\mathrm{JKLMNOPQR} \!" src="/images/math/a/9/d/a9d3a8ae5e05b7bd96f20871e0c1cb96.png" />";}i:237;a:2:{i:0;s:20:"\mathrm{STUVWXYZ} \!";i:1;s:137:"<img class="mwe-math-fallback-png-inline tex" alt="\mathrm{STUVWXYZ} \!" src="/images/math/e/a/8/ea8b007cc18c226d2143fd4c43f0cca4.png" />";}i:238;a:2:{i:0;s:25:"\mathrm{abcdefghijklm} \!";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\mathrm{abcdefghijklm} \!" src="/images/math/9/f/6/9f6eb1d0200709ff7caf09f99faa4bd4.png" />";}i:239;a:2:{i:0;s:25:"\mathrm{nopqrstuvwxyz} \!";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\mathrm{nopqrstuvwxyz} \!" src="/images/math/b/8/d/b8dbd6a0585c8b2ce9094a777e2e716e.png" />";}i:240;a:2:{i:0;s:22:"\mathrm{0123456789} \!";i:1;s:139:"<img class="mwe-math-fallback-png-inline tex" alt="\mathrm{0123456789} \!" src="/images/math/f/6/8/f68e3877be64b002381f33959430445c.png" />";}i:241;a:2:{i:0;s:21:"\mathsf{ABCDEFGHI} \!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\mathsf{ABCDEFGHI} \!" src="/images/math/8/a/3/8a3b93220f8167b67275c84486fbfefd.png" />";}i:242;a:2:{i:0;s:21:"\mathsf{JKLMNOPQR} \!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\mathsf{JKLMNOPQR} \!" src="/images/math/c/8/4/c846a434b8192403806e5afa67cb56c8.png" />";}i:243;a:2:{i:0;s:20:"\mathsf{STUVWXYZ} \!";i:1;s:137:"<img class="mwe-math-fallback-png-inline tex" alt="\mathsf{STUVWXYZ} \!" src="/images/math/4/6/5/465dc4c154760665cb218bf372b5077b.png" />";}i:244;a:2:{i:0;s:25:"\mathsf{abcdefghijklm} \!";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\mathsf{abcdefghijklm} \!" src="/images/math/e/e/0/ee0e512b5e7b926eb2ad3ccb2e97f99e.png" />";}i:245;a:2:{i:0;s:25:"\mathsf{nopqrstuvwxyz} \!";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\mathsf{nopqrstuvwxyz} \!" src="/images/math/c/6/8/c681c7261b4988870a4d21531838e1ff.png" />";}i:246;a:2:{i:0;s:22:"\mathsf{0123456789} \!";i:1;s:139:"<img class="mwe-math-fallback-png-inline tex" alt="\mathsf{0123456789} \!" src="/images/math/4/c/0/4c0a1005670f8615d3f6a5e2a3f7ebae.png" />";}i:247;a:2:{i:0;s:65:"\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} \!";i:1;s:182:"<img class="mwe-math-fallback-png-inline tex" alt="\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} \!" src="/images/math/5/6/3/563865ef112b2951163ce8e1069f9f8e.png" />";}i:248;a:2:{i:0;s:53:"\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho} \!";i:1;s:170:"<img class="mwe-math-fallback-png-inline tex" alt="\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho} \!" src="/images/math/c/d/a/cdaf253be44a861a7d892226543e6672.png" />";}i:249;a:2:{i:0;s:53:"\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}\!";i:1;s:170:"<img class="mwe-math-fallback-png-inline tex" alt="\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}\!" src="/images/math/d/3/d/d3df02b6333f8234da8af066da224e14.png" />";}i:250;a:2:{i:0;s:22:"\mathcal{ABCDEFGHI} \!";i:1;s:139:"<img class="mwe-math-fallback-png-inline tex" alt="\mathcal{ABCDEFGHI} \!" src="/images/math/d/7/2/d728a6ce6448bfd13bfee7b34b988477.png" />";}i:251;a:2:{i:0;s:22:"\mathcal{JKLMNOPQR} \!";i:1;s:139:"<img class="mwe-math-fallback-png-inline tex" alt="\mathcal{JKLMNOPQR} \!" src="/images/math/2/3/1/231d55516d700b93504c5391b0bbd482.png" />";}i:252;a:2:{i:0;s:21:"\mathcal{STUVWXYZ} \!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\mathcal{STUVWXYZ} \!" src="/images/math/6/7/1/671cdb09089e8aea4d1c10963dff47bb.png" />";}i:253;a:2:{i:0;s:23:"\mathfrak{ABCDEFGHI} \!";i:1;s:140:"<img class="mwe-math-fallback-png-inline tex" alt="\mathfrak{ABCDEFGHI} \!" src="/images/math/1/0/8/1086f52f9d3b3a3409c30f9df307803d.png" />";}i:254;a:2:{i:0;s:23:"\mathfrak{JKLMNOPQR} \!";i:1;s:140:"<img class="mwe-math-fallback-png-inline tex" alt="\mathfrak{JKLMNOPQR} \!" src="/images/math/c/9/9/c99678db9d429d52ea0eb02bba3b72f6.png" />";}i:255;a:2:{i:0;s:22:"\mathfrak{STUVWXYZ} \!";i:1;s:139:"<img class="mwe-math-fallback-png-inline tex" alt="\mathfrak{STUVWXYZ} \!" src="/images/math/d/e/8/de83cd08cc780451bd2330d3d40b1532.png" />";}i:256;a:2:{i:0;s:27:"\mathfrak{abcdefghijklm} \!";i:1;s:144:"<img class="mwe-math-fallback-png-inline tex" alt="\mathfrak{abcdefghijklm} \!" src="/images/math/3/6/4/3648203f3849eb6a103cab171143bff5.png" />";}i:257;a:2:{i:0;s:27:"\mathfrak{nopqrstuvwxyz} \!";i:1;s:144:"<img class="mwe-math-fallback-png-inline tex" alt="\mathfrak{nopqrstuvwxyz} \!" src="/images/math/6/1/6/61605c6e5c504c766b330ca61d747920.png" />";}i:258;a:2:{i:0;s:24:"\mathfrak{0123456789} \!";i:1;s:141:"<img class="mwe-math-fallback-png-inline tex" alt="\mathfrak{0123456789} \!" src="/images/math/d/7/c/d7ce6e5c0f153732ba276fbfc47f019b.png" />";}i:259;a:2:{i:0;s:5:"x y z";i:1;s:122:"<img class="mwe-math-fallback-png-inline tex" alt="x y z" src="/images/math/d/1/6/d16fb36f0911f878998c136191af705e.png" />";}i:260;a:2:{i:0;s:12:"\text{x y z}";i:1;s:129:"<img class="mwe-math-fallback-png-inline tex" alt="\text{x y z}" src="/images/math/c/c/6/cc6e918f4c63d050ae99d4381c7bb2d5.png" />";}i:261;a:2:{i:0;s:26:"\text{if} n \text{is even}";i:1;s:143:"<img class="mwe-math-fallback-png-inline tex" alt="\text{if} n \text{is even}" src="/images/math/d/2/f/d2f16386d2a4bbd2fd4b7187fcf73a52.png" />";}i:262;a:2:{i:0;s:26:"\text{if }n\text{ is even}";i:1;s:143:"<img class="mwe-math-fallback-png-inline tex" alt="\text{if }n\text{ is even}" src="/images/math/8/2/9/82915036ba72b9f1dacfd528d40f4371.png" />";}i:263;a:2:{i:0;s:27:"\text{if}~n\ \text{is even}";i:1;s:144:"<img class="mwe-math-fallback-png-inline tex" alt="\text{if}~n\ \text{is even}" src="/images/math/9/7/1/971bad3f2ace3107b439f9af94476aed.png" />";}i:264;a:2:{i:0;s:64:"{\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}";i:1;s:181:"<img class="mwe-math-fallback-png-inline tex" alt="{\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}" src="/images/math/3/2/2/3220b8a1d12128d1ada4a82d5c3d3723.png" />";}i:265;a:2:{i:0;s:49:"x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}";i:1;s:166:"<img class="mwe-math-fallback-png-inline tex" alt="x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}" src="/images/math/4/4/3/443e636a7722cec5d8f7b005deb2433a.png" />";}i:266;a:2:{i:0;s:17:"e^{i \pi} + 1 = 0";i:1;s:134:"<img class="mwe-math-fallback-png-inline tex" alt="e^{i \pi} + 1 = 0" src="/images/math/f/8/9/f897005615c391e14cd50112cda44665.png" />";}i:267;a:2:{i:0;s:71:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";i:1;s:188:"<img class="mwe-math-fallback-png-inline tex" alt="\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0" src="/images/math/9/5/d/95dfa34eee8b069de07f18e7f3b43cea.png" />";}i:268;a:2:{i:0;s:21:"e^{i \pi} + 1 = 0\,\!";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="e^{i \pi} + 1 = 0\,\!" src="/images/math/9/e/9/9e9a547076c6820b95e439dd1a5d6a32.png" />";}i:269;a:2:{i:0;s:71:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";i:1;s:188:"<img class="mwe-math-fallback-png-inline tex" alt="\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0" src="/images/math/9/5/d/95dfa34eee8b069de07f18e7f3b43cea.png" />";}i:270;a:2:{i:0;s:17:"e^{i \pi} + 1 = 0";i:1;s:134:"<img class="mwe-math-fallback-png-inline tex" alt="e^{i \pi} + 1 = 0" src="/images/math/f/8/9/f897005615c391e14cd50112cda44665.png" />";}i:271;a:2:{i:0;s:71:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";i:1;s:188:"<img class="mwe-math-fallback-png-inline tex" alt="\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0" src="/images/math/9/5/d/95dfa34eee8b069de07f18e7f3b43cea.png" />";}i:272;a:2:{i:0;s:29:"\color{Apricot}\text{Apricot}";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Apricot}\text{Apricot}" src="/images/math/b/8/9/b8948aeb7bdca5bd4e18d613ac6c5696.png" />";}i:273;a:2:{i:0;s:35:"\color{Aquamarine}\text{Aquamarine}";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Aquamarine}\text{Aquamarine}" src="/images/math/f/c/4/fc435c38d6cd34147f1b0562b0e580c0.png" />";}i:274;a:2:{i:0;s:37:"\color{Bittersweet}\text{Bittersweet}";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Bittersweet}\text{Bittersweet}" src="/images/math/d/6/7/d67b10dd93c2300ee8d13b5099078d1b.png" />";}i:275;a:2:{i:0;s:25:"\color{Black}\text{Black}";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Black}\text{Black}" src="/images/math/3/6/4/364fc160f6c30914ad3d70a6bb551dc6.png" />";}i:276;a:2:{i:0;s:23:"\color{Blue}\text{Blue}";i:1;s:140:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Blue}\text{Blue}" src="/images/math/5/f/7/5f795126f5d16b97c60578f01b368cd6.png" />";}i:277;a:2:{i:0;s:33:"\color{BlueGreen}\text{BlueGreen}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{BlueGreen}\text{BlueGreen}" src="/images/math/3/0/2/302ea2ab02b2998679c1f973dfb17395.png" />";}i:278;a:2:{i:0;s:35:"\color{BlueViolet}\text{BlueViolet}";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="\color{BlueViolet}\text{BlueViolet}" src="/images/math/f/7/d/f7d3a6b44f64ec4d9b289bf8ac436d92.png" />";}i:279;a:2:{i:0;s:31:"\color{BrickRed}\text{BrickRed}";i:1;s:148:"<img class="mwe-math-fallback-png-inline tex" alt="\color{BrickRed}\text{BrickRed}" src="/images/math/a/2/f/a2f94714d1809cb3f71016db0e8c2315.png" />";}i:280;a:2:{i:0;s:25:"\color{Brown}\text{Brown}";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Brown}\text{Brown}" src="/images/math/9/9/c/99cfd151aa2998fb6b309c8c50393c32.png" />";}i:281;a:2:{i:0;s:37:"\color{BurntOrange}\text{BurntOrange}";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\color{BurntOrange}\text{BurntOrange}" src="/images/math/3/e/3/3e3b04676ace992e28aaa5608455a289.png" />";}i:282;a:2:{i:0;s:33:"\color{CadetBlue}\text{CadetBlue}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{CadetBlue}\text{CadetBlue}" src="/images/math/f/d/3/fd392c22a7bb76e6203788f0a5e6584b.png" />";}i:283;a:2:{i:0;s:41:"\color{CarnationPink}\text{CarnationPink}";i:1;s:158:"<img class="mwe-math-fallback-png-inline tex" alt="\color{CarnationPink}\text{CarnationPink}" src="/images/math/6/0/7/6079cf2eacc794bf3e99bc9fc233e2d0.png" />";}i:284;a:2:{i:0;s:31:"\color{Cerulean}\text{Cerulean}";i:1;s:148:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Cerulean}\text{Cerulean}" src="/images/math/9/7/5/9759c3640f8f5a2cfa5cfa5c4bc64e2f.png" />";}i:285;a:2:{i:0;s:43:"\color{CornflowerBlue}\text{CornflowerBlue}";i:1;s:160:"<img class="mwe-math-fallback-png-inline tex" alt="\color{CornflowerBlue}\text{CornflowerBlue}" src="/images/math/0/7/2/072ea0cddb81b6996a86c5c60042fc8c.png" />";}i:286;a:2:{i:0;s:23:"\color{Cyan}\text{Cyan}";i:1;s:140:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Cyan}\text{Cyan}" src="/images/math/3/2/1/321ecf031772dbe95758cab0dfaa6f27.png" />";}i:287;a:2:{i:0;s:33:"\color{Dandelion}\text{Dandelion}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Dandelion}\text{Dandelion}" src="/images/math/7/8/6/78686b75a31528404d2e9b365f892142.png" />";}i:288;a:2:{i:0;s:35:"\color{DarkOrchid}\text{DarkOrchid}";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="\color{DarkOrchid}\text{DarkOrchid}" src="/images/math/1/9/b/19bc495f720e6bb920eed9545880e383.png" />";}i:289;a:2:{i:0;s:29:"\color{Emerald}\text{Emerald}";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Emerald}\text{Emerald}" src="/images/math/b/4/3/b4310eecc8d70893a71a728574dc9f0f.png" />";}i:290;a:2:{i:0;s:37:"\color{ForestGreen}\text{ForestGreen}";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\color{ForestGreen}\text{ForestGreen}" src="/images/math/b/8/9/b89859eb7faadeb40830600590478e6e.png" />";}i:291;a:2:{i:0;s:29:"\color{Fuchsia}\text{Fuchsia}";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Fuchsia}\text{Fuchsia}" src="/images/math/3/0/7/3073bfb913846b8b74d221b3de291348.png" />";}i:292;a:2:{i:0;s:33:"\color{Goldenrod}\text{Goldenrod}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Goldenrod}\text{Goldenrod}" src="/images/math/a/f/6/af66a8061a03abb89bc4d205503d437f.png" />";}i:293;a:2:{i:0;s:23:"\color{Gray}\text{Gray}";i:1;s:140:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Gray}\text{Gray}" src="/images/math/1/e/5/1e5478f23b28143107d25266b55ef78a.png" />";}i:294;a:2:{i:0;s:25:"\color{Green}\text{Green}";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Green}\text{Green}" src="/images/math/9/4/7/9474b1edd45b5aefe4533543fe85bbbd.png" />";}i:295;a:2:{i:0;s:37:"\color{GreenYellow}\text{GreenYellow}";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\color{GreenYellow}\text{GreenYellow}" src="/images/math/9/0/6/906467f5d3fa98cfa97b4194f268d5c7.png" />";}i:296;a:2:{i:0;s:37:"\color{JungleGreen}\text{JungleGreen}";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\color{JungleGreen}\text{JungleGreen}" src="/images/math/f/7/2/f72158890930502ffd7dae256812f7e4.png" />";}i:297;a:2:{i:0;s:31:"\color{Lavender}\text{Lavender}";i:1;s:148:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Lavender}\text{Lavender}" src="/images/math/f/2/f/f2fa7339ac0b50f73409f1e05eb77800.png" />";}i:298;a:2:{i:0;s:33:"\color{LimeGreen}\text{LimeGreen}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{LimeGreen}\text{LimeGreen}" src="/images/math/c/4/c/c4c5d14dea2c682d5f4148eab87e332f.png" />";}i:299;a:2:{i:0;s:29:"\color{Magenta}\text{Magenta}";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Magenta}\text{Magenta}" src="/images/math/d/9/b/d9bfd6c63b5b8c21f53e52a74a75eb97.png" />";}i:300;a:2:{i:0;s:31:"\color{Mahogany}\text{Mahogany}";i:1;s:148:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Mahogany}\text{Mahogany}" src="/images/math/d/b/b/dbb2ef205ba8d4d3586b1b9785c54c25.png" />";}i:301;a:2:{i:0;s:27:"\color{Maroon}\text{Maroon}";i:1;s:144:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Maroon}\text{Maroon}" src="/images/math/5/8/6/5861b59a922bda9d96cf03cb8a184a8a.png" />";}i:302;a:2:{i:0;s:25:"\color{Melon}\text{Melon}";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Melon}\text{Melon}" src="/images/math/e/9/b/e9b605ab8c6a1135ac9bb24e540e645b.png" />";}i:303;a:2:{i:0;s:39:"\color{MidnightBlue}\text{MidnightBlue}";i:1;s:156:"<img class="mwe-math-fallback-png-inline tex" alt="\color{MidnightBlue}\text{MidnightBlue}" src="/images/math/3/c/1/3c196c0de1592080c250b05208cb29c1.png" />";}i:304;a:2:{i:0;s:31:"\color{Mulberry}\text{Mulberry}";i:1;s:148:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Mulberry}\text{Mulberry}" src="/images/math/7/8/f/78fe49c7ffa31d0309ecad4e17c8533b.png" />";}i:305;a:2:{i:0;s:31:"\color{NavyBlue}\text{NavyBlue}";i:1;s:148:"<img class="mwe-math-fallback-png-inline tex" alt="\color{NavyBlue}\text{NavyBlue}" src="/images/math/b/5/7/b57ac6d698f2a553d1de298b8ae86f55.png" />";}i:306;a:2:{i:0;s:35:"\color{OliveGreen}\text{OliveGreen}";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="\color{OliveGreen}\text{OliveGreen}" src="/images/math/1/f/f/1ff90d0c4e6d6901579206062701309a.png" />";}i:307;a:2:{i:0;s:27:"\color{Orange}\text{Orange}";i:1;s:144:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Orange}\text{Orange}" src="/images/math/1/d/d/1dd73f756801b262f01f87912b369339.png" />";}i:308;a:2:{i:0;s:33:"\color{OrangeRed}\text{OrangeRed}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{OrangeRed}\text{OrangeRed}" src="/images/math/6/d/f/6df4aca479f5fa8acae9c21141636557.png" />";}i:309;a:2:{i:0;s:27:"\color{Orchid}\text{Orchid}";i:1;s:144:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Orchid}\text{Orchid}" src="/images/math/e/0/3/e03e079ac7c0138cc85bb20894e42c7d.png" />";}i:310;a:2:{i:0;s:25:"\color{Peach}\text{Peach}";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Peach}\text{Peach}" src="/images/math/1/6/a/16a4afaaa911b78f102f2e088c596715.png" />";}i:311;a:2:{i:0;s:35:"\color{Periwinkle}\text{Periwinkle}";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Periwinkle}\text{Periwinkle}" src="/images/math/1/0/4/104bee7d6969d0403571f7aa65390384.png" />";}i:312;a:2:{i:0;s:33:"\color{PineGreen}\text{PineGreen}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{PineGreen}\text{PineGreen}" src="/images/math/5/8/2/5821d738015d4bae29a90be43c9dc760.png" />";}i:313;a:2:{i:0;s:23:"\color{Plum}\text{Plum}";i:1;s:140:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Plum}\text{Plum}" src="/images/math/d/e/3/de3328ac78da89a5e86e1917ec8fb87b.png" />";}i:314;a:2:{i:0;s:37:"\color{ProcessBlue}\text{ProcessBlue}";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\color{ProcessBlue}\text{ProcessBlue}" src="/images/math/e/2/0/e20ab4232d3130d086b8de76eee6b53c.png" />";}i:315;a:2:{i:0;s:27:"\color{Purple}\text{Purple}";i:1;s:144:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Purple}\text{Purple}" src="/images/math/f/e/f/fefd1c1377e3d29213e81e866583adad.png" />";}i:316;a:2:{i:0;s:33:"\color{RawSienna}\text{RawSienna}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{RawSienna}\text{RawSienna}" src="/images/math/7/4/5/745d3d1a6a79b318a497e6fbcb57dc02.png" />";}i:317;a:2:{i:0;s:21:"\color{Red}\text{Red}";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Red}\text{Red}" src="/images/math/9/e/2/9e2052c4c91b5216205fe642a06c5ac1.png" />";}i:318;a:2:{i:0;s:33:"\color{RedOrange}\text{RedOrange}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{RedOrange}\text{RedOrange}" src="/images/math/2/a/0/2a026699e64707b449d7c3811d752725.png" />";}i:319;a:2:{i:0;s:33:"\color{RedViolet}\text{RedViolet}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{RedViolet}\text{RedViolet}" src="/images/math/2/a/c/2ac9ad9fbd882591f7971ff477880fe6.png" />";}i:320;a:2:{i:0;s:33:"\color{Rhodamine}\text{Rhodamine}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Rhodamine}\text{Rhodamine}" src="/images/math/2/7/d/27d615add22f24e5689271903afd2ea8.png" />";}i:321;a:2:{i:0;s:33:"\color{RoyalBlue}\text{RoyalBlue}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{RoyalBlue}\text{RoyalBlue}" src="/images/math/6/e/2/6e26c2a826a4d55150b804f2e71444af.png" />";}i:322;a:2:{i:0;s:37:"\color{RoyalPurple}\text{RoyalPurple}";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\color{RoyalPurple}\text{RoyalPurple}" src="/images/math/d/d/4/dd4a6069922baf4c048592b1bccef491.png" />";}i:323;a:2:{i:0;s:33:"\color{RubineRed}\text{RubineRed}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{RubineRed}\text{RubineRed}" src="/images/math/7/7/1/771e441e86b10ef3db7b7cb90d9570d1.png" />";}i:324;a:2:{i:0;s:27:"\color{Salmon}\text{Salmon}";i:1;s:144:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Salmon}\text{Salmon}" src="/images/math/1/2/0/1204c3c0547f50b71bda5357deba7948.png" />";}i:325;a:2:{i:0;s:31:"\color{SeaGreen}\text{SeaGreen}";i:1;s:148:"<img class="mwe-math-fallback-png-inline tex" alt="\color{SeaGreen}\text{SeaGreen}" src="/images/math/e/8/9/e897b90beb4e669c01a63c3d2ac2d954.png" />";}i:326;a:2:{i:0;s:25:"\color{Sepia}\text{Sepia}";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Sepia}\text{Sepia}" src="/images/math/e/3/b/e3b0037782599bf00cec26b758627e4b.png" />";}i:327;a:2:{i:0;s:29:"\color{SkyBlue}\text{SkyBlue}";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\color{SkyBlue}\text{SkyBlue}" src="/images/math/0/3/b/03bc1de1505a991d0f8c2db1a9211740.png" />";}i:328;a:2:{i:0;s:37:"\color{SpringGreen}\text{SpringGreen}";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\color{SpringGreen}\text{SpringGreen}" src="/images/math/7/d/e/7de66b44de4a77d808c6ad47e0ba3502.png" />";}i:329;a:2:{i:0;s:21:"\color{Tan}\text{Tan}";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Tan}\text{Tan}" src="/images/math/6/9/7/6975e0f90106c5e304d39dfebc6ad1d0.png" />";}i:330;a:2:{i:0;s:31:"\color{TealBlue}\text{TealBlue}";i:1;s:148:"<img class="mwe-math-fallback-png-inline tex" alt="\color{TealBlue}\text{TealBlue}" src="/images/math/2/b/1/2b19a41a6ca9691cdbd5fa9f15665d5a.png" />";}i:331;a:2:{i:0;s:29:"\color{Thistle}\text{Thistle}";i:1;s:146:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Thistle}\text{Thistle}" src="/images/math/8/2/8/828c123619d3d3e078aa28bbb362c389.png" />";}i:332;a:2:{i:0;s:33:"\color{Turquoise}\text{Turquoise}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Turquoise}\text{Turquoise}" src="/images/math/e/d/b/edbea9eb14e35cbadb5e2df41afae369.png" />";}i:333;a:2:{i:0;s:27:"\color{Violet}\text{Violet}";i:1;s:144:"<img class="mwe-math-fallback-png-inline tex" alt="\color{Violet}\text{Violet}" src="/images/math/8/5/d/85da72dd0a892dd3364fefd94a14cf7c.png" />";}i:334;a:2:{i:0;s:33:"\color{VioletRed}\text{VioletRed}";i:1;s:150:"<img class="mwe-math-fallback-png-inline tex" alt="\color{VioletRed}\text{VioletRed}" src="/images/math/9/b/5/9b5d2430fd995e45f7974583ab86db0c.png" />";}i:335;a:2:{i:0;s:43:"\color{WildStrawberry}\text{WildStrawberry}";i:1;s:160:"<img class="mwe-math-fallback-png-inline tex" alt="\color{WildStrawberry}\text{WildStrawberry}" src="/images/math/0/9/6/0962e3794c0315fd26b9668555ebff1c.png" />";}i:336;a:2:{i:0;s:37:"\color{YellowGreen}\text{YellowGreen}";i:1;s:154:"<img class="mwe-math-fallback-png-inline tex" alt="\color{YellowGreen}\text{YellowGreen}" src="/images/math/7/2/a/72a3756fa95c0da850b33ccb7b3e3900.png" />";}i:337;a:2:{i:0;s:39:"\color{YellowOrange}\text{YellowOrange}";i:1;s:156:"<img class="mwe-math-fallback-png-inline tex" alt="\color{YellowOrange}\text{YellowOrange}" src="/images/math/1/1/9/119eb093f2ffcbd3d77a13f55f185f52.png" />";}i:338;a:2:{i:0;s:10:"a \qquad b";i:1;s:127:"<img class="mwe-math-fallback-png-inline tex" alt="a \qquad b" src="/images/math/e/5/0/e505263bc9c94f673c580f3a36a7f08a.png" />";}i:339;a:2:{i:0;s:9:"a \quad b";i:1;s:126:"<img class="mwe-math-fallback-png-inline tex" alt="a \quad b" src="/images/math/d/a/8/da8c1d9effa4501fd80c054e59ad917d.png" />";}i:340;a:2:{i:0;s:4:"a\ b";i:1;s:121:"<img class="mwe-math-fallback-png-inline tex" alt="a\ b" src="/images/math/6/9/2/692d4bffca8e84ffb45cf9d5facf31d6.png" />";}i:341;a:2:{i:0;s:12:"a \mbox{ } b";i:1;s:129:"<img class="mwe-math-fallback-png-inline tex" alt="a \mbox{ } b" src="/images/math/a/2/d/a2dcf5a19724cb3344c10f6da10ad886.png" />";}i:342;a:2:{i:0;s:4:"a\;b";i:1;s:121:"<img class="mwe-math-fallback-png-inline tex" alt="a\;b" src="/images/math/b/5/a/b5ade5d5393fd7727bf77fa44ec8b564.png" />";}i:343;a:2:{i:0;s:4:"a\,b";i:1;s:121:"<img class="mwe-math-fallback-png-inline tex" alt="a\,b" src="/images/math/7/b/e/7bea99aed60ba5e1fe8a134ab43fa85f.png" />";}i:344;a:2:{i:0;s:2:"ab";i:1;s:119:"<img class="mwe-math-fallback-png-inline tex" alt="ab" src="/images/math/1/8/7/187ef4436122d1cc2f40dc2b92f0eba0.png" />";}i:345;a:2:{i:0;s:11:"\mathit{ab}";i:1;s:128:"<img class="mwe-math-fallback-png-inline tex" alt="\mathit{ab}" src="/images/math/9/e/b/9eb2e32cf7426cbd216d0dca18e6584e.png" />";}i:346;a:2:{i:0;s:4:"a\!b";i:1;s:121:"<img class="mwe-math-fallback-png-inline tex" alt="a\!b" src="/images/math/0/f/b/0fbcad5fadb912e8afa6d113a75c83e4.png" />";}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:176:"<img class="mwe-math-fallback-png-inline 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:178:"<img class="mwe-math-fallback-png-inline 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:139:"<img class="mwe-math-fallback-png-inline tex" alt="\int_{-N}^{N} e^x\, dx" src="/images/math/4/e/0/4e053ca66cfc79a2397c40aa34c66a25.png" />";}i:350;a:2:{i:0;s:24:"\sum_{i=0}^\infty 2^{-i}";i:1;s:141:"<img class="mwe-math-fallback-png-inline tex" alt="\sum_{i=0}^\infty 2^{-i}" src="/images/math/a/f/9/af926e99e79600018438bc1ddea6da71.png" />";}i:351;a:2:{i:0;s:57:"\text{geometric series:}\quad \sum_{i=0}^\infty 2^{-i}=2 ";i:1;s:174:"<img class="mwe-math-fallback-png-inline tex" alt="\text{geometric series:}\quad \sum_{i=0}^\infty 2^{-i}=2 " src="/images/math/4/f/3/4f3cab8bdfda51452401e6897c24319a.png" />";}i:352;a:2:{i:0;s:5:"\iint";i:1;s:122:"<img class="mwe-math-fallback-png-inline tex" alt="\iint" src="/images/math/0/e/6/0e66f8f6b272ca5db6f0b3f1c63a7560.png" />";}i:353;a:2:{i:0;s:5:"\oint";i:1;s:122:"<img class="mwe-math-fallback-png-inline tex" alt="\oint" src="/images/math/0/5/8/058bf10c50ba4ee074da24c60a590314.png" />";}i:354;a:2:{i:0;s:90:"\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset \mathbf D \cdot \mathrm{d}\mathbf A";i:1;s:207:"<img class="mwe-math-fallback-png-inline tex" alt="\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset \mathbf D \cdot \mathrm{d}\mathbf A" src="/images/math/2/e/1/2e1f7e4168ae003494bbec19102f4967.png" />";}i:355;a:2:{i:0;s:114:"\int\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\cdot\mathrm{d}\mathbf A";i:1;s:231:"<img class="mwe-math-fallback-png-inline tex" alt="\int\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\cdot\mathrm{d}\mathbf A" src="/images/math/4/d/0/4d0e5fd5543dece7d0ff39eff990efbb.png" />";}i:356;a:2:{i:0;s:139:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\cdot\mathrm{d}\mathbf A";i:1;s:256:"<img class="mwe-math-fallback-png-inline 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:357;a:2:{i:0;s:132:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\;\cdot\mathrm{d}\mathbf A";i:1;s:249:"<img class="mwe-math-fallback-png-inline tex" alt="\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\;\cdot\mathrm{d}\mathbf A" src="/images/math/d/c/5/dc59fde59ad9a9ab03d6e0eafdb6e65a.png" />";}i:358;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:133:"<img class="mwe-math-fallback-png-inline 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:227:"<img class="mwe-math-fallback-png-inline 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:16:"{\scriptstyle S}";i:1;s:133:"<img class="mwe-math-fallback-png-inline tex" alt="{\scriptstyle S}" src="/images/math/7/f/f/7ff140fff7dde71951767d28cb5304ac.png" />";}i:361;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:227:"<img class="mwe-math-fallback-png-inline 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:362;a:2:{i:0;s:57:"\oint_C \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";i:1;s:174:"<img class="mwe-math-fallback-png-inline tex" alt="\oint_C \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 " src="/images/math/0/f/3/0f3f1a7580395190da1d7e7bba5a72e6.png" />";}i:363;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:133:"<img class="mwe-math-fallback-png-inline tex" alt="{\scriptstyle S}" src="/images/math/7/f/f/7ff140fff7dde71951767d28cb5304ac.png" />";}i:364;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:213:"<img class="mwe-math-fallback-png-inline 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:365;a:2:{i:0;s:68:"\oint_{\partial S} \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";i:1;s:185:"<img class="mwe-math-fallback-png-inline tex" alt="\oint_{\partial S} \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 " src="/images/math/2/2/9/229ef1d17720ecf0b771d0783ce81c24.png" />";}i:366;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:133:"<img class="mwe-math-fallback-png-inline tex" alt="{\scriptstyle S}" src="/images/math/7/f/f/7ff140fff7dde71951767d28cb5304ac.png" />";}i:367;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:213:"<img class="mwe-math-fallback-png-inline 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:368;a:2:{i:0;s:11:"\bold{P} = ";i:1;s:128:"<img class="mwe-math-fallback-png-inline tex" alt="\bold{P} = " src="/images/math/5/b/2/5b2cfaf066bee44f213c6c2882e172c7.png" />";}i:369;a:2:{i:0;s:30:"{\scriptstyle \partial \Omega}";i:1;s:147:"<img class="mwe-math-fallback-png-inline tex" alt="{\scriptstyle \partial \Omega}" src="/images/math/3/0/c/30c24016df2b868da4e3a8ec58e45ce7.png" />";}i:370;a:2:{i:0;s:47:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";i:1;s:164:"<img class="mwe-math-fallback-png-inline tex" alt="\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0" src="/images/math/7/3/5/7357641bffa0e625f2d806b7357b7ee5.png" />";}i:371;a:2:{i:0;s:11:"\bold{P} = ";i:1;s:128:"<img class="mwe-math-fallback-png-inline tex" alt="\bold{P} = " src="/images/math/5/b/2/5b2cfaf066bee44f213c6c2882e172c7.png" />";}i:372;a:2:{i:0;s:30:"{\scriptstyle \partial \Omega}";i:1;s:147:"<img class="mwe-math-fallback-png-inline tex" alt="{\scriptstyle \partial \Omega}" src="/images/math/3/0/c/30c24016df2b868da4e3a8ec58e45ce7.png" />";}i:373;a:2:{i:0;s:47:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";i:1;s:164:"<img class="mwe-math-fallback-png-inline tex" alt="\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0" src="/images/math/7/3/5/7357641bffa0e625f2d806b7357b7ee5.png" />";}i:374;a:2:{i:0;s:20:"\overset{\frown}{AB}";i:1;s:137:"<img class="mwe-math-fallback-png-inline tex" alt="\overset{\frown}{AB}" src="/images/math/8/7/4/8748475980cbfc9c9028b4b298d2f438.png" />";}i:375;a:2:{i:0;s:17:"ax^2 + bx + c = 0";i:1;s:134:"<img class="mwe-math-fallback-png-inline tex" alt="ax^2 + bx + c = 0" src="/images/math/0/c/4/0c4913db725b72609d4825124dda12aa.png" />";}i:376;a:2:{i:0;s:17:"ax^2 + bx + c = 0";i:1;s:134:"<img class="mwe-math-fallback-png-inline tex" alt="ax^2 + bx + c = 0" src="/images/math/0/c/4/0c4913db725b72609d4825124dda12aa.png" />";}i:377;a:2:{i:0;s:32:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";i:1;s:149:"<img class="mwe-math-fallback-png-inline tex" alt="x={-b\pm\sqrt{b^2-4ac} \over 2a}" src="/images/math/a/1/f/a1f76f347b763aa6fc880cbc641fc29f.png" />";}i:378;a:2:{i:0;s:32:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";i:1;s:149:"<img class="mwe-math-fallback-png-inline tex" alt="x={-b\pm\sqrt{b^2-4ac} \over 2a}" src="/images/math/a/1/f/a1f76f347b763aa6fc880cbc641fc29f.png" />";}i:379;a:2:{i:0;s:56:"2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)";i:1;s:173:"<img class="mwe-math-fallback-png-inline tex" alt="2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)" src="/images/math/8/9/4/894f312e78ebc09a4e78c11b79cf4a8c.png" />";}i:380;a:2:{i:0;s:56:"2 = \left(
\frac{\left(3-x\right) \times 2}{3-x}
\right)";i:1;s:181:"<img class="mwe-math-fallback-png-inline tex" alt="2 = \left(&#10;\frac{\left(3-x\right) \times 2}{3-x}&#10;\right)" src="/images/math/8/9/4/894f312e78ebc09a4e78c11b79cf4a8c.png" />";}i:381;a:2:{i:0;s:67:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";i:1;s:184:"<img class="mwe-math-fallback-png-inline tex" alt="S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}" src="/images/math/a/a/0/aa0dc58e7114c5b91f6113130dcbc1d5.png" />";}i:382;a:2:{i:0;s:67:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";i:1;s:184:"<img class="mwe-math-fallback-png-inline tex" alt="S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}" src="/images/math/a/a/0/aa0dc58e7114c5b91f6113130dcbc1d5.png" />";}i:383;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:178:"<img class="mwe-math-fallback-png-inline 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:384;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:182:"<img class="mwe-math-fallback-png-inline tex" alt="\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds&#10;= \int_a^x f(y)(x-y)\,dy" src="/images/math/4/4/6/4465ba032469b775777205effe6cdc0f.png" />";}i:385;a:2:{i:0;s:38:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";i:1;s:155:"<img class="mwe-math-fallback-png-inline tex" alt="\det(\mathsf{A}-\lambda\mathsf{I}) = 0" src="/images/math/6/9/1/691187249f1e86a2e459362d66b5a743.png" />";}i:386;a:2:{i:0;s:38:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";i:1;s:155:"<img class="mwe-math-fallback-png-inline tex" alt="\det(\mathsf{A}-\lambda\mathsf{I}) = 0" src="/images/math/6/9/1/691187249f1e86a2e459362d66b5a743.png" />";}i:387;a:2:{i:0;s:18:"\sum_{i=0}^{n-1} i";i:1;s:135:"<img class="mwe-math-fallback-png-inline tex" alt="\sum_{i=0}^{n-1} i" src="/images/math/9/c/3/9c3090bae1d9eccd9e1747ecc51eaece.png" />";}i:388;a:2:{i:0;s:18:"\sum_{i=0}^{n-1} i";i:1;s:135:"<img class="mwe-math-fallback-png-inline tex" alt="\sum_{i=0}^{n-1} i" src="/images/math/9/c/3/9c3090bae1d9eccd9e1747ecc51eaece.png" />";}i:389;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:195:"<img class="mwe-math-fallback-png-inline 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:390;a:2:{i:0;s:79:"\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:200:"<img class="mwe-math-fallback-png-inline tex" alt="\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}&#10;{3^m\left(m\,3^n+n\,3^m\right)}" src="/images/math/5/c/d/5cd6041b50d619f041f121baea301898.png" />";}i:391;a:2:{i:0;s:35:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";i:1;s:170:"<img class="mwe-math-fallback-png-inline tex" alt="u&#039;&#039; + p(x)u&#039; + q(x)u=f(x),\quad x&gt;a" src="/images/math/d/7/b/d7b3799aedae667fcc79b43ba678b94a.png" />";}i:392;a:2:{i:0;s:35:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";i:1;s:170:"<img class="mwe-math-fallback-png-inline tex" alt="u&#039;&#039; + p(x)u&#039; + q(x)u=f(x),\quad x&gt;a" src="/images/math/d/7/b/d7b3799aedae667fcc79b43ba678b94a.png" />";}i:393;a:2:{i:0;s:61:"|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)";i:1;s:178:"<img class="mwe-math-fallback-png-inline 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:394;a:2:{i:0;s:61:"|\bar{z}| = |z|,
|(\bar{z})^n| = |z|^n,
\arg(z^n) = n \arg(z)";i:1;s:186:"<img class="mwe-math-fallback-png-inline tex" alt="|\bar{z}| = |z|,&#10;|(\bar{z})^n| = |z|^n,&#10;\arg(z^n) = n \arg(z)" src="/images/math/2/e/a/2eac34dbc8ebbccb22ce8dfe9d5c1a86.png" />";}i:395;a:2:{i:0;s:35:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="\lim_{z\rightarrow z_0} f(z)=f(z_0)" src="/images/math/0/2/1/02122c7e5ff915c4616fb457747c8bf4.png" />";}i:396;a:2:{i:0;s:35:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";i:1;s:152:"<img class="mwe-math-fallback-png-inline tex" alt="\lim_{z\rightarrow z_0} f(z)=f(z_0)" src="/images/math/0/2/1/02122c7e5ff915c4616fb457747c8bf4.png" />";}i:397;a:2:{i:0;s:170:"\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";i:1;s:291:"<img class="mwe-math-fallback-png-inline tex" alt="\phi_n(\kappa)&#10;= \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:398;a:2:{i:0;s:170:"\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";i:1;s:303:"<img class="mwe-math-fallback-png-inline tex" alt="\phi_n(\kappa) =&#10;\frac{1}{4\pi^2\kappa^2} \int_0^\infty&#10;\frac{\sin(\kappa R)}{\kappa R}&#10;\frac{\partial}{\partial R}&#10;\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR" src="/images/math/7/f/b/7fb11db1e8b5890998b2f0f59f0e3d60.png" />";}i:399;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:203:"<img class="mwe-math-fallback-png-inline 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:400;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:211:"<img class="mwe-math-fallback-png-inline tex" alt="\phi_n(\kappa) =&#10;0.033C_n^2\kappa^{-11/3},\quad&#10;\frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}" src="/images/math/8/f/7/8f72d606f5f91bd51583a0a08b36eed9.png" />";}i:401;a:2:{i:0;s:100:"f(x) = \begin{cases}1 & -1 \le x < 0 \\
\frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise}\end{cases}";i:1;s:236:"<img class="mwe-math-fallback-png-inline tex" alt="f(x) = \begin{cases}1 &amp; -1 \le x &lt; 0 \\&#10;\frac{1}{2} &amp; x = 0 \\ 1 - x^2 &amp; \text{otherwise}\end{cases}" src="/images/math/3/e/3/3e3579f4c1c6a95f181f227fd3ede7de.png" />";}i:402;a:2:{i:0;s:104:"
f(x) =
\begin{cases}
1 & -1 \le x < 0 \\
\frac{1}{2} & x = 0 \\
1 - x^2 & \text{otherwise}
\end{cases}
";i:1;s:264:"<img class="mwe-math-fallback-png-inline tex" alt="&#10;f(x) =&#10;\begin{cases}&#10;1 &amp; -1 \le x &lt; 0 \\&#10;\frac{1}{2} &amp; x = 0 \\&#10;1 - x^2 &amp; \text{otherwise}&#10;\end{cases}&#10;" src="/images/math/3/e/3/3e3579f4c1c6a95f181f227fd3ede7de.png" />";}i:403;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:239:"<img class="mwe-math-fallback-png-inline 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:404;a:2:{i:0;s:123:"{}_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:252:"<img class="mwe-math-fallback-png-inline tex" alt="{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)&#10;= \sum_{n=0}^\infty&#10;\frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}&#10;\frac{z^n}{n!}" src="/images/math/c/0/2/c02cbc6ec9c57aca74ebc3a0314dea79.png" />";}i:405;a:2:{i:0;s:25:"\frac{a}{b}\ \tfrac{a}{b}";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\frac{a}{b}\ \tfrac{a}{b}" src="/images/math/5/4/e/54e172be623599fef29e40733c94895e.png" />";}i:406;a:2:{i:0;s:25:"\frac{a}{b}\ \tfrac{a}{b}";i:1;s:142:"<img class="mwe-math-fallback-png-inline tex" alt="\frac{a}{b}\ \tfrac{a}{b}" src="/images/math/5/4/e/54e172be623599fef29e40733c94895e.png" />";}i:407;a:2:{i:0;s:18:"S=dD\,\sin\alpha\!";i:1;s:135:"<img class="mwe-math-fallback-png-inline tex" alt="S=dD\,\sin\alpha\!" src="/images/math/3/8/5/385776efb87d3eb7fe18587efd484ef5.png" />";}i:408;a:2:{i:0;s:18:"S=dD\,\sin\alpha\!";i:1;s:135:"<img class="mwe-math-fallback-png-inline tex" alt="S=dD\,\sin\alpha\!" src="/images/math/3/8/5/385776efb87d3eb7fe18587efd484ef5.png" />";}i:409;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:173:"<img class="mwe-math-fallback-png-inline 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:410;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:173:"<img class="mwe-math-fallback-png-inline 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:411;a:2:{i:0;s:167:"\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}";i:1;s:320:"<img class="mwe-math-fallback-png-inline tex" alt="\begin{align}&#10;u &amp; = \tfrac{1}{\sqrt{2}}(x+y) \qquad &amp; x &amp;= \tfrac{1}{\sqrt{2}}(u+v)\\&#10;v &amp; = \tfrac{1}{\sqrt{2}}(x-y) \qquad &amp; y &amp;= \tfrac{1}{\sqrt{2}}(u-v)&#10;\end{align}" src="/images/math/7/8/7/787eb92e00313cb866a89579fde92108.png" />";}i:412;a:2:{i:0;s:168:"\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}";i:1;s:321:"<img class="mwe-math-fallback-png-inline tex" alt="\begin{align}&#10;u &amp; = \tfrac{1}{\sqrt{2}}(x+y) \qquad &amp; x &amp;= \tfrac{1}{\sqrt{2}}(u+v) \\&#10;v &amp; = \tfrac{1}{\sqrt{2}}(x-y) \qquad &amp; y &amp;= \tfrac{1}{\sqrt{2}}(u-v)&#10;\end{align}" src="/images/math/7/8/7/787eb92e00313cb866a89579fde92108.png" />";}i:413;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 &lt;math&gt; 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 &amp;lt;math&amp;gt; tags. [[Image:foobar.jpg|thumb|&lt;math&gt;2+2</strong>
";}i:414;a:2:{i:0;s:66:" with a thumbnail- math enabled [[Image:foobar.jpg|thumb|<math>2+2";i:1;s:189:"<img class="mwe-math-fallback-png-inline tex" alt=" with a thumbnail- math enabled [[Image:foobar.jpg|thumb|&lt;math&gt;2+2" src="/images/math/4/b/1/4b1d6eacd0bcc60a0aadf0d34626ee74.png" />";}i:415;a:2:{i:0;s:41:"<script>alert(document.cookies);</script>";i:1;s:170:"<img class="mwe-math-fallback-png-inline tex" alt="&lt;script&gt;alert(document.cookies);&lt;/script&gt;" src="/images/math/5/9/f/59f1117d63b4ce95a694d44b588f0840.png" />";}i:416;a:2:{i:0;s:11:"\widehat{x}";i:1;s:128:"<img class="mwe-math-fallback-png-inline tex" alt="\widehat{x}" src="/images/math/9/9/8/998309e831dfb051f233c92b4b8a825b.png" />";}i:417;a:2:{i:0;s:13:"\widetilde{x}";i:1;s:130:"<img class="mwe-math-fallback-png-inline tex" alt="\widetilde{x}" src="/images/math/e/9/e/e9e91996778a6d6f5cdf4cc951955206.png" />";}i:418;a:2:{i:0;s:9:"\euro 200";i:1;s:126:"<img class="mwe-math-fallback-png-inline tex" alt="\euro 200" src="/images/math/1/8/8/18867d4c568a19ae7b2388346e504ec3.png" />";}i:419;a:2:{i:0;s:8:"\geneuro";i:1;s:125:"<img class="mwe-math-fallback-png-inline tex" alt="\geneuro" src="/images/math/9/8/b/98b63c235ee187a38267e0e170b10e9d.png" />";}i:420;a:2:{i:0;s:14:"\geneuronarrow";i:1;s:131:"<img class="mwe-math-fallback-png-inline tex" alt="\geneuronarrow" src="/images/math/a/a/4/aa4a1ed370f4ee705c6930384bf89502.png" />";}i:421;a:2:{i:0;s:12:"\geneurowide";i:1;s:129:"<img class="mwe-math-fallback-png-inline tex" alt="\geneurowide" src="/images/math/4/4/0/4404468e6187fb04e4f7e1f15e550825.png" />";}i:422;a:2:{i:0;s:13:"\officialeuro";i:1;s:130:"<img class="mwe-math-fallback-png-inline tex" alt="\officialeuro" src="/images/math/d/7/0/d708de0eed23dbd6f02b99ea9073547b.png" />";}i:423;a:2:{i:0;s:8:"\digamma";i:1;s:125:"<img class="mwe-math-fallback-png-inline tex" alt="\digamma" src="/images/math/2/f/0/2f057b6e514c8ca2d9cf9a3e549f8865.png" />";}i:424;a:2:{i:0;s:21:"\Coppa\coppa\varcoppa";i:1;s:138:"<img class="mwe-math-fallback-png-inline tex" alt="\Coppa\coppa\varcoppa" src="/images/math/8/3/0/8308ee5003aa36112414cad8ef874f85.png" />";}i:425;a:2:{i:0;s:8:"\Digamma";i:1;s:125:"<img class="mwe-math-fallback-png-inline tex" alt="\Digamma" src="/images/math/5/c/f/5cfd6e5df6c87798542dca2e22c1e7cb.png" />";}i:426;a:2:{i:0;s:12:"\Koppa\koppa";i:1;s:129:"<img class="mwe-math-fallback-png-inline tex" alt="\Koppa\koppa" src="/images/math/5/2/5/52593a0cdac178d165985ac014788b97.png" />";}i:427;a:2:{i:0;s:12:"\Sampi\sampi";i:1;s:129:"<img class="mwe-math-fallback-png-inline tex" alt="\Sampi\sampi" src="/images/math/e/9/d/e9dabb19e4c27bf23d3c2a3629474562.png" />";}i:428;a:2:{i:0;s:24:"\Stigma\stigma\varstigma";i:1;s:141:"<img class="mwe-math-fallback-png-inline tex" alt="\Stigma\stigma\varstigma" src="/images/math/7/b/9/7b9233276816994a33a5e968202cef6e.png" />";}i:429;a:2:{i:0;s:17:"\text{next years}";i:1;s:134:"<img class="mwe-math-fallback-png-inline tex" alt="\text{next years}" src="/images/math/6/6/9/6691dbc0b36631a68b78dd5ace256d80.png" />";}i:430;a:2:{i:0;s:18:"\text{next year's}";i:1;s:140:"<img class="mwe-math-fallback-png-inline tex" alt="\text{next year&#039;s}" src="/images/math/2/3/6/236fd262b1976d04bc0e7a969d61aede.png" />";}i:431;a:2:{i:0;s:18:"\text{`next' year}";i:1;s:140:"<img class="mwe-math-fallback-png-inline tex" alt="\text{`next&#039; year}" src="/images/math/0/5/8/05854b483a833f067cb6ae72319b44bc.png" />";}i:432;a:2:{i:0;s:6:"\sin x";i:1;s:123:"<img class="mwe-math-fallback-png-inline tex" alt="\sin x" src="/images/math/c/d/b/cdba58911c590ced3e2435dfa39f6873.png" />";}i:433;a:2:{i:0;s:7:"\sin(x)";i:1;s:124:"<img class="mwe-math-fallback-png-inline tex" alt="\sin(x)" src="/images/math/3/e/2/3e21673ce6c9b09f9ec50b7237248576.png" />";}i:434;a:2:{i:0;s:7:"\sin{x}";i:1;s:124:"<img class="mwe-math-fallback-png-inline tex" alt="\sin{x}" src="/images/math/f/b/5/fb5551723991d4dcb974a23c162ae813.png" />";}i:435;a:2:{i:0;s:9:"\sin x \,";i:1;s:126:"<img class="mwe-math-fallback-png-inline tex" alt="\sin x \," src="/images/math/7/6/a/76a8e1a01bd233c1e4e16d63b2bbf939.png" />";}i:436;a:2:{i:0;s:10:"\sin(x) \,";i:1;s:127:"<img class="mwe-math-fallback-png-inline tex" alt="\sin(x) \," src="/images/math/1/6/c/16c69b0a3658d3b398f72c518d869a03.png" />";}i:437;a:2:{i:0;s:10:"\sin{x} \,";i:1;s:127:"<img class="mwe-math-fallback-png-inline tex" alt="\sin{x} \," src="/images/math/8/3/9/839639707da39f691e702c2399cbf943.png" />";}i:438;a:2:{i:0;s:6:"\sen x";i:1;s:123:"<img class="mwe-math-fallback-png-inline tex" alt="\sen x" src="/images/math/f/b/8/fb82a78d580396c62cecb4cf018f3769.png" />";}i:439;a:2:{i:0;s:7:"\sen(x)";i:1;s:124:"<img class="mwe-math-fallback-png-inline tex" alt="\sen(x)" src="/images/math/8/3/a/83a10e6756c8e59055178dc1f593130a.png" />";}i:440;a:2:{i:0;s:7:"\sen{x}";i:1;s:124:"<img class="mwe-math-fallback-png-inline tex" alt="\sen{x}" src="/images/math/0/4/f/04fde4f7a7e478015066f378050b1979.png" />";}i:441;a:2:{i:0;s:9:"\sen x \,";i:1;s:126:"<img class="mwe-math-fallback-png-inline tex" alt="\sen x \," src="/images/math/0/a/c/0ac592b8f31b4698766c50c532f446a7.png" />";}i:442;a:2:{i:0;s:10:"\sen(x) \,";i:1;s:127:"<img class="mwe-math-fallback-png-inline tex" alt="\sen(x) \," src="/images/math/b/b/5/bb5469d24fcdd52aa60cb9ee90ba697d.png" />";}i:443;a:2:{i:0;s:10:"\sen{x} \,";i:1;s:127:"<img class="mwe-math-fallback-png-inline tex" alt="\sen{x} \," src="/images/math/d/4/8/d4882a4bcf5db1da3e30d905da8b394e.png" />";}i:444;a:2:{i:0;s:18:"\operatorname{sen}";i:1;s:135:"<img class="mwe-math-fallback-png-inline tex" alt="\operatorname{sen}" src="/images/math/f/a/9/fa9660c7eb053ca8d3c9a87fa86635d9.png" />";}i:445;a:2:{i:0;s:11:"\dot \vec B";i:1;s:128:"<img class="mwe-math-fallback-png-inline tex" alt="\dot \vec B" src="/images/math/e/6/4/e64939568ecb506a86a392373cec0458.png" />";}i:446;a:2:{i:0;s:18:"\tilde \mathcal{M}";i:1;s:135:"<img class="mwe-math-fallback-png-inline tex" alt="\tilde \mathcal{M}" src="/images/math/5/5/0/55072ce6ef8c840c4b7687bd8a028bde.png" />";}i:447;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>
";}i:448;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>
";}}