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F(t,t_{0},x)", + "006badbfc63bbd21.png": "p=(p_{x},p_{y},p_{z})", + "0082d4aa943b9f8c.png": "|\\frac{d^{2}y}{dx^{2}}|\\approx\\frac{1}{R}", + "0083f66ddd05c46c.png": "m_{i,j}=x^{i}\\cdot x^{j}", + "0090db2a639b5c98.png": "S_{ijk}\\rightarrow S_{ij}(\\omega_{k})", + "00915f0ffe17930e.png": "(g^{a}modp,g,p)", + "009d124a50399bba.png": "J_{i}=\\sum_{j}L_{ij}\\frac{\\partial F_{j}}{\\partial x_{j}}", + "009fb93aab47d6f5.png": "\\{f_{X}(\\cdot;\\theta)|\\theta\\in\\Theta\\}", + "00ad7566b9f1d872.png": "\\dot{x}(t)=f(x(t))", + "00ba90fe7f71d8c6.png": "\\Omega((logn)/n^{2})", + "00c46c9b07b39bb7.png": "l_{n}=kl_{n}\\cdot\\frac{b_{n}}{b_{a}}\\cdot\\frac{s_{n}}{s_{a}}", + "00d4fc6636cbf2d9.png": "\\tilde{g}_{n}=[\\begin{matrix}g_{n}\\\\ \\gamma_{n}\\end{matrix}]", + "00db5331b85f4d47.png": "N=|V|", + "00eaf4f2d3d20bb1.png": "B=ln(-b)", + "00fcddfee1ebfee6.png": "2sin(x/2)", + "00fee560e6c9af79.png": "\\sqrt{1-\\omega^{2}r_{0}^{2}}", + "010d0f9e951a7a44.png": "x_{i}^{\\prime}\\equiv\\frac{1}{1+e^{-\\frac{x_{i}-\\mu_{i}}{\\sigma_{i}}}}", + "010d4fea2361f01f.png": "Inj(M_{i})<\\epsilon(n)", + "0111fa141bb73b48.png": "-a^{n}u[-n-1]", + "0114e881d8b22bbb.png": "(\\Lambda(A):A\\in B_{b}(S))", + "011f1f41eb55b661.png": "(\\frac{lnN}{N})\\rightarrow0", + "0121d7fdad59c8ab.png": "\\Leftrightarrow|PA|^{2}=9|PB|^{2}", + "01292cf19c2c9c7c.png": "u=1+l^{2}+m^{2}", + "013a32b84ce6252f.png": "\\{L(u,v):u,v\\in X\\}", + "01453872d3d2afe5.png": "=J+\\epsilon_{0}\\frac{\\partial E}{\\partial t}", + "014f7412fa06f5c0.png": "||L_{x}||_{(l^{p})^{*}}=||x||_{q}", + "015e012d8baa97f3.png": "\\epsilon,\\delta,K>0", + "016a39f81ff20b8d.png": "\\frac{\\partial}{\\partial\\overline{z}}w(z)=0", + "01752f0f5fba0225.png": "L=(\\begin{matrix}1&0\\\\ \\frac{-1}{f}&1\\end{matrix})", + "0175c1fb5814dc11.png": "\\Omega=\\sqrt{|\\chi_{g,e}|^{2}+\\delta^{2}}", + "0180366e774d93be.png": "\\Omega(eg)=g^{-1}\\Omega(e)g", + "01859fc130dc9008.png": "(++++)", + "01917677eaf160bb.png": "Pr(s|I)\\propto1/s", + "0199f657babdf636.png": "\\prod_{p}p/(p-1)", + "01a2f3186b7e33e1.png": "(2n,n,\\lambda,1)", + "01a53ae1e3a9b918.png": "E:R^{n}\\rightarrow T_{p}M", + "01ab618a2350036f.png": "f_{n}\\rightarrow\\chi_{[1,2)}", + "01b552b8a037ab13.png": "T_{pq}(e_{p}\\otimes e_{q})", + "01b74db41e479782.png": "\\vec{x}\\in S", + "01c37bbe7ea55c56.png": "T+ATT=1+E", + "01cdd808862eab64.png": "T^{t}:=S^{1}\\times\\cdot\\cdot\\cdot\\times S^{1}", + "01cf085d26abe325.png": "G^{p^{k}}=\\{g^{p^{k}}|g\\in G\\}", + "01d12458811a5a38.png": "\\Omega=arg(-z_{2},z_{1})", + "01d2b56291c7ffdd.png": "N_{i}\\overline{r_{i}}", + "01d2f97f90ed79e6.png": "m\\equiv\\frac{RF_{,R}}{F}", + "01d4d9a9dc145333.png": "K_{m}=\\frac{1}{2}(k_{1}+k_{2})", + "01d54b93c127e89c.png": "F^{0}[f]=f", + "01d90fce29b20f64.png": "A\\models_{X}^{+}Rt_{1}...t_{n}", + "01e4c8973307a964.png": "|g,n\\rangle\\rightarrow|e,n-1\\rangle", + "01e6c79f4d27bc54.png": "N(t)=N_{0}2^{-t/t_{1/2}}", + "01f3445177808c3d.png": "X_{2i}\\epsilon R^{Q}", + "0204f1101b3f4033.png": "(x,y,\\theta,\\kappa,\\kappa^{\\prime})", + "02248037ee4a5528.png": "(h,h(\\hat{k}),h(\\hat{l}))", + "022b4cfb5a5a3856.png": "d^{\\prime}=V_{ud}d+V_{us}s", + "022be26e0a8ab535.png": "|\\psi\\rangle=\\sum_{n=0}^{\\infty}a_{n}|\\psi_{n}\\rangle", + "0235a447c15a24d7.png": "nlog_{2}n-\\frac{n}{ln2}", + "023a443f36a838ff.png": "\\nabla_{\\vec{\\theta}}=D_{d}\\nabla", + "024279a4b8037bae.png": "f(y)=2+2y+y^{2}", + "0247a5d7e1002d66.png": "|V_{0}|\\gg E_{f}", + "0255dc5b14261907.png": "1+x+\\frac{x^{2}}{2}", + "025f51bee0e59494.png": "g=g_{-1}\\oplus g_{0}\\oplus g_{1}", + "02657f6bba1d2004.png": "f_{a}(bx)=f_{f_{a}(b)}(x)", + "026fd85034106735.png": "T^{-1}=(T_{b}^{a})^{-1}", + "02720f6a67e8bc09.png": "L_{10}=(C/P)^{p}", + "0272a794109d5d2d.png": "P_{F}=\\sqrt{P_{P}\\cdot P_{L}}", + "0276c02c9b9222e9.png": "f^{-1}(y)=\\sqrt{y}", + "028414d36ea98262.png": "\\Delta b/b^{2}\\approx\\Delta f/f^{2}", + "02894b4ff1ee6c7b.png": "0/x=0,x/x=1", + "028cf1f0507df703.png": "U_{i}(I)=I_{L_{i}}", + "029b5da0999d4903.png": "\\omega_{\\{(k,i),(k^{\\prime},i^{\\prime}),(k^{\\prime\\prime},i^{\\prime\\prime})\\}}", + "029decc2d74fd082.png": "abca^{-1}b^{-1}d\\sim?", + "02ace78dfc726867.png": "2sin(\\theta/2)r", + "02aced0c052805c6.png": "1/x\\approx1-x", + "02b1dc6d4efd493a.png": "\\Omega(R)=cP(R)", + "02b7060b95d998eb.png": "-|I|>I_{0}", + "02c39c1be9d660b7.png": "1-4\\pi r^{3}/3V", + "02c6f6dea91a2a06.png": "(RU^{2}D^{-1}BD^{-1})", + "02c9daf282f5a1e3.png": "\\sum_{x\\in\\{0,1\\}^{T}}|x\\rangle|f(x)\\rangle", + "02d5b5f98ac5fbd2.png": "f_{z}(x)=e^{ix^{t}Zx/2}", + "02da6f52e30f674d.png": "2^{k}t_{0}", + "02dcdb815d18cdf1.png": "f(x_{t},t)=x_{t}e^{\\theta t}", + "02de91b624143438.png": "y^{2}=x^{3}-n^{2}x", + "030373f9d3edac3b.png": "\\frac{R_{U}}{r_{e}}\\approx\\frac{r_{H}}{r_{e}}\\approx10^{42}", + "030a0f18b6fcb87b.png": "\\pi(x)-\\pi(\\frac{x}{2})\\ge1", + "030ea5646116a251.png": "M_{2}=P_{1}^{\\prime}|P_{2}|...", + "0316d949cd776194.png": "X_{k}=p(e^{2\\pi i\\frac{k}{2^{n}}})", + "032278982233fefa.png": "L_{r},L_{t},L_{L}/10", + "032360b882783120.png": "\\kappa_{2}=\\mu_{2}^{\\prime}-{\\mu_{1}^{\\prime}}^{2}", + "0325d90612c71772.png": "\\hat{\\Sigma}_{j,/j}", + "03277de2f80a8aaf.png": "Y_{n+1}=I-XY_{n}", + "0333d9584ff7c0d0.png": "f^{-1}(x)=\\frac{1}{f(x)}", + "0339bd185b869ac1.png": "\\frac{dD}{dt}=\\frac{1}{\\epsilon_{f}}\\frac{d\\epsilon_{p}}{dt}", + "034e1c65312b7f9d.png": "u_{min}=min\\{u_{i}\\}", + "035a670b49c3ce36.png": "Li(x)=\\int_{0}^{x}\\frac{dt}{log(t)}", + "036ac8debd6a3120.png": "j_{z}=-\\frac{1}{\\mu_{0}}\\nabla^{2}A", + "036f0970a5c42b1e.png": "\\langle x^{*},x\\rangle", + "03762d643e1dbb50.png": "\\nabla\\cdot P=-\\rho_{b}", + "037c0549cfc11f2d.png": "A\\cap B=\\overline{\\overline{A}\\cup\\overline{B}}", + "0384f21195efa622.png": "z_{n+1}={z_{n}}^{2}+c", + "038c609ec875dc17.png": "\\Phi_{lm}=\\vec{r}\\times\\nabla Y_{lm}", + "039523fde61322a2.png": "D(EQ)\\le n-1", + "03a5fbf204ec2a69.png": "(x_{i},x_{i+1})\\in E", + "03ab27a5e969801b.png": "e^{e^{e^{e^{7.705}}}}<10^{10^{10^{964}}}", + "03b25f204c7b47de.png": "J_{(1)}=J_{(2)}", + "03b5b80e61ede1ac.png": "\\pm z_{1}^{c_{1}}...z_{n}^{c_{n}}", + "03c1e5d37f7dc43d.png": "\\overline{g}_{\\kappa\\lambda}=\\eta_{\\kappa\\lambda}=", + "03d0d068dbfaa5c5.png": "Q(\\sqrt{d})/Q", + "03d40d713cff6b26.png": "4^{n}+2^{n+1}-1", + "03d80f03e7257f44.png": "[1,f(x,y)]", + "03dc827f8b4f9386.png": "(b\\overline{g}+g\\overline{b})/\\sqrt{2}", + "03dd32b2bd99f8c1.png": "Q_{\\alpha}=M_{,\\alpha}", + "03e43d8e767e5aec.png": "\\nabla\\cdot(u,v)=u_{x}+v_{y}", + "03ec1cf693f33af4.png": "e^{-ix}=\\frac{1}{e^{ix}}", + "03f04833cb837350.png": "\\frac{2log(l-1)-logl}{2}", + "03f4d7169d322943.png": "lim_{\\Delta x\\rightarrow0}g(\\Delta x)=0", + "03f960eefb034cc9.png": "1-C_{xy}", + "040b8e680187356c.png": "R_{j}^{*}=d/a_{j}", + "0414df14fce6c763.png": "\\frac{1}{3}=0.(3)", + "0417a1bac9ff37fa.png": "T(ax+by)-T(0)", + "0419c6098f354d5f.png": "I_{K}(m_{K})/H_{K}", + "0422ffb14648ef14.png": "U_{t}=e^{itA},t\\in R", + "042f9dd4f246cd51.png": "x^{*}=\\nabla f(\\nabla f^{*}(x^{*}))", + "04303e80bb3b363f.png": "p_{j}(x)=j\\sum_{i=1}^{j}|x_{i}|", + "043083dc47710e3f.png": "V=f(t)=V_{0}e^{-\\frac{t}{\\tau}}", + "0439c6e2406abd02.png": "k=3.45(N+1)", + "043ab312194e307f.png": "H_{1}:\\{0,1\\}^{*}\\rightarrow G_{1}^{*}", + "044414882ca1e523.png": "O(n^{\\sqrt{k}})", + "0448d738a6ef71e5.png": "\\Psi_{A}(1,2,...,N_{A})", + "04671785d6764ac7.png": "s(r,E,\\hat{\\Omega},t)", + "046bcbd7b4683540.png": "\\Rightarrow\\frac{1}{2x}<[1/x]", + "047c8a1e14a47a8d.png": "cr+cs=a^{2}+b^{2}", + "0480cf86b72aaad9.png": "R=df/dn(n=0)", + "0496e150b09423d4.png": "{(\\hat{k}_{F})}^{\\kappa\\lambda\\mu\\nu}", + "049c5fa2130b640a.png": "A(t)=e^{W\\cdot t}A(0)", + "049c87d8b46e48e3.png": "\\sqrt{16-x^{2}}", + "04a29575b6d95c14.png": "\\frac{dD}{dt}=\\frac{1}{\\epsilon_{f}}\\frac{d\\epsilon_{p}}{dt}", + "04b22a5fda1d3489.png": "H_{n}(x)=\\sum_{k=0}^{n}a_{n,k}x^{k}", + "04bce9e95c175534.png": "\\frac{1}{N}\\frac{\\sqrt{N}}{2}=\\frac{1}{2\\sqrt{N}}", + "04c6131d52decb32.png": "[n:=n+1]", + "04d04edbd034c6e2.png": "U_{p}=\\frac{F^{2}}{4\\omega^{2}}", + "04d5cd7876505b42.png": "\\hat{\\Omega}=U^{\\dagger}\\hat{\\Omega}U", + "04d613d7897993bb.png": "\\lambda^{N+1}=\\prod_{i=0}^{N}(p-q_{i})", + "04d7ed69bae7380c.png": "(a-b)t+b", + "04d8125ee94f096c.png": "\\overline{F}(x)\\equiv Pr[X>x]", + "04e1ad3980a3a81f.png": "g^{-1}\\mu(A)=\\mu(gA)", + "04eb7017ff882087.png": "\\nabla^{2}p=f(\\nu,V)", + "04eb8f8a476f98f6.png": "\\eta=1-\\frac{1}{r_{v}^{\\gamma-1}}", + "04edac9fe8bf5338.png": "ACDA_{si}=\\frac{Vd_{hsd}}{V_{i}}", + "04edd2773e1d1be2.png": "P(Z\\ge k)\\le\\frac{1}{2k^{2}}", + "050334e823c90724.png": "\\bigcap_{n\\in N}J^{n}=\\{0\\}", + "05085e53669a2d82.png": "I^{+}(S)\\cap T", + "0514870f7b7882a9.png": "\\int_{0}^{1}\\frac{sin(1/x)}{x}dx", + "05158c8c6594ffd7.png": "(\\overline{3},1,-\\frac{4}{3})", + "0518e4f59a069378.png": "-\\sqrt{n},...,\\sqrt{n}", + "051c96516aa53311.png": "(a+t,b+t]", + "051dca26f81bbffa.png": "\\frac{1}{n}E(f-Ef)^{2}", + "052b8aebfd8741b9.png": "2m-2t\\}", + "08f4619467e95ff3.png": "040.74", + "0968b61900d3a4dc.png": "\\nabla\\cdot P=-\\rho_{b}", + "096fe07ae326f06a.png": "\\frac{1}{|G|}\\sum_{g\\in G}|(Y^{X})_{\\omega,g}|", + "09715ec39f0c2819.png": "\\overline{\\psi}D_{\\mu}\\psi", + "097203e11785c263.png": "-0.3>\\alpha>-1.6", + "0973507dc864aa87.png": "\\tilde{T}_{i}:=T_{\\tilde{G},\\tilde{H}_{i}}", + "097ced5833a094ca.png": "(1-x^{2})^{-1/2}", + "0984051648ae664e.png": "p(n-1)\\le1/22p(a)", + "0a6fecda94ca0221.png": "\\oint_{C}\\frac{f^{\\prime}(z)}{f(z)}dz", + "0a70d74bf9b2eba7.png": "=\\frac{1}{2}\\cdot\\dot{m}\\cdot(v_{1}^{2}-v_{2}^{2})", + "0a82ae1c73230c54.png": "g\\rightarrow gl_{V}", + "0a8f249fbbb13ad9.png": "H_{inv}H=I", + "0aa2738d330a10b0.png": "H=0,t>0", + "0aa2d65f1b102143.png": "\\frac{I}{I_{0}}=\\frac{p^{2}}{p_{0}^{2}}", + "0ab193d6f1d094e4.png": "\\overline{\\pi}:M(A)\\rightarrow M(B)", + "0ab789b89c8b47a5.png": "A_{0}\\bigcap A_{1}=\\{2\\}\\ni2", + "0ab953d35aa0cecc.png": "(e-1)n!", + "0abffc0139ad1f24.png": "E=E_{0}(e^{i\\omega t}+c.c.)", + "0ad82b8021023add.png": "\\triangle T_{comp}/T_{1}", + "0ae0ab7019ee6abe.png": "\\frac{y_{n}}{x_{n}}\\frac{X}{Y}=\\frac{x/x_{n}}{y/y_{n}}", + "0ae890c9f14365a9.png": "v", + "0b04ccb97348b3e9.png": "E[X]=\\overline{X}", + "0b0cdb9e7a02b1fb.png": "|f_{i}(x)-f_{i}(y)|=1", + "0b1e98386999a707.png": "(\\frac{K^{\\prime}/K}{\\cdot})", + "0b3341ef57260874.png": "\\overline{v}=\\frac{\\overline{q}}{\\overline{k}}", + "0b376cbe2739da2a.png": "\\varphi(x,y)=xM_{\\varphi}y^{\\sigma T}", + "0b3a4c5b6bcffcac.png": "p=\\frac{1}{V_{P}^{2}}P_{TOT}R", + "0b3f07c92b43e765.png": "Q(t)=\\frac{Q_{max}}{1+ae^{-bt}}", + "0b600c55f732df38.png": "t=\\sqrt{1-1/\\xi^{2}}", + "0b6149b006088afc.png": "w(P,Q):=\\frac{G}{F}", + "0b6b891a498aaa02.png": "\\sqrt{-g}_{,\\rho}=\\sqrt{-g}\\Gamma_{\\sigma\\rho}^{\\sigma}", + "0b6cee8742f4f0d9.png": "\\hat{X}^{opt}(z^{n})", + "0b73af34ed6b4f29.png": "R(\\theta,\\delta_{1})\\le R(\\theta,\\delta_{2})", + "0b75224d7ae40e63.png": "[F_{k}:F]=k", + "0b9b49aa839ae3fb.png": "(T_{m}^{i+1})", + "0baa955b2b9a6d65.png": "\\hat{\\sigma}_{+}\\approx\\hat{b}^{\\dagger}", + "0baddebeb93d38ba.png": "D<\\sqrt{m}", + "0bb32915866650e6.png": "\\frac{\\partial\\phi}{\\partial t}=\\frac{\\partial}{\\partial z}[(1-\\phi)u]", + "0bbbaf370d6931dd.png": "x^{\\prime\\prime}\\in D(p,w^{\\prime\\prime})", + "0bcf5bc6c24b0fa5.png": "n(n+1+\\alpha+\\beta)", + "0bd04bf6fdae56d7.png": "1^{5/4}", + "0bd3c391559df5f8.png": "\\frac{E_{s}}{N_{0}}=\\frac{E_{b}}{N_{0}}log_{2}M", + "0bd4d27e8ad0a22c.png": "1+\\frac{a}{ax+b}", + "0bd85b3131013c97.png": "\\int_{V}e^{-\\pi\\langle\\phi,S\\phi\\rangle}D\\phi", + "0beaec42ad3cba9e.png": "P_{i}\\propto\\frac{exp(-\\frac{E}{kT})}{Z}", + "0beb4acc918f8df5.png": "\\Pi=\\sum_{i,j}\\Pi^{ij}\\partial_{i}\\wedge\\partial_{j}", + "0bee7c59a4b5b8c8.png": "\\prod_{\\sigma\\in G_{F}}\\sigma(J^{a_{\\sigma}})", + "0bf3a691b368917a.png": "A^{\\prime}=PAP^{-1}", + "0c0252cfbc8de82d.png": "\\Omega=arg(-z_{2},z_{1})", + "0c03b73cd83b636e.png": "WA_{k}=TH_{k}*FF", + "0c05339b9336c026.png": "\\chi\\rightarrow\\{-1,+1\\}", + "0c1d8d61d5a7fffa.png": "(\\nabla f,-1)", + "0c2134effe22a91b.png": "\\sum_{j=1}^{n}x_{i,m+j}=b_{m+j}", + "0c29c827ec5045c2.png": "\\pi(k+\\frac{1}{2})", + "0c2a72e2584399c6.png": "sin(2\\theta)=\\frac{gd}{v^{2}}", + "0c3751ac574906be.png": "\\gamma=\\frac{\\sum_{i}\\gamma_{i}c_{V,i}}{\\sum_{i}c_{V,i}}", + "0c3c88e2510b0140.png": "\\sum_{i=1}^{n}\\alpha_{i}^{2}\\lambda_{i}", + "0c52db8f022de542.png": "T(w[t])\\in\\Sigma", + "0c5fd5da55b32939.png": "2c>\\frac{q}{2}", + "0c63684ae90911ef.png": "x+y=-13", + "0c71f0a447899d7d.png": "\\eta_{+-}\\ne\\eta_{00}", + "0c734ef611811291.png": "D_{0}=\\frac{\\alpha^{2}h}{3n}I_{s}", + "0c7551db2bc392fa.png": "V(t)=\\dot{X}(t)", + "0c7e387c380456c0.png": "\\dot{\\rho}_{m}+3H\\rho_{m}=0", + "0c85d0debc929438.png": "dete^{A}=expTr(A)", + "0c8e962e861f39a5.png": "\\prod_{j=1}^{n}(\\alpha-\\alpha_{j})=0", + "0c97da6fa27e7184.png": "exp_{R}B(\\hat{R})", + "0ca27ade4c47aafe.png": "L^{1,1}=L^{1}", + "0ca67c880c1eecbd.png": "GF(p)[x]/f(x)", + "0cb0ea927be7affc.png": "L[y]=y^{(n)}", + "0cbb3a55359f022c.png": "T=\\dot{m}V_{w}", + "0cc4819b2bb829db.png": "U_{x}:H_{x}\\rightarrow K_{\\eta(x)}", + "0ccbbca34ec098de.png": "(1-\\delta(l", + "0cd488519bda6d88.png": "\\frac{2V}{V+2}>2", + "0ce49b97f6cb33bb.png": "O(V^{3}/2^{\\Omega(logn)^{1/2}})", + "0ced08c10d2ea026.png": "r_{2}(H_{i}/H_{i}^{\\prime})", + "0ced8e46bfa50e5f.png": "(U,R_{\\delta_{\\Phi,\\epsilon}})", + "0cf3ab818cbab542.png": "u=1+l^{2}+m^{2}", + "0cf987000cfbaa45.png": "16pi/3=H^{2}", + "0d17d9ecd65b41c1.png": "u^{\\prime\\prime}+(1/2)fu=0", + "0d1875541c4fad5e.png": "f-f(0)\\kappa", + "0d19ca038efd8368.png": "(m^{d})^{e}modn=m", + "0d1bed94afa729d7.png": "\\frac{||\\alpha_{1}e_{1}+\\alpha_{2}e_{2}||}{(|\\alpha_{1}|+|\\alpha_{2}|)}", + "0d1ec62418ecebc5.png": "x^{(0)}=[\\begin{matrix}1.0\\\\ 1.0\\end{matrix}]", + "0d25df9353c44bc9.png": "\\bigoplus_{k=1}^{\\infty}b_{k}", + "0d2b453a8f934034.png": "x(t)=\\frac{1}{2k}(t^{2}-k^{2})", + "0d2bbf6b9ff2b595.png": "L=\\sum_{r=0}^{4}p_{r}(x)\\frac{d^{r}}{dx^{r}}", + "0d506e131a7a1df9.png": "-\\frac{1}{2}\\sum_{i,j=1}^{m-1}x_{i}A_{ij}x_{j}", + "0d6e4fafb8a34b04.png": "\\frac{x}{\\sqrt{x^{2}+a^{2}}}=sin\\theta_{1}", + "0d6fe0254d0df0ee.png": "\\frac{\\pi}{180}M_{r}cos\\varphi", + "0d92f5d164e8aeeb.png": "\\hat{S}=\\frac{1}{2}[\\begin{matrix}\\sigma&0\\\\ 0&\\sigma\\end{matrix}]", + "0d9bf6643d1c9681.png": "(\\begin{matrix}n\\\\ k\\end{matrix})modm", + "0da58aa323c18138.png": "k(Y)(\\sqrt[3]{Y^{2}})", + "0daa75a24bb4a4e9.png": "max_{F}trace(KF)", + "0db445cdd4625e07.png": "C\\approx PV(\\frac{1}{n}+\\frac{2}{3}i)", + "0db57aa0b354773c.png": "p_{n-1}(x_{i})", + "0db8a63af36ff2da.png": "50\\approx\\sqrt{30\\times77}\\Omega", + "0dc2e66233466963.png": "U_{2n}=\\frac{2U_{n}u_{n}}{U_{n}+u_{n}}", + "0dc82ec554bcbe23.png": "\\Phi_{lm}=\\vec{r}\\times\\nabla Y_{lm}", + "0dca4acbd94ee4c9.png": "\\frac{\\omega_{1}}{\\omega_{2}}\\notin R", + "0de163e6b5e6ef8c.png": "\\psi=[1,-1]", + "0de4a0511cf93332.png": "r_{1},r_{2},...,r_{100n}", + "0def1fef3f0f6c6b.png": "(e-1)n!", + "0df90289a9af4066.png": "\\theta_{n}:=I_{[-N,N]}\\frac{\\nabla f}{|\\nabla f|}", + "0e00d55646953569.png": "I(v)=\\langle v,v\\rangle=|v|^{2}", + "0e0ed35edf461047.png": "\\frac{1}{2}m\\overline{v^{2}}=\\frac{3}{2}kT", + "0e10e7832d783225.png": "50cos(\\frac{\\pi}{4})7.24355", + "0e147f0ce28a3278.png": "c^{2}=\\frac{2\\kappa Gh}{D(1-\\nu)}", + "0e1b172ef364b930.png": "B=\\mu_{0}\\frac{NI}{l_{m}}", + "0e204b013430b1b0.png": "f(\\rho)<-1", + "0e3896999d7d83a1.png": "\\sum_{i=a+1}^{b}\\frac{1}{i}", + "0e4571abcc545217.png": "W=W^{\\prime}+\\mu^{-1}", + "0e4f3d34193c72a7.png": "m,m_{1},m_{2}\\in M", + "0e609c655da6196f.png": "a=(x-1)\\div0.005", + "0e60c5e72e87fbca.png": "inf_{x:g(x)\\le y}f(x)", + "0e6dd2a9057bea6b.png": "Pr(X_{n}/n>0)\\rightarrow1", + "0e7f403e4ab33b39.png": "detO:=e^{-\\zeta_{O}^{\\prime}(0)}", + "0e881d28e012fcd1.png": "\\sum\\frac{1}{8n}", + "0e9b63d14b54b705.png": "E(k)=\\frac{\\hbar^{2}k^{2}}{2m^{*}}", + "0ea11c2551e8367a.png": "E_{1j}=\\frac{O_{j}}{N_{j}}N_{1j}", + "0eae846632c5dab9.png": "lim_{x\\rightarrow+\\infty}f(x)", + "0eb498bf410f2edd.png": "C(n-1,k)", + "0eb57e8a202450c1.png": "[,,]", + "0ecabff0ef4b9d0d.png": "[X]_{2}", + "0ed4cbfd86cbcfe9.png": "H=(f_{xx}+f_{yy})/2", + "0edf342009448fc0.png": "|M_{1}|=|M_{2}|=1", + "0ee691162b5dadaf.png": "|\\frac{q}{p}|=1", + "0ee7b6be528c938f.png": "[J_{\\pm},V_{0}]=\\sqrt{2}V_{\\pm}", + "0eed4591f7576b88.png": "|G:H|<\\infty", + "0efd03cf18865ae5.png": "\\psi(\\Omega)^{\\psi(\\Omega)}", + "0f1279d7350c6a0f.png": "r_{p}\\ne r_{p(k+1)}", + "0f1306d7dec6ef13.png": "I_{1}=C_{abcd}C^{abcd}", + "0f2eb2dde840d20e.png": "\\vec{x}\\rightarrow r(\\vec{x};q)", + "0f325c9be5e0f1f9.png": "WA_{k}=TH_{k}*FF", + "0f32d70c9a301e54.png": "J(f)\\le+\\infty", + "0f3ec21c42360618.png": "\\mu(A)=\\zeta(1_{A})", + "0f456162b2e700be.png": "a_{n}=\\frac{a_{n-1}}{9}=\\frac{a_{0}}{9^{n}}", + "0f481260b727b489.png": "H=0,t>0", + "0f5630a152a09b31.png": "f:R(X)\\rightarrow R(S_{R})", + "0f6771e0f18a549d.png": "\\frac{|v\\rangle+i|w\\rangle}{\\sqrt{2}}", + "0f6b7ceb7a22de0d.png": "V_{x}=\\frac{dx}{dt}V_{x}^{\\prime}=\\frac{dx^{\\prime}}{dt^{\\prime}}", + "0f784fea5cd5b693.png": "c_{3,1}(\\hat{a},w(\\hat{\\epsilon},\\hat{b}c),\\hat{d})", + "0f89f5370f1ef174.png": "Z_{in0}=\\frac{V_{1}}{I_{in0}}=Z", + "0f8b61fe58da9291.png": "\\frac{1}{12}(\\begin{matrix}4&8&4\\\\ 5&7&-4\\\\ 1&-1&4\\end{matrix})", + "0f8bb3df8b2639b0.png": "\\vec{\\Psi}:R^{d}\\supset U\\rightarrow R^{n}", + "0f8caba52a726db5.png": "\\tilde{u}=\\sum_{i=1}^{n}u_{i}\\tilde{\\omega}^{i}", + "0f903236cc1621e3.png": "|\\begin{matrix}A&B/2\\\\ B/2&C\\end{matrix}|", + "0f906d1696ef518c.png": "(u^{\\prime}(x,z,t),w^{\\prime}(x,z,t))", + "0f9769db1fed30e0.png": "t:=(e^{h}-1)^{-1}", + "0fa647342b6d1f7c.png": "[F_{k}:F]=k", + "0fad6782e4e30475.png": "[v=\\frac{1}{2}\\sqrt{\\pi}erf(x)]", + "0fafcff79c28b378.png": "(\\overline{A})^{\\epsilon}=A^{\\epsilon}", + "0fb2085506cdf2d3.png": "00)\\rightarrow1", + "10163f1746765a61.png": "(j-(-j))", + "101f63cd2a807a51.png": "x_{k+1}=x_{k}+\\frac{1}{m}", + "10223f47f37d67a5.png": "\\epsilon,\\delta,K>0", + "1045d588d1f8569a.png": "4a^{3}+27b^{2}\\ne0", + "104722f1560468ca.png": "\\delta_{j,j_{1}}\\delta_{m,m_{1}}", + "1049b30e4fd641f5.png": "\\alpha=-kcot(kL/2)", + "10517f7ea9844bce.png": "\\nabla h_{i}(i\\in E)", + "1053347b5aed8d89.png": "\\eta(-\\frac{1}{\\tau})=\\sqrt{-i\\tau}\\eta(\\tau)", + "1054c0b283aa2695.png": "k[X]=\\bigoplus_{\\lambda}k[X]_{(\\lambda)}", + "105ebcc4d6455481.png": "\\rho=A\\cdot\\tau^{2}-B", + "106238594d5bed29.png": "D=\\frac{\\mu_{q}k_{B}T}{q}", + "106314044e73a8d4.png": "32x+4(1-x)=1", + "1067afd5a52b0b9d.png": "\\hat{H}=-m\\cdot B(t)", + "107c852a2ef6e357.png": "i^{*}O(-D)", + "108b2cbc0f320da0.png": "k=\\pm4,\\pm2,-1", + "109648cb8168780d.png": "g_{DS}=\\frac{\\partial I_{DS}}{\\partial V_{DS}}", + "109cc69845d33b5c.png": "x_{i}=\\frac{c_{i}}{c}=\\frac{c_{i}}{\\sum c_{i}}", + "10a19fd47f22e526.png": "(exp(M_{t}/2))_{t\\ge0}", + "10a41ef5cbcad23e.png": "\\varphi\\rightarrow\\frac{-\\nabla f}{|\\nabla f|}", + "10a44b829b9850da.png": "a\\not\\equiv3(mod4)", + "10d2128dcecfc7a5.png": "CO=\\frac{VO_{2}}{C_{a}-C_{v}}", + "10f731d3a4043228.png": "\\frac{\\partial V}{\\partial p_{1}}=-\\lambda x_{1}^{m}", + "10fa6516b1904732.png": "(t^{2},t^{3})A", + "110e2b79100f1d3b.png": "\\frac{1}{2}\\psi(0)", + "1112ede868a8c336.png": "1+2+3+4=10", + "111e46c93115d4b1.png": "cdf_{y}(i)=iK", + "112630b209eac9cc.png": "1-e^{-1}=0.61", + "1128dd6f20dbba83.png": "Lu(x,t)=0", + "11346b922cd75bb6.png": "K=+1", + "1153d3fbebe4af7e.png": "F(x,y)-c=0", + "116068bbd12ea46e.png": "\\frac{3K-M}{3K+M}", + "11863afce4adf711.png": "\\theta=\\frac{1}{N}(\\frac{s}{q})\\frac{dq}{ds}", + "1186ebd74ebcbd83.png": "1+3=4mod13", + "118ea3f9aafaf54d.png": "S=\\frac{h_{f}}{L}=\\frac{1}{\\rho g}\\frac{\\Delta p}{L}", + "1195704a0e927428.png": "z=\\frac{t^{2}+tq+q^{2}}{t+q}", + "1197ffb8c50af6fb.png": "g(x)=1_{x\\ge1-\\alpha}", + "11a33b36ea6c7f8f.png": "R_{1}=\\frac{2a+b}{3}", + "11a78631a629a7a3.png": "(\\nabla_{c}\\nabla_{d}-\\nabla_{d}\\nabla_{c})", + "11ac11b06417edb1.png": "\\rho_{A}=|\\psi\\rangle_{A}\\langle\\psi|_{A}", + "11b2c9901428884f.png": "lim_{i\\rightarrow\\infty}\\frac{f(i)}{i}=\\frac{1}{2}", + "11b2fba03607677b.png": "O(\\lambda_{\\delta}(n)logn)", + "11cd9dd6252ad06b.png": "P=\\frac{1}{3}\\frac{U}{V}", + "11d138fa49ad7786.png": "2\\sqrt{-\\frac{p}{3}}", + "11d77f1c1a514c2c.png": "\\theta=\\frac{1}{N}(\\frac{s}{q})\\frac{dq}{ds}", + "11e0344c014ce297.png": "\\hat{M}=(\\hat{m}_{ij})\\in R^{I\\times J}", + "11e4197d77bff434.png": "\\mu_{eff}=K(\\frac{\\partial u}{\\partial y})^{n-1}", + "11e64b3b16744f2b.png": "\\frac{1}{2M-r}", + "11f12f54ae575c99.png": "F_{2}/F_{1}\\approx2.512^{\\Delta m}", + "12001cdad8f3dfaf.png": "O(nlog(log(n)))", + "120403997f05e7d2.png": "\\alpha_{t}\\leftarrow0.01L\\alpha_{t}", + "12042db420cedea5.png": "1/p,q,w", + "1206b1535bdfb069.png": "|\\frac{d^{2}y}{dx^{2}}|\\approx\\frac{1}{R}", + "120a39e13203ec91.png": "\\phi(x)=Ax+x_{0}", + "120e043a67fccccb.png": "I/I_{0}=e^{-m\\tau}", + "12155339f1507c09.png": "|\\phi_{2^{i}}\\rangle", + "121eab3af05c0382.png": "\\frac{1}{2}+i\\frac{2\\pi n}{logn}", + "1224d67e9dec0eab.png": "F(z)=F^{\\prime}(z)F^{\\prime\\prime}(z)", + "12257554d665e020.png": "k_{r}^{+}>0", + "12286fbd4474ddf5.png": "-\\frac{1}{sinx}d^{2}x=dt^{2}", + "12321bba773ea2f1.png": "P_{n}^{(m)}(\\cdot)", + "1237c99a9e83762c.png": "-|1\\rangle", + "1237f7aa382a6071.png": "I_{m}A=AI_{n}=A", + "12631090f74d4a31.png": "P_{\\pi}^{-1}=P_{\\pi^{-1}}=P_{\\pi}^{T}", + "1263906e96748ad4.png": "\\beta_{max}=(\\frac{R^{2}}{PQ})^{\\frac{1}{3}}", + "126775c628a55020.png": "0.3>\\alpha>-0.3", + "126f12423d6b3786.png": "2r_{-}=\\sqrt{2}(r_{-}+r_{+})", + "126f7b8167c40ba8.png": "\\rho=\\frac{1}{h^{n}C}P", + "1281130bb941408a.png": "F=\\sigma T^{4}(\\frac{R}{D})^{2}", + "1289e10d564b99bb.png": "(\\frac{m}{s})", + "128b300b1c6f30b5.png": "Z_{p^{r}}[X]", + "1297d79fd1e4a43f.png": "F\\subseteq P^{(1)}", + "129af5bfb6c4f26c.png": "\\tau=\\mu_{eff}(\\dot{\\gamma})\\dot{\\gamma}", + "12a2fc178b31c34d.png": "a_{P}sini=", + "12a4a938375a6955.png": "(t^{\\prime}-t)/\\epsilon", + "12b0e3611d122ada.png": "exp_{R}B(\\hat{R})", + "12b33524b848a3f8.png": "\\int\\psi_{e}^{\\prime*}\\mu_{e}\\psi_{e}d\\tau_{e}", + "12bf1f0969730d43.png": "\\sum_{j}M_{j-1}^{*}/M_{j}^{*}=\\infty", + "12c257b04bc9f22e.png": "E(S)=a_{1}M", + "12cdc1d971313e14.png": "\\sigma=|c|\\frac{\\Delta t}{\\Delta x}\\in N", + "12d2a5b6e3c836c0.png": "E[Z_{i}]=0", + "12d4141dc38607c6.png": "(A^{-1})_{ji}=|A|_{ij}^{-1}", + "12d5d42c5a5fd58b.png": "H\\Phi_{0}(x)=E_{0}\\Phi_{0}(x)", + "12dce02dd6222428.png": "(\\frac{2}{\\pi}", + "12e0265890316d77.png": "G=\\oplus_{i}C_{d_{i}}", + "12e196c2841e83a1.png": "lim_{x\\rightarrow0}\\frac{f(x)}{g(x)}=\\frac{3}{2}", + "130d557aa7fb63a7.png": "D^{\\epsilon}(\\rho||\\sigma)", + "13131c43370057b4.png": "1/\\tau=k_{a}+k_{b}", + "1326d4258e8e90f0.png": "x_{1}-x_{2}+x_{0}=0", + "1337d1686593f043.png": "pH=-log\\{H^{+}\\}", + "133a41b738902a96.png": "k=\\omega\\sqrt{LC}=\\frac{\\omega}{u}", + "133e49f546572937.png": "E=50\\frac{\\pi^{2}\\hbar^{2}}{2mL^{2}}", + "134399b5e742bbe6.png": "R=\\{-1,+2\\}", + "134583cae9c84060.png": "f(r)=(1+r)^{-3/2}", + "134a7d7f1476cad6.png": "|T_{0}^{L}|+|T_{0}^{R}|", + "135943c2a01812f3.png": "(a+t,b+t]", + "1368415721d5e82f.png": "(g,g^{x},...,g^{(x^{q})},R)", + "137cf3b5bdc1547d.png": "P[S_{0}=k]", + "13865aa8d48395f3.png": "H_{1}:\\{0,1\\}^{*}\\rightarrow G_{1}^{*}", + "13903a790ca7b144.png": "<\\psi_{1s}|\\psi_{1s}>=1", + "139ea2a84a3dcfdc.png": "x_{1}-x_{2}+x_{0}=0", + "13a4f66d5ad42f0c.png": "\\sqrt[n]{\\frac{a}{b}}=\\frac{\\sqrt[n]{a}}{\\sqrt[n]{b}}", + "13a67e041fe80620.png": "H^{*}(g)", + "13aa001b8ec82b6d.png": "(d-a)^{2}+4bc", + "13cd96d3005df377.png": "\\dot{x}(t)=f(x(t))", + "13d960a2e5d63f5e.png": "\\theta_{n}:=I_{[-N,N]}\\frac{\\nabla f}{|\\nabla f|}", + "13de333fec90a0fb.png": "\\vec{S}_{i},\\vec{S}_{j}", + "13e26f876021f801.png": "f_{+},\\varphi", + "13e6ca7c84c9e1a5.png": "j_{z}=-\\frac{1}{\\mu_{0}}\\nabla^{2}A", + "13f1901dd843e05c.png": "F_{i}*\\frac{dV_{g}}{dT}=\\frac{dC}{dT}", + "13f8a699cd3f1a44.png": "2(\\alpha-\\chi)=\\Gamma", + "13fd5acee0c037d3.png": "I_{K}(f)/H", + "141644e19aa4bc2a.png": "X_{k}=p(e^{2\\pi i\\frac{k}{2^{n}}})", + "142b873a15b7bc17.png": "\\Rightarrow b=1-\\frac{n-1}{n}b", + "14384ed17ba831a6.png": "X^{2}-X+1", + "14509a040c856127.png": "u^{\\pm i}\\rightarrow e^{\\pm i\\phi}u^{\\pm i}", + "1458dcc25331502b.png": "A_{\\vec{r}}^{*}", + "1459b591bacfbc6c.png": "\\hat{var}(X_{j})", + "146bbe5ce7b34805.png": "L^{\\otimes m}", + "14767fa23a54a184.png": "f^{(m^{*}+1)}(b)=0", + "148bef704e5a20b6.png": "Z_{i}^{(m)}=mY_{i}^{(m)}", + "148fc90df6aebe25.png": "P(t)=\\frac{1}{1+e^{-t}}", + "14980a3039656e71.png": "2^{km}e^{-\\epsilon\\alpha n/2}", + "149d833826086a9d.png": "\\int_{0}^{t}e^{As}Bu(s)ds", + "149dd4581c77a40e.png": "Z^{+}\\cup\\{0\\}", + "14a8aeb5b23cb09c.png": "\\frac{d^{2}\\theta}{dt^{2}}+1=0", + "14bac194cf6b49e7.png": "exp(-(x^{2})/4)", + "14c5e617d61b4d14.png": "\\sigma_{D}^{2}=\\frac{kT_{D}}{m_{D}}", + "14dfc53a228f7b44.png": "\\sum_{t}||f_{t}-\\overline{f}||_{H_{k}}", + "14e54ceada46eeaa.png": "n=t|m-T|^{-2}pq", + "14ee38cbbd133506.png": "K=(\\frac{\\omega}{c},k)", + "14fcce767c061258.png": "E_{d}=\\frac{P}{Q_{d}}\\times\\frac{dQ_{d}}{dP}", + "150a063526724004.png": "lim_{x\\rightarrow0}\\frac{O(x)}{O(x)}", + "150a3c38d98acac6.png": "(E^{\\dagger}(R),I-E^{\\dagger}(R))", + "150f7c962d0e9dd2.png": "1\\le a_{\\mu(i)}1", + "15fa82735619cad0.png": "[\\Omega]\\in H^{3}(M,R)", + "15fd7769a97359b9.png": "\\frac{dL}{dt}=-k_{1}L+L_{b}", + "15ff5ff95f2cfcb4.png": "\\lceil|k|/n\\rceil", + "16257cdd2352cd98.png": "(\\phi^{\\Rightarrow x})^{\\Rightarrow y}=\\phi^{\\Rightarrow x\\wedge y}", + "1640ae25968b72e2.png": "1\\le Ra_{D}\\le10^{5}", + "164da554e1fa5e83.png": "T_{t}=e^{t\\frac{d}{dx}}", + "165065bf909f1892.png": "m_{P}/m_{P}^{2}", + "166743ea8741c691.png": "v_{(G;c)}(\\emptyset)=0", + "16857a377f3a7cd8.png": "n_{\\alpha,R}=n_{\\alpha,0}e^{-\\frac{e\\phi_{\\alpha}}{k_{B}T_{\\alpha}}}", + "16891011b9ec5ea9.png": "\\Omega(dlogn)\\le t(d,n)", + "168f7046d10c2629.png": "ee=|F_{+}-F_{-}|", + "169b1d715c7e9117.png": "(\\lambda_{i}^{+},\\lambda_{i}^{-})", + "16a940510d425878.png": "E=f(a)=f(-a)", + "16ac3bd2dfbb6aff.png": "(d\\vec{b})-1", + "16ace34386f6b3e5.png": "\\hbar\\omega_{p}/T_{e}=0.1", + "16b0e4424c68300e.png": "\\Delta\\overline{l}=\\Delta\\eta", + "16bb6b7d3724d86e.png": "\\frac{1}{N}\\frac{\\sqrt{N}}{2}=\\frac{1}{2\\sqrt{N}}", + "16c9f684caf6685c.png": "\\Delta\\frac{W}{L}\\equiv\\frac{W_{2}}{L_{2}}-\\frac{W_{1}}{L_{1}}", + "16cb7cb5ce563acb.png": "1,2,\\cdot\\cdot\\cdot,n", + "16cef76517956059.png": "J_{\\phi}=D_{\\phi}\\frac{\\partial\\phi}{\\partial x_{i}}", + "16e13d2dc9fc9860.png": "(\\frac{R}{M})^{j}P_{j}", + "16e663460cc38261.png": "10log\\frac{T}{t_{1}}", + "16e72d5eed5dd6d4.png": "\\pi_{n}(S^{k})=0", + "16f28255e4ca0fe5.png": "sinc(x)=\\frac{sinx}{x}", + "16f834dc19035117.png": "\\nabla_{i}=\\partial_{i}+i(\\partial_{i}\\phi)", + "170371e3b144db14.png": "cot(-\\beta)=-cot\\beta", + "170cc6a895025412.png": "E[X]:=\\rho(-X)", + "170ccef202434603.png": "n-(p+q)", + "1711c11ce23595c3.png": "[\\begin{matrix}1&-\\frac{1}{G}\\\\ 0&1\\end{matrix}]", + "1712d6b259f1e83d.png": "\\gamma_{\\alpha}(x):=\\frac{x_{+}^{\\alpha-1}}{\\Gamma(\\alpha)}", + "17199a55a322b939.png": "1(", + "171bf6800394bb8d.png": "f(x)=arcsin\\frac{\\pi}{x}", + "171cb6b8b7805126.png": "D_{LA}=z\\frac{g}{g+1}", + "172a7a0a4cf51a77.png": "Spec\\oplus_{n\\ge0}I^{n}/I^{n+1}", + "172eb3d1d43100d7.png": "\\pm\\frac{1}{2}\\sqrt{x}", + "17316f66aee414a2.png": "(\\hat{A}\\cdot\\hat{B})", + "1731e7db4678a0f6.png": "tr_{B}(|\\psi\\rangle\\langle\\psi|)=\\rho", + "173316919a976b78.png": "Q^{T}Q=I.", + "17357341b0d3c92b.png": "\\{f_{X}(\\cdot;\\theta)|\\theta\\in\\Theta\\}", + "17372351e3d06ee7.png": "(E)-(G)-(H)", + "173d5ca1f12acab9.png": "sin(2\\theta)=\\frac{gd}{v^{2}}", + "174403be06d06b0a.png": "max_{a\\le x\\le b}|f(x)-p(x)|", + "174cb7ebf4124aa7.png": "I=\\frac{\\dot{\\gamma}d}{\\sqrt{P/\\rho}}", + "174f7a2ee7aabd91.png": "F_{i}*\\frac{dV_{g}}{dT}=\\frac{dC}{dT}", + "175258181988267d.png": "g_{\\mu,\\nu}^{\\lambda}(q)\\in Z[q]", + "17547df8b697855a.png": "g_{i}=f_{i}/f_{i-1}", + "1759f83a5a847bd2.png": "(\\frac{\\gamma}{\\delta},\\frac{\\alpha}{\\beta})", + "175cb441aac88798.png": "\\sum_{j\\in S}p_{ij}V(j)<\\infty", + "1763939098445393.png": "p_{n+1}=2+\\sum_{i=1}^{n}g_{i}", + "176648c4f4d704af.png": "\\frac{n}{m}+2m-1h/2", + "17bb36af30ae0486.png": "P|", + "17bfccca5afd67f8.png": "B=\\{b_{j}(y_{t})\\}", + "17ce1dbed1e715b3.png": "1+ln(\\frac{\\sigma}{\\sqrt{2}})+\\frac{\\gamma}{2}", + "17d859c8690a508a.png": "2H=-\\nabla\\cdot\\hat{n}", + "17d8a068dae241b8.png": "af^{*}(\\frac{x^{*}}{a})", + "17d8ef90945c93c1.png": "(i\\omega-\\xi)^{-1}", + "17ddf096f50644fd.png": "\\frac{\\rho}{3}r^{3}(\\theta)\\hat{\\theta}d\\theta", + "17ded19b881f2c44.png": "|V_{0}|\\gg E_{f}", + "17e5f33acfaafc2a.png": "\\frac{1}{n+1}x^{n+1}+C", + "17eabe2a170e9cf0.png": "q_{ii},q_{ij}q_{ji}", + "180835ca5e467617.png": "\\delta E=\\sqrt{k_{B}T^{2}C}", + "1809f7956efce914.png": "\\Lambda=Z_{p}[[\\Gamma]]", + "180d86e8a3ead7b9.png": "2^{\\aleph_{0}}=|R|", + "181cef6af8c980b1.png": "p(\\sigma|I)\\propto1/\\sigma", + "18215eb9ffb245a0.png": "\\{\\dot{x}_{1},...,\\dot{x}_{n}\\}", + "18251313351ed60d.png": "(it)^{r}\\psi(t)", + "182aa03d5a8b6ca0.png": "P(Z\\ge k)\\le\\frac{1}{2k^{2}}", + "182e7d699b934324.png": "-csc^{2}\\frac{\\pi}{2}", + "183a5a0732af4a46.png": "y^{2}-x^{2}(a^{2}-x^{2})", + "183f549c8644b528.png": "\\sigma=\\alpha r_{e}^{2}Z^{2}P(E,Z)", + "184c58fa9f88cb4b.png": "\\dot{m}=\\rho V_{d}A", + "185187a1f219443f.png": "F_{t}=2^{b}+1", + "18521488a731fd6d.png": "A=(\\begin{matrix}0&X\\\\ -X^{t}&0\\end{matrix})", + "18575019b822813d.png": "K_{x}Na_{1-x}Cl", + "185c5f7123615a55.png": "A=0,B=1", + "1860414430a21ea6.png": "||f||_{BV}=V_{f}(I)", + "186af6177ff2293f.png": "p(a/2)>2p(a)", + "1880048d586ae7a1.png": "f_{EW}(|\\vec{a}-\\vec{b}|)", + "1882662b702cf0f5.png": "\\int_{0}^{\\pi}x^{n}sin(x)dx", + "188852d0914fac9a.png": "(n-1)|(m-k)", + "1894935f6dd21eaa.png": "1-\\frac{x}{2}+\\frac{3x^{2}}{8}-\\frac{5x^{3}}{16}", + "189643ed1ccb950b.png": "A=(\\begin{matrix}0&X\\\\ -X^{t}&0\\end{matrix})", + "189ad91adf493aa8.png": "1-\\delta+o(1)", + "18a57da90c42fdc0.png": "\\approx\\frac{3.45c}{H_{0}}", + "18ac14a7221edc38.png": "O(log^{2}(B))", + "18b99a97aa15a165.png": "\\sqrt{1-\\omega^{2}r_{0}^{2}}", + "18b9c8bff4e37408.png": "de-let[f(qq)]", + "18c64b032138a7b7.png": "=\\frac{T(t)\\times T^{\\prime}(t)}{2}", + "18d4d271d583dea4.png": "\\sum_{k=0}^{m}(\\begin{matrix}m\\\\ k\\end{matrix})(\\begin{matrix}n\\\\ r+k\\end{matrix})", + "18d51c77d5a97867.png": "y:[x_{0},x_{1}]\\rightarrow V", + "18dca0a56c3fc561.png": "1+2+3+4=10", + "18e89dacf0401a2c.png": "\\pi(x)-\\pi(x/2)", + "18e8bc2de466093a.png": "\\pi^{\\prime}\\frac{B-1}{2}V", + "1b4e2f2b65e12c1a.png": "p(x)|(x^{r}-1)", + "1b68ebd10f8dbd74.png": "(\\begin{matrix}\\mu_{1}&\\mu_{2}&\\gamma\\\\ \\nu_{1}&\\nu_{2}&\\nu\\end{matrix})", + "1b697f8bc2195351.png": "(sys)^{2}\\le\\gamma_{2}area", + "1b83ebb8531560f9.png": "1+x+\\frac{x^{2}}{2}", + "1b997f840ef6800b.png": "A_{m_{1}}\\cap\\cdot\\cdot\\cdot\\cap A_{m_{p}}", + "1ba71f801e979bca.png": "\\{a_{k}\\}_{k=0}^{k=\\infty}", + "1bb14888ab3f14c8.png": "G^{p^{k}}=\\{g^{p^{k}}|g\\in G\\}", + "1bb281e015233ee6.png": "sup_{t}|G_{n}(t)|", + "1bb701a3e591ffd1.png": "I_{1}=C_{abcd}C^{abcd}", + "1bbb028f89dccb07.png": "u=y^{1-3}=y^{-2}", + "1bca6eb7863c83bd.png": "\\hat{A}_{1}=x[0]", + "1bce26ea857f67df.png": "(3)Z(p^{\\infty})", + "1be0ac391d64efa6.png": "J^{\\mu}=\\partial_{\\nu}D^{\\mu\\nu}", + "1be2a95395c1f717.png": "p_{i}(q_{i},\\dot{q}_{i},t)=\\frac{\\partial L}{\\partial\\dot{q}_{i}}", + "1be6bc573681e20a.png": "(CH_{3})_{2}C", + "1bfc7e01666d8476.png": "C_{X}=C_{Y}=[0,1]", + "1c29a099037b6cd9.png": "A/m=k", + "1c360feace830f73.png": "exp(-\\sum d_{i})", + "1c42087b3f3ab120.png": "A_{1}<\\cdot\\cdot\\cdot0", + "1c516703a5868281.png": "\\frac{1}{2}\\frac{mg}{L}x^{2}", + "1c5b6f428e894634.png": "f^{\\mu}=x^{\\mu}L", + "1c62eda78d8df922.png": "E_{i}=C\\frac{M_{i}}{N_{i}}", + "1c63d6e5570e4f8c.png": "2\\Omega_{x}>\\Omega_{z}", + "1c64dc246085f27d.png": "{t_{k}}_{(i)}=x_{(i)}\\cdot w_{(k)}", + "1c661913e87a5fad.png": "Pr(t|B_{i}^{-})", + "1c66c494d75443e6.png": "\\vartheta=[\\vartheta^{f},\\vartheta^{s},\\vartheta^{n}]", + "1c6ba8f8d09662c1.png": "tr_{B}(|\\psi\\rangle\\langle\\psi|)=\\rho", + "1c82d3c26650c8d4.png": "0=E\\{(\\hat{x}-x)y\\}", + "1c8c89f5f307f8d1.png": "\\hat{U}=e^{\\frac{-i\\hat{H}t}{\\hbar}}", + "1c97a44b431cdd1f.png": "\\sum x*a^{i}=\\frac{x}{1-a}", + "1c984f0956d53662.png": "(x+200)^{2}(x+58)", + "1c9b0c7d3dffc746.png": "t^{\\prime}=\\gamma(1-av)t", + "1ca189b1b9fbbc14.png": "\\psi\\le\\frac{3}{\\sqrt{3}+1}", + "1ca571343b914e7a.png": "E=rc^{4}/2G", + "1ca81a3b21e1fbf7.png": "\\sqrt{16-x^{2}}", + "1cb34e84bf47fe8e.png": "Z_{p^{m}}[x]", + "1cb3e8e88962871c.png": "1/r^{\\prime}+1/r=1", + "1cb972d3af127fb1.png": "e^{x}+O(x^{n+1})", + "1cbabadbf5fd8595.png": "f^{-1}(y)=\\pm\\sqrt{y}", + "1cc7c15480f7952e.png": "Q=[\\begin{matrix}T\\\\ N\\\\ B\\end{matrix}]", + "1ccd198e4b3a55df.png": "\\frac{\\rho^{4}}{\\lambda^{4}}\\ll8\\frac{z^{3}}{\\lambda^{3}}", + "1cd25eece2786bd0.png": "(t_{bj}+t_{j})", + "1cd4d0b75bf03525.png": "\\pi_{4}=\\frac{hL}{k}=Nu", + "1cde0bdee083e841.png": "(0,1/2)", + "1ce66852ecd024c6.png": "M_{X}(t):=E[e^{tX}]", + "1ce7d51737cb4691.png": "K_{sp}=(x)(2x)^{2}", + "1cf6356e19ab6463.png": "P=(n-\\Delta/2)", + "1cfa0fb472eef763.png": "C^{\\prime}(a,q,0)=0", + "1cfef00893ac9f1c.png": "abca^{-1}b^{-1}d\\sim?", + "1d0c3ac30e0eba69.png": "v<\\sqrt{r\\mu g}", + "1d17f2876a60ad1e.png": "E[h(x,X_{1})]\\equiv0", + "1d182930680aa43b.png": "V\\sim{\\chi^{\\prime}}_{k}^{2}(0)", + "1d2be69cd21e01ed.png": "D(a_{k,k},r_{k})", + "1d2f6306adabdb9e.png": "[-\\pi<\\theta<\\pi]", + "1d3e4524baab0fa3.png": "v_{t}=90\\sqrt{d}", + "1d400889da6588da.png": "EV=g\\wedge\\bigcirc S_{0}^{2}V", + "1d5195f241ac1227.png": "E(T^{2})=\\frac{2}{\\theta^{2}}", + "1d51e2f15f12bd65.png": "F^{(\\begin{matrix}l+d\\\\ d\\end{matrix})}\\rightarrow F^{|F|^{l}}", + "1d60aa708e4800a0.png": "\\eta_{a\\mu\\nu}\\overline{\\eta}_{b\\mu\\nu}=0", + "1d64acd4250ba727.png": "Z\\cup[(0,1)\\cap Q]", + "1d66954a3bc164b3.png": "Zstep=\\sqrt{HbTws}", + "1d6b0847c7c5fe58.png": "\\underline{\\varphi(\\beta/\\alpha)}", + "1d77f0d348771601.png": "\\sum_{i=1}^{n}i^{2}", + "1d7e801aa499e51b.png": "\\overline{g}_{\\kappa\\lambda}=\\eta_{\\kappa\\lambda}=", + "1d8988bb862dfbaa.png": "p=(p_{x},p_{y},p_{z})", + "1d9fb016c5c2fadd.png": "\\sqrt{x}=-1", + "1da375e84634406f.png": "[n,n-m]_{2}", + "1dac38fdc12b7731.png": "2^{n}sin\\frac{x}{2^{n}}", + "1db44f1280f9714a.png": "(n+1)^{k_{n+1}}", + "1db87b14ad495188.png": "J^{\\mu}=\\partial_{\\nu}D^{\\mu\\nu}", + "1dc7824432cf06b8.png": "-E_{act}/R", + "1dd5bb804261dc8d.png": "\\overline{\\beta}=\\beta(1-\\frac{K^{2}}{4\\gamma^{2}})", + "1dd9449feeca83cd.png": "X_{i}-\\overline{X}", + "1de6f3d57c7dd88e.png": "\\lambda x.((\\lambda x.x)x)", + "1df19b20f84d23a5.png": "J_{\\phi}=D_{\\phi}\\frac{\\partial\\phi}{\\partial x_{i}}", + "1df6080bf36ce66b.png": "y(t)=ae^{-be^{-ct}}", + "1e0d292bb2a2d4af.png": "F=eEexp(-i\\omega t)", + "1e287192a3a20ee9.png": "r^{2},\\sqrt{r},exp(r)", + "1e453bd7b12d306b.png": "1_{[0,\\alpha\\sqrt{n}]}(||p_{\\sigma}||)", + "1e4a1247399ff56b.png": "l=\\frac{1}{2}k\\lambda=\\frac{1}{2}k\\frac{c}{f}", + "1e53e57434dfda75.png": "X(u,v,w;z,x)", + "1e618ec20f6a832d.png": "V=1096.7\\sqrt{H/d}", + "1e61d0803572a02e.png": "a_{n}-2a_{n+1}", + "1e62238da3f16d1e.png": "\\omega\\times v=\\dot{Q}Q^{-1}v", + "1e8b7046471d6b19.png": "\\phi_{t}^{-1},t\\in[0,1]", + "1e8fa52489cb5b34.png": "L_{p}=\\sum_{e\\in p}L_{e}", + "1e912f3558db60b6.png": "\\frac{d^{2}x}{dt^{2}}+\\frac{\\gamma PA^{2}}{mV}x=0", + "1ea1d3af85436b4e.png": "\\hat{\\sigma}_{+}\\approx\\hat{b}^{\\dagger}", + "1ea9211a12a4b307.png": "<0.084", + "1eae48d9ac3aa86a.png": "\\omega_{\\lambda}\\in H_{dR}^{1}(V_{\\lambda})", + "1eb13b8d23d7d554.png": "\\frac{19}{13}<\\sqrt{3}", + "1ec4e81761858d3e.png": "\\frac{1}{2}Z", + "1ec9dbd42a2a9fa5.png": "\\tilde{V}_{x}=|V_{x}|", + "1ed58f4d9cbf3820.png": ")", + "1ed94def0d6b0b86.png": "\\{\\begin{matrix}p\\\\ q,r,s\\end{matrix}\\}", + "1ee30d49ff130d0e.png": "lim_{\\Delta x\\rightarrow0}g(\\Delta x)=0", + "1ee74f421f2d1d94.png": "O_{T^{\\prime}}\\rightarrow f_{*}O_{T}", + "1eef2e2df18391f1.png": "|\\psi_{A,B}^{\\lambda}\\rangle", + "1eefa397897dabd9.png": "C_{\\Psi}=\\frac{16}{5}\\sqrt{\\pi}", + "1eefbf8de4c29162.png": "B:=\\{|k\\rangle\\}_{k=0}^{N-1}", + "1ef9cddc0958c8ec.png": "\\sigma_{y}^{2}(\\tau)=\\frac{2\\pi^{2}\\tau}{3}h_{-2}", + "1efc569af71f4a19.png": "=C_{c}", + "1efdec968181c9e5.png": "E=H=T+V", + "1f04fb6d93bcc1c9.png": "A_{q}(n,d,w)", + "1f0d121451af8cea.png": "\\sum_{t}||f_{t}-\\overline{f}||_{H_{k}}", + "1f129dc5b831e697.png": "s)", + "1f1b3b52efa77e56.png": "\\hbar k_{3}\\approx\\hbar k_{1}+\\hbar k_{2}", + "1f27c9506621261e.png": "-0.5\\le\\beta<-0.25", + "1f291a7bdf32fd53.png": "\\partial_{x}\\eta=\\eta^{\\prime}", + "1f2d4ee0d02b8c2f.png": "Ck_{n}=kT_{n-1}+1", + "1f349a18d2be4d2f.png": "B=\\mu_{0}\\frac{NI}{l_{m}}", + "1f3edab5f57f349e.png": "e-2h(h-R)<0", + "1f3f84fc726a1976.png": "E=i\\hbar\\frac{\\partial}{\\partial t}", + "1f48edf2599a2704.png": "B\\subset P^{1}(k)", + "1f5d41b96bab231a.png": "\\frac{d}{dx}=i\\frac{1}{i}\\frac{d}{dx}", + "1f6db174535c2a4e.png": "A^{\\prime}=\\hat{B}(\\varphi,\\hat{n})A", + "1f712b9f6802e254.png": "P_{i}(t=0)-", + "1f744a10191fe3e9.png": "\\frac{d}{dx}(sin(x^{2}))", + "1f78702572a6ceb4.png": "A\\cong k[[x_{1},...,x_{d}]]", + "1f7f5d0e2db202bc.png": "0\\le x\\le2^{2^{k}}", + "1f816cb2c58c03fc.png": "lim_{n\\rightarrow\\infty}Pr(X_{n}=0)", + "1f8a51e31c74aa7d.png": "R=\\{-1,+2\\}", + "1f8c1e6019d5a81d.png": "E_{L}[u]=E_{M}[u]", + "1fa04ae89003efed.png": "f_{i}=\\frac{\\sigma_{i}^{2}}{\\sigma_{i}^{2}+\\alpha^{2}}", + "1fa16f9b2ca264db.png": "L^{-1}(x)\\approx x\\frac{3-x^{2}}{1-x^{2}}", + "1faa13b69f2841b4.png": "\\phi(x)=Ax+x_{0}", + "1fb4ad5555f57700.png": "s_{i}=(a_{i}-d_{i})^{+}", + "1fb59512b735f3ea.png": "\\tilde{\\omega}(x)=\\omega\\times x", + "1fb9ca66e453c68c.png": "Y:=\\Delta([a,b])", + "1fc1944482180fad.png": "\\kappa_{2}=\\mu_{2}^{\\prime}-{\\mu_{1}^{\\prime}}^{2}", + "1fc34c59e9c7ead9.png": "\\nabla\\cdot P=-\\rho_{b}", + "1fd291dd2a777077.png": "I(x)=\\frac{I_{0}}{1+\\beta cxI_{0}}", + "1fd9152f450eb7a2.png": "(x_{i},y_{j};x_{i+1},y_{j+1})", + "1feebcdfb2886023.png": "W^{k,p}\\subseteq W^{m,q}", + "1ff6dcc7286a2008.png": "1/e^{z}=e^{-z}", + "20030a3dbbd5a0e7.png": "f=\\sum_{e\\in\\Gamma}c_{e}T^{e}", + "2008bc81cc00ba68.png": "L(u)=(a_{1},a_{2})", + "200a1dba135f5b21.png": "z^{-1}=z^{*}/||z||", + "202d618b2b6a07fe.png": "\\beta_{(s)3}<0", + "2030bdb1ba36988d.png": "\\sqrt{13}\\approx3.606", + "2030d2d10990cf9b.png": "(0,\\frac{\\pi}{2}]", + "2035503109aea155.png": "1-C_{xy}", + "2049a1a9c2228680.png": "\\vartheta=[\\vartheta^{f},\\vartheta^{s},\\vartheta^{n}]", + "2058c453059484a0.png": "L(u)=(a_{1},a_{2})", + "205e4bf13bfaf50c.png": "P_{1}=(1:\\sqrt{2}:1)", + "206a126881554b75.png": "!_{\\tau}", + "206d56f6b88f77c5.png": "\\int f_{n}\\le\\int f", + "208d6b82d41edad1.png": "|\\omega_{\\Delta}^{free}|\\le\\omega_{l}", + "20924ce47449e8f5.png": "t_{1}=X^{c}g_{1}^{s_{1}}g_{2}^{s_{2}}", + "20b404558ac3cb63.png": "(0,e^{-x^{2}/2}/\\sqrt{2\\pi}]", + "20b961636290aa9f.png": "m\\equiv\\frac{RF_{,R}}{F}", + "20d05fcb1e782152.png": "t=\\pm\\frac{1}{1,3}", + "20d19978f7fb82b0.png": "I=C(dV/dT)", + "20dae97e505f5835.png": "b=2(l\\cdot(o-c))", + "20e19076d904f4c7.png": "\\alpha_{t}=\\frac{1}{2}ln(\\frac{W_{+}}{W_{-}})", + "20e5cf7e1e7364a1.png": "\\delta_{\\epsilon}A=[\\epsilon,A]-d\\epsilon", + "20eedf3fcd7085fa.png": "(\\pi R^{2}D)", + "20f7af188fd73830.png": "\\gamma(u)=\\frac{1}{\\sqrt{1-\\frac{u\\cdot u}{c^{2}}}}", + "20fb65cf7f9d508f.png": "\\Delta w=\\eta y(x_{n})x_{n}", + "2108928a0f01dfd1.png": "j:=1:(i-1)", + "210c7cf6bfabe250.png": "\\Gamma=\\frac{P_{1}P_{2}...}{S_{1}S_{2}...}", + "2118189fc96c36fc.png": "\\Rightarrow b=1-\\frac{n-1}{n}b", + "21242454877f3bcf.png": "\\partial\\{(I^{2},\\varphi_{\\lambda},S_{\\lambda})\\}_{\\lambda\\in\\Lambda}", + "213a6486d19ac572.png": "\\overline{u}=\\sqrt{\\langle u^{2}\\rangle}", + "2141bbdc6009b0f1.png": "(-4)^{2k+1}\\equiv1", + "214d35d2d05b6497.png": "G_{\\alpha\\beta}=-8\\pi GT_{\\alpha\\beta}", + "2163e1089bc70d00.png": "(1+2)\\times(3+4)", + "2168451ba57de800.png": "\\frac{x_{1}-x}{x_{1}-x_{0}}", + "216ae9fb18166723.png": "tr(\\gamma^{0}\\Gamma^{\\dagger}\\gamma^{0})", + "2178a8087f095b49.png": "j\\mapsto(\\begin{matrix}-1&1\\\\ 1&1\\end{matrix})", + "217b7fe6bee6c5cd.png": "0.5=E[X_{1}]", + "217ce1a9e373382f.png": "p(n-1)\\le1/20}\\lambda_{j}^{-s}", + "22fd6ca725b06082.png": "n_{\\perp}^{2}=\\epsilon(1-Q^{2})", + "22ff4022f617d51d.png": "(x_{i},y_{j};x_{i+1},y_{j+1})", + "2300da3b3fe1be5b.png": "\\frac{1}{13^{13}}", + "2301aa36593b0743.png": "U(g,e)", + "230b97975eb3fae2.png": "\\frac{d^{m}(x^{m})}{(dx)^{m}}=m!", + "230fc7a4823ccb96.png": "\\sqrt{\\frac{t_{1}}{T}}", + "232bb214ec60b8bb.png": "[[x,x],x]=0", + "232bdb2cff8b2a4b.png": "\\frac{4}{\\nu-6}\\sqrt{2(\\nu-4)}", + "2331bebe80afbf75.png": "q=q(0)+j\\frac{p(0)}{\\omega L}", + "2335e998d768fb04.png": "Y_{(II)}", + "234120e6b603327e.png": "\\sqrt{n}\\ge\\frac{1.96\\sigma}{0.5}", + "23415fc7ae9a2916.png": "[\\hat{a}(t),\\hat{a}^{\\dagger}(t)]=1", + "23663439072ea85d.png": "\\Psi_{A}(1,2,...,N_{A})", + "2374d9e6d97cc612.png": "f_{n}\\rightarrow\\chi_{[1,2)}", + "2375ec3d0cf87a25.png": "(\\nabla f,-1)", + "237c0e08b07b2bb0.png": "[x_{0}:...:x_{n}]", + "2382cb5634bbb7fc.png": "\\Omega m=kgA^{-2}m^{3}s^{-3}", + "238a44c2444173a4.png": "\\hat{a_{i}}\\hat{a_{j}}^{\\dagger}", + "238c4f4cfe444e13.png": "D=\\frac{S}{mil}\\cdot\\frac{mag}{10}", + "238f229bbab99ea3.png": "\\frac{1}{10^{3}\\pi}", + "2398edcc60b77549.png": "(\\rho=1000\\frac{kg}{m^{3}})", + "23a0bc11da5c2d52.png": "lim_{t\\rightarrow\\infty}\\frac{t^{\\alpha}}{ae^{t}}=0", + "23a4585d1e3629fb.png": "U=D+(\\frac{wvkj}{w+v})", + "23b01a148402bcbf.png": "\\frac{1}{|G|}\\sum_{g\\in G}|(Y^{X})_{\\omega,g}|", + "23b7e1e40aae0c09.png": "\\lambda^{2}-p(1-p)", + "23c1e45d56aeb99e.png": "\\nabla\\cdot P=-\\rho_{b}", + "23c7b9d4f3a2749c.png": "y=-\\frac{221}{423}", + "24063a2c8b8a2232.png": "(A_{0}\\vee A_{1}\\vee\\cdot\\cdot\\cdot)", + "240813c320b59f90.png": "m(n)\\approx0.570591", + "24103fdd40bfd39b.png": "k=1,2,3,......", + "2410955735c428e0.png": "\\frac{ds}{dy}=T_{0}\\frac{\\sqrt{2g}}{\\pi}\\frac{1}{\\sqrt{y}}", + "2423ee27761a588b.png": "P_{max}=\\frac{1}{4}p_{max}Q_{max}", + "2428d37cb402c288.png": "n^{3}log(n)^{3}", + "242aa372aa934cfe.png": "A^{k}=VJ^{k}V^{-1}", + "243079c73a04be7e.png": "2c^{2}=4a^{2}+4a+2", + "2437c969be9daa00.png": "U^{(k)}x_{w}^{(k)}=x^{(k)}", + "24397ea098f3a4fc.png": "(cos(\\phi),sin(\\phi),0)", + "2443ff57d7dac767.png": "R(1+\\langle L_{i}\\rangle)^{-1}", + "244994af57a09a4d.png": "Q_{n}=\\frac{\\pi}{ntan\\frac{\\pi}{n}}", + "2463d55c6ea51ddf.png": "\\frac{25!}{100!}\\frac{88!}{13!}", + "246779c23653e49a.png": "+(1-f)", + "247021b37005854d.png": "\\hat{g}=\\frac{k}{T^{2}}", + "2470ce5d4cf513ca.png": "v=\\sqrt{\\gamma\\frac{P_{0}}{\\rho}}", + "24728c37acffff26.png": "k\\in[0;\\infty)", + "24754d09b449df2e.png": "B(s)=8s^{3}+24s^{1}", + "2479e1fb6bbf87bd.png": "U=\\frac{1}{R}=\\frac{\\dot{Q}_{A}}{\\Delta T}=\\frac{k}{L}", + "249bf59774c8b093.png": "3^{3^{3^{3^{46}}}}", + "249fe19065317e09.png": "I=-\\frac{1}{2}log(1-\\rho^{2})", + "24a2d3a48613f6b7.png": "\\hat{x}_{k+1}", + "24a4eeeac1514bf6.png": "Q=(p-iW)b", + "24a6ec5559f10bb7.png": "\\int f_{n}\\le\\int f", + "24ac47f383733884.png": "P_{1}=(1:\\sqrt{2}:1)", + "24af11c48ee34cea.png": "v\\approx\\hat{v}=\\sum_{i=1}^{n}\\theta_{n}\\phi_{n}", + "24b92127ddc412fd.png": "Z\\cup[(0,1)\\cap Q]", + "24bb4122555722b8.png": "A\\subset\\{1,2,...,n\\}", + "24bfcf422bfb751e.png": "2\\pi^{2}k\\delta(x)\\delta(y)\\hat{z}", + "24c2766d6da6fe7e.png": "P+\\frac{1}{2}\\rho v^{2}=P_{0}", + "24c4cf063d86444b.png": "S_{h}\\approx S_{h^{\\prime}}S_{h-h^{\\prime}}", + "24c6f39a2df51d6a.png": "t=\\frac{1}{\\lambda}\\times ln(\\frac{1}{\\frac{P}{P+D}})", + "24c9236f8a376ea1.png": "|Gx|=|G:G_{x}|", + "24d5407a80d59f3f.png": "2^{112}(=2^{2*56})", + "24db05195ad7dd10.png": "Q\\times U", + "24e59e10a944c13c.png": "x^{2}+y^{2}=a^{2}-b^{2}", + "24eb7e8bcf9b9665.png": "x_{n+k+1}", + "24ef795146fed28d.png": "[-(b+1),+(b+1)]", + "24f064e27caf8d85.png": "R\\ge(2^{a-1}-1)", + "250129ae3c356c86.png": "|M_{1}|=|M_{2}|=1", + "250373b09c2bba28.png": "n_{Io}-2\\cdot n_{Eu}=0", + "250db1f450dc3725.png": "\\overline{\\psi}D_{\\mu}\\psi", + "25135d35b9839b16.png": "V(0)=\\dot{V}(0)=0", + "25188d92dfd0abff.png": "2^{S}", + "25268ae84bdb6b4c.png": "0-0=0", + "2527159ba1222fbb.png": "A-x", + "254f5f27075a4f05.png": "\\{0,1,2\\}=Z_{3}", + "254fbcae9a3811aa.png": "\\sum x*a^{i}=\\frac{x}{1-a}", + "25600f531a10d121.png": "\\frac{1}{a}+\\frac{1}{b}+\\frac{1}{c}<\\frac{s}{T}", + "25651f28378fad3c.png": "D\\rightarrow D/m_{D}", + "259023d5cd932024.png": "A_{m}(0,2)=1,2,1", + "25915df2cc5676b1.png": "\\frac{\\partial u}{\\partial x}\\frac{\\partial v}{\\partial y}+uv=k", + "2594e87301ec485b.png": "w=\\sqrt{KW-UV}", + "259813d2b3eee1ed.png": "g(x)=\\sqrt[3]{x^{2}}", + "25a79070e5f0c89b.png": "E_{n}^{(0)}-H_{0}", + "25b7840e7eb0273c.png": "\\Omega(dlogn)\\le t(d,n)", + "25bba29cd79345ce.png": "(a+t,b+t]", + "25d210a714977688.png": "T=\\frac{1}{nR}lim_{p\\rightarrow0}pV", + "25dd54f02a7faf50.png": "f^{-1}(y)=\\frac{\\sqrt[3]{y}-8}{2}", + "25f4d1f1fc154d3f.png": "C_{l}=\\frac{2\\gamma}{V_{\\infty}c}(2)", + "25f80858c5104b1e.png": "D_{ii}=\\frac{\\sigma_{i}}{\\sigma_{i}^{2}+\\alpha^{2}}", + "260459b7d0f02440.png": "(P(X),\\Delta,\\cap)", + "2609a281c35de378.png": "Z_{n}=Z/nZ", + "261ccd28867e8ae9.png": "\\omega^{2}=-U^{2}(\\frac{2k}{rd})\\theta^{2}", + "261d9a38b814880b.png": "D_{ii}=\\frac{\\sigma_{i}}{\\sigma_{i}^{2}+\\alpha^{2}}", + "2623ac69d7d9e19b.png": "-\\sqrt{n},...,\\sqrt{n}", + "2638a18dce8d8a75.png": "A=\\int\\lambda dE_{A}(\\lambda)", + "2643e5b07a04e2e0.png": "\\Delta z=H(z)\\Delta\\chi", + "264d08442742e094.png": "||v||_{L_{2}(\\Gamma)}\\le\\int_{\\Omega}vdx", + "2653c8374d402278.png": "=J+\\epsilon_{0}\\frac{\\partial E}{\\partial t}", + "2657fe8bbacf0a3d.png": "Y_{t}=f(t)+e_{t}", + "265c81923ae5ccb4.png": "lim_{\\Delta x\\rightarrow0}g(\\Delta x)=0", + "2661fd1d17198eba.png": "x=[\\begin{matrix}A^{T}\\\\ B^{T}\\end{matrix}]^{+}[\\begin{matrix}e\\\\ f\\end{matrix}]", + "266790e250d3f677.png": "Ee=\\frac{1}{2}K(2cm)^{2}", + "266fa5763f3fd2ba.png": "Z(T,V,N)=e^{-\\beta A}", + "2670b01bd872bd84.png": "\\sum_{n=1}^{m}(a_{n}+|a_{n}|)", + "26753e038525f59a.png": "|\\alpha|=\\alpha_{1}+\\cdot\\cdot\\cdot+\\alpha_{n}", + "2683ca147e5463c1.png": "s_{\\mu}*s_{\\nu}=\\sum_{\\lambda}g_{\\mu\\nu}^{\\lambda}s_{\\lambda}", + "268cf642e088aa5c.png": "(4)Z^{(\\omega)}", + "269acc1680398048.png": "1+\\frac{a}{ax+b}", + "26a53a055da31d82.png": "End(K[x])", + "26adaa4977fe89af.png": "(\\frac{mol}{m^{2}\\cdot s})", + "26b02eebf7987f4c.png": "\\sum_{a}\\sum_{b}\\frac{1}{|az+b|^{s}}", + "26d5d6dc8d880251.png": "\\hat{p}_{x}=-i\\hbar\\frac{d}{dx}", + "26e6166d34ee6bfb.png": "tr^{2}H>4", + "26eba9c4d66a2080.png": "(8)\\Psi_{0}\\hat{=}0,\\Psi_{1}\\hat{=}0", + "26fb912d2dd39daf.png": "(-\\infty,0],(0,\\infty)", + "27020c325240651f.png": "r=2+cos(\\pi-\\theta)", + "270280744f3463a1.png": "\\hat{A}_{1}=x[0]", + "270449e5820969ae.png": "\\langle A\\rangle_{\\psi}=||A\\psi||^{2}", + "270c66ffb21bffd8.png": "O(m^{g(k)}n^{k})", + "270f19e91a4f8146.png": "L_{\\alpha+1}:=Def(L_{\\alpha})", + "2710741b51983342.png": "\\forall_{x}\\exists_{y}G(x,y)", + "27143b61cf86f5ee.png": "\\epsilon=\\frac{\\epsilon_{s}+g}{1+g^{*}\\epsilon}", + "27201abce9d7cdab.png": "\\tilde{T}_{i}:=T_{\\tilde{G},\\tilde{H}_{i}}", + "27203e3e89bfb03c.png": "\\sigma^{2}*(X^{\\prime}X)^{-1}", + "2720afe169563601.png": "w(P,Q):=\\frac{G}{F}", + "2729c06a9c65239f.png": "\\gamma_{i}={\\phi_{i}}^{2}", + "2730334e8b996566.png": "2^{2^{65536}}", + "2732a96de7e721cf.png": "1/2\\sqrt{3}", + "273321b1fce6ce42.png": "dz-E_{t}h(x,t)dt", + "2740ecfc9804eb7a.png": "H_{eu}^{2}=\\frac{\\sigma_{a}^{2}+\\sigma_{d}^{2}}{\\sigma_{P}^{2}}", + "2748bf48005fa236.png": "\\delta\\omega=(\\omega_{+}-\\omega_{-})", + "274a68ba849e0549.png": "P=[I|0]", + "27592191eef7aac8.png": "\\frac{1}{3}=0.(3)", + "2765520a648d28fe.png": "2cos\\frac{\\pi}{3}=1", + "276fbe607922350f.png": "x^{3}(x^{2}-x-1)+1", + "27762549f9d75be6.png": "1-e^{-1}=0.61", + "27797369e2d0e9d5.png": "\\frac{\\pi}{180}M_{r}cos\\varphi", + "277f22d68cc0af29.png": "[\\begin{matrix}p_{1}&\\cdot\\cdot\\cdot&p_{i}\\end{matrix}]", + "27859c256ca35ce5.png": "R/R_{1},R/R_{2}", + "279121b9bb0a9296.png": "\\frac{\\partial f}{\\partial t\\partial s}=j\\circ\\frac{\\partial f}{\\partial s\\partial t}", + "279537ab7320eb4c.png": "y=\\sum_{r=0}^{\\infty}a_{r}s^{r+c}", + "279ea1ccd8c56672.png": "H_{\\epsilon}f\\rightarrow Hf.", + "27ac8b497f2008b5.png": "H_{0}(\\langle\\vec{X}\\rangle_{m})<\\infty", + "27c39f789601c1de.png": "2^{90(1024)}", + "27e94939161aafb4.png": "\\lfloor b_{i}x\\rfloor-b_{i}x", + "280733180706ac23.png": "F\\subseteq P^{(1)}", + "28132af3aedc3d26.png": "r=k_{2}[H_{2}][N_{2}O_{2}]", + "283fda54ab3fc2af.png": "\\psi\\le\\frac{3}{\\sqrt{3}+1}", + "286056bab9785d71.png": "M/R\\le1/RR", + "286a05808b306379.png": "\\int K=1/6", + "287c99d0166fbc1f.png": "z_{n+1}+2z_{n}\\epsilon+\\epsilon^{2}", + "28844304d13bfb55.png": "y_{i}E(\\alpha_{i})=Q(\\alpha_{i})", + "289116ba87eb2e9f.png": "\\sqrt{\\rho}=\\rho=|\\phi\\rangle\\langle\\phi|", + "28914c4367289507.png": "\\frac{f(7,4)}{g(7,4)}", + "289931d64da2de41.png": "\\psi_{0}=\\psi_{1}+\\psi_{2}.(1)", + "28a1a4dc35ac0a4a.png": "\\alpha=1-\\frac{D_{s}P_{n}}{D_{n}P_{s}}", + "28a26c038ba72908.png": "J_{\\hat{n}}", + "28a4e8c421f8db63.png": "0\\le S_{k}\\le S_{k+1}", + "28ab551b3f0ea650.png": "S=S[1]S[2]...S[n]", + "28adf664b89bd87f.png": "E[h(x,X_{1})]\\equiv0", + "28b772767707b059.png": "R=\\rho\\frac{L}{A}=\\rho\\frac{L}{Wt}", + "28bb056336a99226.png": "\\psi\\mapsto e^{i\\epsilon^{IJ}(x)\\sigma_{IJ}}\\psi", + "28bf58662f915bf3.png": "\\Sigma=\\prod_{i\\in N}\\Sigma^{i}", + "28d7c244dd474980.png": "G^{-1}=G,G^{0}=G_{0}", + "28e0dd9d6344619d.png": "|\\frac{4}{3}|>1", + "28e437f9400d46cb.png": "log_{e}(3)=1.0986...", + "28ebbe2ccdc003b3.png": "S^{2}C^{3}", + "28fb39b73cc59587.png": "p(x_{k+1}|\\hat{\\xi}_{k}^{i})", + "28ffb2355f60bd61.png": "H_{n}(S^{n})\\cong Z", + "2902f0e8c3fcfe5b.png": "p_{o}=p_{o+}", + "291fd5311d8567d7.png": "m=1...M,", + "2924048d0fbebf40.png": "|f_{n}(x)-f_{n}(y)|<\\epsilon", + "2927af5cb8c9a6e9.png": "D_{I^{+2}}", + "2932531b27801066.png": "\\frac{\\partial}{\\partial\\overline{z}}w(z)=0", + "2951314e6b314e5a.png": "41/18\\approx2.3", + "2951eb451e0f74cc.png": "A_{0}\\equiv e^{-\\pi y^{2}}", + "29581cb4d84d51d5.png": "\\approx\\int_{\\partial N}f^{\\mu}ds_{\\mu}", + "2963b303d1b6d643.png": "\\{g_{m,n}:m,n\\in Z\\}", + "297955923a92759f.png": "||\\varphi_{n}-\\varphi_{m}||_{d}<\\epsilon", + "297ac5dbb85ff744.png": "P(Z\\ge k)\\le\\frac{1}{2k^{2}}", + "298d64c939be2392.png": "\\epsilon((-1)^{F})=1", + "2996933ef3b8a306.png": "v<\\sqrt{r\\mu g}", + "29986f0088ec69ae.png": "S={\\langle Q\\rangle}^{\\perp}", + "29b1257bd7754622.png": "0\\le\\alpha_{i},\\beta_{i}\\le1", + "29c6e3bbd4110742.png": "\\sum_{i=1}^{m}c_{i}x_{i}+\\sum_{j=1}^{n}d_{j}t_{j}", + "29c84d2673a3e5ce.png": "C_{c}^{\\infty}(K_{i})", + "29cd9e9fe4d06481.png": "V=\\sqrt{2.67x}", + "29d0e0999a971786.png": "d[P]/dt=k_{1}[A][M]", + "29d96f9eb11a9fd6.png": "log(e^{x^{\\prime}}+e^{y^{\\prime}})", + "29e8aafa49e76b80.png": "\\langle\\overline{T}T\\rangle_{ETC}", + "29f0614dca65166a.png": "J_{ij}=\\delta_{i,j+1}", + "29fda895c6f3a141.png": "=f(x-\\frac{u}{t})\\rightarrow f(x)", + "2a041948c0524518.png": "a_{1}+a_{14}", + "2a0e6d98bcbd0b5e.png": "R_{1}=\\frac{2a+b}{3}", + "2a1742ac0475c624.png": "Spec_{X}(Sym(L^{*}))", + "2a186a484e7c0c23.png": "\\eta(\\theta)^{\\prime}\\cdot T(x)", + "2a19c336441f025b.png": "f_{N}-g\\in a\\backslash b_{N}", + "2a256c96eb6674c8.png": "[\\begin{matrix}cos\\theta&sin\\theta&0\\\\ -sin\\theta&cos\\theta&0\\\\ 0&0&1\\end{matrix}]", + "2a2785e497a966fc.png": "(\\delta^{k}F)(0)", + "2a2c405c2284b359.png": "v_{i}\\in H_{0}^{3},i=1,2,3", + "2a2d213e0280dc31.png": "\\frac{a_{n}}{\\sum_{i=1}^{n-1}a_{i}}", + "2a396f0f5462d00b.png": "\\frac{dx_{i}}{dt}=x_{i}f_{i}(x)", + "2a3e95b294c1d39a.png": "\\delta H/\\delta\\Phi=0", + "2a44c64f67226315.png": "J_{k}:=\\bigoplus_{j=1}^{k}U_{j}", + "2a4affc0271f2035.png": "\\approx\\int_{\\partial N}f^{\\mu}ds_{\\mu}", + "2a6394f6081a71ec.png": "|y|\\in O(|x|^{k})", + "2a640c05f8c4f9a5.png": "H_{1}=-\\vec{d}\\cdot\\vec{E}", + "2a663b4f3d44b90d.png": "\\oplus_{i=1}^{m}L^{2}(R,\\mu_{i})", + "2a70abb745bd0046.png": "D_{a}=E_{a}-I_{a}", + "2a7281da18c2acc2.png": "2^{2}+2+1-1", + "2a78ef0b8400e09e.png": "n(\\frac{m-1}{m})^{n-1}", + "2a7b211a18b517c5.png": "(0,\\frac{\\pi}{2}]", + "2a8106ec6e59af0b.png": "a\\in R;x,y\\in R^{n}", + "2a87cfb89fb4d052.png": "w(P,Q):=\\frac{G}{F}", + "2a89376adf9ca262.png": "\\propto exp(-z/H)", + "2a972749a736e095.png": "x^{2}+y^{2}=a^{2}-b^{2}", + "2aae59595ece6402.png": "\\gamma(u)=\\frac{1}{\\sqrt{1-\\frac{u\\cdot u}{c^{2}}}}", + "2ab0ce8f29f5ec70.png": "lim_{x\\rightarrow0}\\frac{O(x)}{O(x)}", + "2ab1a0616f167aa1.png": "p_{1}/\\pi_{1}\\Omega_{z}", + "2d5791174f31d6cd.png": "\\Gamma=C([0,1],X)", + "2d5d02a17b166b28.png": "(\\nabla f,-1)", + "2d66efb867bbef27.png": "\\neg(xc", + "2e9ca0c976502809.png": "(a_{k_{0}},a_{k_{1}},...)", + "2ea2dd9cb8f69387.png": "det\\varphi_{w}^{\\prime}(0)=-1", + "2ea570958471cfff.png": "(\\hat{b}^{\\dagger})", + "2ea5ed707eb75151.png": "\\lambda\\gamma(\\sum_{g=1}^{G}||w_{g}||_{2})", + "2ea850912fef14c3.png": "X[(p+m)\\Delta_{F}]", + "2eace9b32dfbd829.png": "f^{-1}(y)=\\sqrt{y}", + "2ebad41c253599af.png": "A^{2}=dI+\\lambda J", + "2ebfd75ed5a4f806.png": "F=\\frac{1}{4\\pi\\epsilon_{r}\\epsilon_{0}}\\frac{q_{1}q_{2}}{r^{2}}", + "2ed4f8925e898a7b.png": "A^{\\prime}=\\hat{B}(\\varphi,\\hat{n})A", + "2ed79be555d3dfcd.png": "J_{(1)}=J_{(2)}", + "2ed93a56325fbd3c.png": "0+0=0", + "2edbd173b5985d05.png": "x=\\frac{1}{u}(u\\wedge v)", + "2edd355445a15351.png": "\\mu_{g,3}\\approx\\sum_{i=1}^{n}g_{,i}^{3}\\mu_{i,3}", + "2ede36d7dab778bb.png": "\\frac{n_{1}}{n_{2}}sin\\theta_{1}>1", + "2ee8c4e8d6c5adc2.png": "\\alpha=\\frac{2\\omega k_{0}}{c}=\\frac{\\omega\\kappa_{2}}{n_{0}c}", + "2efa90334697c46c.png": "\\sqrt{n}\\ge\\frac{1.96\\sigma}{0.5}", + "2eff8a73591dd09f.png": "\\nu_{p}(n!)", + "2f0084328617f363.png": "\\Phi_{e}=\\int\\frac{U_{e}}{T^{2}}dT", + "2f027df3b4d27587.png": "[\\begin{matrix}f\\\\ g\\end{matrix}]=[\\begin{matrix}A&B\\\\ C&D\\end{matrix}][\\begin{matrix}x\\\\ y\\end{matrix}]", + "2f13a776d4863dbd.png": "(0=N-1", + "2f4b5b09841e3a4e.png": "f(y)=2+2y+y^{2}", + "2f5237ad1b267210.png": "x_{k+1}=x_{k}+\\alpha p_{k}", + "2f5e3123fbfbb556.png": "2^{2^{n}-n-1}\\prod_{k=2}^{n}k^{(\\begin{matrix}n\\\\ k\\end{matrix})}", + "2f5f0c8f959daae9.png": "f(z)=\\frac{e^{iz}}{z}", + "2f642574832f7a5b.png": "\\phi(y,\\dot{y},y^{(\\gamma)})=0", + "2f684e9f422ed180.png": "2,2+it", + "2f78c3e13769e40b.png": "H\\in C^{\\infty}(R^{i})", + "2f7d4d06388dfaac.png": "|\\frac{d^{2}y}{dx^{2}}|\\approx\\frac{1}{R}", + "2f80a424ff58410c.png": "r_{CM}=\\frac{1}{N}\\sum_{i=1}^{N}r^{(i)}", + "2f97515b6c626790.png": "(\\frac{\\partial}{\\partial x^{1}},\\cdot\\cdot\\cdot,\\frac{\\partial}{\\partial x^{n}})", + "2fa6acd525dd62ac.png": "\\varphi=\\frac{\\sqrt{5}+1}{2}", + "2fac991ea87c263d.png": "\\frac{1}{2}s_{1}s_{2}sin(\\theta)", + "2fb1b893fea07930.png": "(T-L_{m})", + "2fc15a3b287d202a.png": "||\\sigma(x)||_{2}", + "2fc5e372e9f5be53.png": "\\exists!x_{n}A(x_{1},...,x_{n})", + "2fcc797b9458378e.png": "F(t,x(t),\\dot{x}(t))", + "2fd419e84f481cff.png": "E_{k}=mc^{2}-m_{0}c^{2}", + "2fd431dfe66c0be0.png": "f^{*}(\\frac{x^{*}}{a})", + "2fdf1ebd63240f20.png": "(3)Z(p^{\\infty})", + "2fdf5a7767008035.png": "\\omega_{\\chi}(x,y)=\\chi([x,y])", + "2febdb900df0d83d.png": "\\frac{2R(x)}{2}=R(x)", + "2ffb3c3c96558181.png": "\\pi_{T}=a\\frac{n^{2}}{V^{2}}", + "2ffca8a5f463c295.png": "|\\psi_{A,B}^{\\lambda}\\rangle", + "30157fc71064b98e.png": "\\frac{d}{dt}(\\frac{dt}{d\\tau})\\approx0", + "301cd3808a44f861.png": "y^{\\prime}\\leftarrow\\tilde{y}^{2}remN", + "30219739140b234b.png": "j\\mapsto(\\begin{matrix}-1&1\\\\ 1&1\\end{matrix})", + "302300c752e1b758.png": "\\lambda x.((\\lambda x.x)x)", + "3026f56961b44114.png": "|\\xi|\\rightarrow1_{+}", + "302781651d2a6f4e.png": "V(\\cdot,\\Omega):BV(\\Omega)\\rightarrow R^{+}", + "30292a47667b22bf.png": "|G:H|<\\infty", + "3033f839364aed7f.png": "X_{k}+\\tau\\nabla log\\pi(X_{k})", + "30370bd361699d2b.png": "A_{i,j}=1", + "3037aee21159ed63.png": "(\\vec{0},\\vec{0})", + "303c7b58401650f5.png": "u_{2}^{\\prime}:=u_{2}-u_{1}", + "3040704eb1ef43bf.png": "exp(2ik\\Omega d^{2}/v)", + "3049fd61ad7c6dea.png": "f^{-1}(y)=\\pm\\sqrt{y}", + "305464de34f9d5d1.png": "b^{e-(p-1)}", + "3064c539e4f0739f.png": "K_{m}=\\frac{1}{2}(k_{1}+k_{2})", + "3065cb0f804a2563.png": "p(x)=x^{3}+2x-3", + "30768d6145733574.png": "F(t,x(t),\\dot{x}(t))", + "307de9d214f22134.png": "d\\overline{v}=-\\frac{e\\cdot\\overline{E}}{m}dt", + "308b02e9474629a2.png": "S_{conf}=k_{B}ln\\Omega_{conf}", + "308e6520b37ffb2b.png": "x\\in[\\pm\\frac{1}{\\sqrt{\\beta(1-q)}}]", + "30a7abea57bc2293.png": "\\Delta U_{system}=Q", + "30b28f6c0d46e3d4.png": "R_{s}^{2}\\gg(X_{s}+X_{m})^{2}", + "30b364988ec09101.png": "\\frac{\\frac{1}{4}}{1-\\frac{1}{4}}=\\frac{1}{3}", + "30b862e6a182701e.png": "ax^{2}+by^{2}+c", + "30c47590846c12e7.png": "F_{X}=\\frac{\\sigma_{X}^{2}}{\\mu_{X}}", + "30c861ef5c14d65e.png": "r_{t}=ln(P_{t}/P_{t-1})", + "30d44458e63d2c9d.png": "F=\\frac{1}{c}\\overline{E}e_{4}+\\overline{B}e_{123}", + "30df39c8373a7a98.png": "lim_{x\\rightarrow0}\\frac{x}{x^{3}}=\\infty.(6)", + "30ef4608bf67e953.png": "v_{pec}=a(t)\\dot{\\chi}(t)", + "30f5960f2c321d07.png": "1+3=4mod13", + "30f8c3cf4bb2e81a.png": "|z|<1/(1-q)", + "30fdc127f5fcd65f.png": "T_{1},...T_{2},...", + "3114f5b8a9867952.png": "\\langle a,\\sqrt{2}\\rangle", + "31275b159fb80838.png": "T=[0,\\infty)", + "312c4a473139b734.png": "\\sum_{k=1}^{n}(\\begin{matrix}k+n-1\\\\ k-1\\end{matrix})", + "312d6080fcbfe920.png": "Q\\otimes_{Z}G=0", + "31313b615c792e54.png": "[M]\\in H_{n}(M)", + "31396db9a993ebf0.png": "E[\\frac{j(n,X)}{a(n,X)}]=1", + "313b97d3746dd53d.png": "log_{10}(2)=0.301", + "31444ce65b48a671.png": "e^{i(k_{i}\\cdot r-\\omega_{i}t)}", + "314d697ac97b165e.png": "1/p,q,w", + "316386e03ee3a8e7.png": "P[S_{0}=k]", + "3166ec068bf0654b.png": "\\tau\\sqrt{\\frac{g}{h}}=9.80", + "316931350c024cf7.png": "(a-b)^{2}c>0", + "31718b4e7ce2d8fa.png": "=e^{-1}.1=e^{-1}", + "31759e9924fce47e.png": "\\sigma_{3}(n)=\\sum_{d|n}d^{3}", + "317824b24ee2e73a.png": "Z^{+}\\cup\\{0\\}", + "317edbf914d0076c.png": "\\hat{\\mu}_{m}=\\frac{1}{n}\\sum x_{i}", + "3181459a00110cdc.png": "1^{f(x)}", + "3188952e20d4772a.png": "n,m=1,...,l_{\\mu}", + "31a502a6638203aa.png": "C^{\\prime}\\rightarrow L=\\frac{1}{\\omega_{c}\\omega_{c}^{\\prime}C^{\\prime}}", + "31af1373a86b2b5d.png": "Z=\\{-1\\}\\cup(0,1)", + "31b1aa04f97f1d74.png": "q|a^{2}-b^{2}p^{*}", + "31b625a3f9e28485.png": "\\bigcup_{n\\in F}(S-n)=N", + "31c5de15ba63d306.png": "\\pm\\epsilon^{ijkl}e_{k}\\wedge e_{l}", + "31ca3b83b3e3df0e.png": "\\{f(x)>t\\}", + "31cdb13689ed2605.png": "E[h(x,X_{1})]\\equiv0", + "31d9352add7ed98f.png": "p=p(r)Y_{10}", + "31dfac8aa6774328.png": "A^{+}P=A^{+}=QA^{+}", + "31e1269660b38dea.png": "U_{t}+A\\cdot U_{x}=0", + "31e1e84f327bd48f.png": "D(x,y)=\\frac{1}{2}", + "31f051b5c0074c96.png": "E_{5}=\\frac{N_{2}-1}{N_{1}-1}", + "31f59e5f816d07f4.png": "0<\\langle k\\rangle<1", + "32088e6346c65c62.png": "(\\alpha\\omega)^{*}=\\omega(\\alpha^{*})", + "3209479c91f37355.png": "S_{z}=\\hbar(s-a^{\\dagger}a)", + "320f0ee85b893fff.png": "\\langle A\\rangle_{\\psi}=||A\\psi||^{2}", + "322b192c922fb181.png": "d<|F|", + "323062ce91dba5d4.png": "U_{a}(z)=", + "323e1a256ed2cfeb.png": "|+X\\rangle", + "323f08003a44a2e5.png": "J(x)\\in X^{\\prime\\prime}", + "3242e006bfc597c1.png": "(1+x)^{n}-(1+nx)", + "324d4c45bb9cf40f.png": "\\Delta z=H(z)\\Delta\\chi", + "32661c7cd4a9d0e6.png": "\\rho:G\\rightarrow GL(d_{\\rho},C)", + "326992ca300710bf.png": "B=b-\\frac{a}{RT}", + "327aa1ece02610da.png": "K_{L}=\\frac{sin(\\alpha)}{sin(\\beta)}", + "328ae57d4d124487.png": "y=x^{2}-x-2", + "328ec836feae9fcf.png": "M_{1}\\equiv\\int d\\zeta\\frac{\\lambda(\\zeta)}{\\zeta^{2}}", + "3297ef1434cb2515.png": "p_{n+1}=2+\\sum_{i=1}^{n}g_{i}", + "32a35fb940058397.png": "(p-c_{0}^{2}\\rho)\\delta_{ij}", + "32b87d8d5010b275.png": "[\\Omega]\\in H^{3}(M,R)", + "32c46dc002237bd7.png": "-x+x=0", + "32c57492d5263e19.png": "\\lceil|k|/n\\rceil", + "32cb4904ef228e57.png": "x=\\frac{i}{f}=\\frac{S}{f}\\sqrt{t}", + "32d8e50701ebca78.png": "d_{\\lambda}=\\frac{n!}{\\prod h_{\\lambda}(i,j)}", + "32e0b33fff744544.png": "FF^{\\dagger}=F^{\\dagger}F=I", + "32e1083c944bc013.png": "D_{LA}=z\\frac{g}{g+1}", + "32e8f4aba31e9fe2.png": "L^{2}(H^{2})", + "330195af61cf9c8f.png": "\\Gamma\\models_{FS}A", + "3306a951927aab04.png": "\\bigcup_{n=1}^{\\infty}A_{n}\\in R", + "330d24e7726e1db5.png": "a>1+b(\\mu-1)", + "330f2aecdd733b57.png": "i_{c_{0}}=asin(\\frac{V_{0}}{V_{1}})", + "3313419fcc8a2f85.png": "\\partial_{\\mu}J^{\\mu}=\\frac{\\partial\\rho}{\\partial t}+\\nabla\\cdot j", + "33163a0537e83a44.png": "T(n,t)=I_{n}(\\alpha t)", + "331891914054c50d.png": "\\underline{n}=n+i\\kappa", + "3319ec0098ac16db.png": "D<\\sqrt{m}", + "332428fc8d2c5444.png": "|x-a/q|<\\frac{1}{q^{c}}", + "33254cd05c27e8ae.png": "\\theta=\\pm arccos\\frac{l-r}{er}", + "33314f70985dc6b1.png": "h^{\\prime}(x)=-\\frac{f^{\\prime}(x)}{(f(x))^{2}}", + "333b3840beb249b1.png": "\\Delta z=H(z)\\Delta\\chi", + "333f0d1d7eceab13.png": "L=-\\partial_{x}^{2}+v(x,t)", + "3346d2228ad64a04.png": "\\sum_{k=1}^{n}k^{m}=nP(n)", + "335f2b602f108102.png": "\\frac{dx}{d\\xi}=x-y", + "337433b519a54503.png": "E_{h}=\\alpha^{2}m_{e}c^{2}", + "337a82691a125653.png": "\\forall i,j:\\epsilon(v_{ij})=\\delta_{ij}", + "338ca31b30cb92de.png": "\\{f_{ij}\\}_{j\\in J_{i}}", + "33919952aeb9afdf.png": "W_{m}H^{k}(X;C)", + "3393d4f5cbbea1b8.png": "[Q^{\\dagger},b\\}=\\frac{dx}{dt}+iF", + "33a53cbb2390f69c.png": "g_{i}(0)=\\frac{\\partial f(z)}{\\partial z_{i}}|_{z=0}", + "33a65c0fd0f9b409.png": "m_{i,j}=x^{i}\\cdot x^{j}", + "33b24cef68d2088d.png": "v^{2}={v_{esc}}^{2}+{v_{\\infty}}^{2}", + "33b33188fea5b05b.png": "Nq=qKq=(Tq)^{2}", + "33b688ac6a6086bd.png": "Z_{bus}={Y_{bus}}^{-1}", + "33bdf13a5cdab8d2.png": "1+t=625t^{2}", + "33ce0e50360224f1.png": "\\frac{\\pi}{180}M_{r}cos\\varphi", + "33d607b1794c95da.png": "\\varphi\\rightarrow\\frac{-\\nabla f}{|\\nabla f|}", + "33d741b33872b181.png": "G=\\frac{p^{\\prime}(x_{k})}{p(x_{k})}", + "33e3f25fd2ec2654.png": "\\Delta S=\\frac{Q}{T}(1)", + "33e87a18c3a6a948.png": "A\\cap B=\\overline{\\overline{A}\\cup\\overline{B}}", + "33e9ffdfefd8d9fb.png": "e^{1/3}=\\sqrt[3]{e}", + "33eb197e5247c5b5.png": "x_{1}-x_{2}+x_{0}=0", + "33f5ea1b2cb5c410.png": "J:V\\rightarrow\\overline{R}", + "33f784aebf3af222.png": "\\bigcup_{n\\in F}(S-n)=N", + "340bb67f39d12e11.png": "\\sum k^{3}={(\\begin{matrix}n+1\\\\ 2\\end{matrix})}^{2}", + "340eb2ad17cf0290.png": "\\theta_{j}\\in{Con_{c}}^{\\{x_{j}\\}\\vee Z}L", + "340f69dc28282102.png": "\\frac{1}{2^{N}}(\\begin{matrix}N\\\\ k\\end{matrix})", + "3425a4f10debe485.png": "r_{1}r_{2},...,r_{k}", + "343d3ea11ed10be3.png": "I_{c}=\\frac{\\Sigma x^{2}}{(\\Sigma x)^{2}}", + "3441eef965d5b39b.png": "\\mu_{a}\\cap(A^{T}\\mu_{b}A)", + "344f774e753f1750.png": "\\sqrt{\\frac{2}{\\pi}}", + "345400ce160fb41c.png": "\\Delta z=H(z)\\Delta\\chi", + "34588e73c52032ae.png": "0\\le x_{1},x_{2},x_{6}\\le10", + "3479b2cc921b33bc.png": "t=0,\\cdot\\cdot\\cdot,T-1", + "347ed0666f12e1ca.png": "x=\\zeta^{-\\frac{1}{N-1}}", + "3489f86c0ce19f01.png": "\\{a^{n}b^{n}|n\\ge1\\}", + "34920f655a13df29.png": "W_{E}=4\\int Y\\sigma^{2}dx", + "34927f0353855290.png": "\\frac{n-5\\pm\\Delta_{n}}{2-2n}", + "349f38b3489118de.png": "{(\\hat{k}_{F})}^{\\kappa\\lambda\\mu\\nu}", + "34a810eb3e199da0.png": "k_{t}:id_{D}\\sim k_{1}", + "34b47539c4aea0cb.png": "(k+1)^{2}=k^{3}", + "34b6769b8cfb49c6.png": "exp(\\overline{z})=\\overline{exp(z)}", + "34b722cd33826ef5.png": "D=(d.d.2d)^{\\frac{1}{3}}", + "34c10b1fed406a07.png": "m_{P}/m_{P}^{2}", + "34c7f991c343a589.png": "b^{2}+h(a)b", + "34cf442e0a8d2002.png": "\\frac{n}{m}+2m-1I_{0}", + "3909b57ff658a0cf.png": "\\vec{m}\\in M", + "3910fa52275844ac.png": "(\\begin{matrix}1\\\\ \\frac{c}{\\rho}\\end{matrix}),(\\begin{matrix}1\\\\ -\\frac{c}{\\rho}\\end{matrix})", + "39114b411229b2c1.png": "\\psi=[1,-1]", + "391446547e089b65.png": "\\overline{\\nu}+p\\rightarrow n+e^{+}", + "3914ec71070715ac.png": "2Rsin(\\frac{a}{2})", + "3917882bd7603ea6.png": "C_{DGT}=\\frac{M\\Delta g}{DtA}", + "3918f930f1b40903.png": "S_{Z}=B^{\\frac{1}{2}}\\cdot T_{Z}.", + "3923f71d49fbf8a9.png": "X=x-mg/k", + "3942e0fc0d6c520e.png": "I(v)=\\langle v,v\\rangle=|v|^{2}", + "3949f317ea05195a.png": "Pr(t|B_{i}^{-})", + "394acc08c46d6113.png": "G=\\frac{p^{\\prime}(x_{k})}{p(x_{k})}", + "394f0f9ecc485888.png": "\\langle G,S\\rangle\\rightarrow\\langle G^{\\prime},S^{\\prime}\\rangle", + "3955b4904ab7b51f.png": "\\psi_{R}\\rightarrow(\\begin{matrix}\\psi_{11}\\\\ \\psi_{21}\\end{matrix})", + "395ee537f6454f6d.png": "\\frac{\\partial f}{\\partial t\\partial s}=j\\circ\\frac{\\partial f}{\\partial s\\partial t}", + "395f2c5d36accb8f.png": "(d\\vec{b})^{-1}", + "396cf9186e3ec15b.png": "\\hat{X}^{opt}(z^{n})", + "3972fc7c28bf8dfb.png": "1+3+5=9", + "397ee3079c0f0716.png": "f_{1}(z)=-\\frac{a_{2}}{a_{1}}f_{2}(z)", + "3984d11d4876e47f.png": "Q(2n,q)(n\\ge2)", + "398a274d519514d2.png": "\\frac{d}{dx}y=t(x)y", + "39957829c3468496.png": "1/(2q^{2})", + "39984788249b0d8c.png": "axmod2^{w}", + "399efab7901eb974.png": "\\Psi=\\sqrt{\\rho}e^{iS/\\hbar}", + "39a1b1e8d4fd688d.png": "\\psi_{2m+1}\\in Z[x,A,B]", + "39ab787e2b134620.png": "-\\frac{\\hbar}{2}\\omega_{0}", + "39b2a8d22f1729fe.png": "-D_{k}r^{k}\\ge0", + "39b6bd8f57d4eb69.png": "S\\in R^{I_{1}\\times I_{2}\\times...\\times I_{N}}", + "39c0a73afc79b3bb.png": "r\\{\\begin{matrix}3,3,3\\\\ 3,3,3\\end{matrix}\\}", + "39c25c9b06839eb5.png": "\\sum_{k=0}^{m}(\\begin{matrix}m\\\\ k\\end{matrix})(\\begin{matrix}n\\\\ r+k\\end{matrix})", + "39c6a44038de51a4.png": "\\lambda x.((\\lambda x.x)x)", + "39d5af8ccb51045d.png": "1-\\sqrt{-5}", + "39ea9e256977c540.png": "\\frac{T}{T_{i}}=\\sqrt{\\frac{M_{i}}{m_{e}}}", + "39eef60fa6d94743.png": "f(\\cdot;v^{(t-1)})", + "39f10ddc2b679ec6.png": "[\\begin{matrix}1&9&-13\\\\ 20&5&-6\\end{matrix}]", + "39f36b1ff90f6e86.png": "q(\\pi)\\prod_{k=1}^{K}q(\\mu_{k},\\Lambda_{k})", + "3a1ab215b9a30629.png": "M=\\frac{1}{2}fr^{2}+vr", + "3a20064769cf2ce1.png": "J_{N(t)}\\le t\\frac{q}{2}", + "3bd90a26d4191579.png": "cos(\\frac{x\\pi}{180})=x", + "3bd97bd3c2a966b2.png": "P_{t,t^{\\prime}}(x|x^{\\prime})", + "3be803d033bcb267.png": "\\delta(q_{s},q_{c})\\rightarrow q_{t}", + "3beb4d3c9fed07f5.png": "\\delta_{j,j_{1}}\\delta_{m,m_{1}}", + "3befe38b8c265ea6.png": "a_{\\pi}=a_{y}=0.5", + "3bf045b925d07821.png": "|\\gamma^{\\prime}(t)|=|\\gamma(t)|", + "3bfa6f323e9b7123.png": "|f_{i}(x)-f_{i}(y)|=1", + "3bfe2a05371645e2.png": "x_{k+1}=x_{k}+\\frac{1}{m}", + "3bfe4bdeed61953f.png": "c_{n}\\approx\\mu^{n}n^{\\gamma-1}", + "3c05c30a2647b85b.png": "\\Delta(1/\\lambda)=1/L", + "3c24365562a7a0ac.png": "g(\\zeta)=f(\\zeta^{-2})^{-\\frac{1}{2}}", + "3c2f548a7fe880ab.png": "\\sigma_{y}^{2}(\\tau)=\\frac{2\\pi^{2}\\tau}{3}h_{-2}", + "3c301c781aaeef10.png": "x=5+\\frac{14}{x}", + "3c30f2c8ac8b31fb.png": "H^{0}(\\Omega_{C}^{1})^{*}", + "3c35ed54a67f46e8.png": "Y_{12}=\\frac{-2S_{12}}{\\Delta_{S}}Y_{0}", + "3c3b50edccdcea58.png": "k\\in\\{1,...,n_{ij}\\}", + "3c4e4f9267d1bd38.png": "\\overline{B_{1}(p)}=\\{p\\}", + "3c67e530bcfa30b1.png": "|\\delta|<|b_{k-1}-b_{k-2}|", + "3c9bb3157e87d07b.png": "sinc(x)=\\frac{sinx}{x}", + "3ca5c7c11ebd3791.png": "\\alpha_{i}\\rightarrow\\alpha_{i}e^{-i\\omega t}", + "3ca991dd0cd0e01a.png": "\\frac{z}{z_{0}}-1", + "3cacadef25058e2f.png": "u=+\\frac{\\partial\\psi}{\\partial y}", + "3cb4ccbe611f0589.png": "FDR\\le\\frac{m_{0}}{m}q", + "3cb7ed5ad4389046.png": "\\delta(q_{s},q_{c})\\rightarrow q_{t}", + "3cb9c47508bbdafb.png": "P/A=\\sigma T^{4}", + "3cd7309f042b5b69.png": "2^{m/15}=e^{m/T}", + "3cdb266434f42d73.png": "CO=\\frac{VO_{2}}{C_{a}-C_{v}}", + "3cdf16036185e8e7.png": "(U(z),0,0)", + "3cf683f889da349a.png": "\\Psi<\\frac{2}{3}", + "3cfc272d1170395c.png": "\\sum_{i}(X_{i},f_{i},\\alpha_{i})=0", + "3cfe4e1ce9544224.png": "\\hat{D}=A(D)", + "3d14c22cac88ccd1.png": "L^{2}\\le\\frac{\\pi}{4}area(\\partial P)", + "3d18fb83c7796990.png": "ACDA_{si}=\\frac{Vd_{hsd}}{V_{i}}", + "3d1f8b3caa8c0e11.png": "\\Gamma(\\frac{1}{4})/\\pi^{1/4}", + "3d21f0aaf2da0c30.png": "U^{2}=\\frac{Wrd^{2}}{4C+md^{2}}", + "3d26bec02de9ea27.png": "g^{\\prime}(\\alpha)-\\frac{k}{\\alpha}g(\\alpha)=0", + "3d2c08692d0718f5.png": "n+\\frac{4n+3}{4n+4}", + "3d3083d6c559facf.png": "P=K\\rho^{1+\\frac{1}{n}}", + "3d30c7ce3181d1b8.png": "f(x)t\\}", + "3e5a2399b9cee5a9.png": "3^{(F_{n}-1)/2}", + "3e624f5c0487069c.png": "\\frac{1}{|A|}\\sum_{a\\in A}f(a)", + "3e6c4332edff875f.png": "\\frac{1}{k}=\\frac{m^{*}}{m}-1", + "3e7d46d3842ac02b.png": "y_{b}+\\epsilon=y(b)", + "3e8333cfeb30ce7e.png": "\\frac{n}{2}sin\\frac{2\\pi}{n}", + "3e94a453d74f4c2a.png": "j_{0}=f^{2}\\partial_{0}\\theta(t)", + "3e97d8015355d488.png": "(1+x)^{n}-(1+nx)", + "3e9a40cecc6426dc.png": "S_{2}=S_{1}-kln\\frac{c_{2}}{c_{1}}", + "3eaf0bb9f828792b.png": "E_{c}:z\\rightarrow e^{z}+c", + "3eaf981ba67820b8.png": "1-\\sqrt{-5}", + "3eb2aced79f7fb15.png": "0<\\mu<\\frac{2}{\\lambda_{max}}", + "3ec15782780e721c.png": "A(t)=\\langle x(t)x(0)\\rangle_{0}", + "3ecec3155ada2a51.png": "\\gamma_{||}|A|^{2}L", + "3ed270d592655e31.png": "Pr(t|B_{i}^{-})", + "3ed4fc147f1a7b58.png": "z=a(2e^{it}-e^{2it})", + "3ed648a1dc8ff4da.png": "x\\equiv\\pm(p+y)/2", + "3ed68a707227ef2d.png": "K_{n}\\sim\\frac{n}{logn}", + "3edbc0bc41eb3dca.png": "R=\\{-1,+2\\}", + "3edfb077b667676e.png": "00", + "42a68d14aeab37e0.png": "\\hat{X}^{opt}(z^{n})", + "42ab6444ce67cb61.png": "t=\\pm\\frac{1}{1,3}", + "42b8cff20495394f.png": "y^{\\prime}=vy\\in\\psi(e,d^{\\prime})", + "42bbfbbc7bda1d81.png": "s=\\frac{v+u}{1+(vu/c^{2})}", + "42c527f350515d6f.png": "i=\\sqrt{-1}", + "42c54007840308d6.png": "(\\frac{m}{s})", + "42cc7a0d6c117f45.png": "r=2M+\\rho^{2}/8M", + "42d06dd4c91e0c3a.png": "n|M_{n}-1", + "42d10d52b893daa9.png": "[\\begin{matrix}s^{2}&psz\\\\ psz&z^{2}\\end{matrix}]", + "42d409ba3477288e.png": "\\frac{1}{2}(2-\\frac{6}{4})=\\frac{1}{4}", + "42d6f76bdc073261.png": "\\sum_{n}\\hat{f}(n)=\\sum_{n}f(n)", + "42f4087d3d891de6.png": "\\sigma_{i}\\in\\{-1,1\\}", + "42f7d4e82b0d6d6d.png": "T_{j}\\subseteq[t]", + "4330e821db8f81da.png": "(F_{p})^{d}", + "4332aeadb2a05a15.png": "J_{\\hat{n}}", + "4343638ec790913b.png": "\\varphi\\rightarrow\\frac{-\\nabla f}{|\\nabla f|}", + "4347b1fed233c6f4.png": "\\pi(0.99)\\times v(1000)", + "434aefd137ccbb71.png": "u\\equiv z_{1}z_{2},v\\equiv z_{3}z_{4}", + "43516067320ebbeb.png": "\\int_{E}f(x)\\mu(dx)", + "435b91ac8db3c4d6.png": "||\\varphi_{n}-\\varphi_{m}||_{d}<\\epsilon", + "435cad7e57498012.png": "\\frac{D^{2}\\tau^{2}}{2}", + "436c1116ef73a324.png": "(\\overline{3},1,-\\frac{4}{3})", + "436c4fa60ca70d6b.png": "E=rc^{4}/2G", + "436cf00fa9dba41c.png": "3\\sqrt{25+10\\sqrt{5}}s^{2}", + "437276d6a51dbd09.png": "\\frac{\\partial S}{\\partial\\varphi}=p_{\\varphi}=-ac", + "43766101eb085f2f.png": "\\{L(u,v):u,v\\in X\\}", + "43848a25c9668a24.png": "Z\\cup[(0,1)\\cap Q]", + "43879534710e5eac.png": "(it)^{r}\\psi(t)", + "4389eb076917c755.png": "D=\\epsilon_{0}E,B=\\mu_{0}H", + "439ac1617f2d5e31.png": "|\\alpha|=\\alpha_{1}+\\cdot\\cdot\\cdot+\\alpha_{n}", + "43aee4503a4123aa.png": "\\pi(k+\\frac{1}{2})", + "43c0f835fc50e8a4.png": "\\sqrt{1},\\sqrt{2},\\sqrt{3},\\sqrt{4},\\sqrt{5}", + "43c1b29f00ea5536.png": "\\frac{q^{2}}{4}+\\frac{p^{3}}{27}>0", + "43f23bfa1d4f236e.png": "\\Omega_{\\pm}=\\omega\\sqrt{1\\pm\\frac{\\Omega}{\\omega}}", + "440be9671000e488.png": "\\Lambda_{id}=\\chi(X)", + "440cfcd869f2938e.png": "P_{H}V|_{H}=T", + "441b99faf32bb857.png": "x=10+2\\epsilon_{3}-5\\epsilon_{8}", + "4420711d81d0c206.png": "\\frac{d^{2}x}{dt^{2}}+\\frac{k}{m}x=0", + "4433fdb2831089ac.png": "f^{\\prime}(a)>y>f^{\\prime}(b)", + "44346eb757774904.png": "\\eta_{c}=\\sum_{i=1}^{N}k_{i}\\eta_{c_{i}}", + "44379a510b23c6ce.png": "A_{m}(0,r)=(\\begin{matrix}r\\\\ m\\end{matrix})", + "444fffa5b0d889ef.png": "\\frac{a}{-b}=\\frac{-a}{b}", + "4454a14c66b4cc3a.png": "L(r,\\theta,\\dot{s},\\dot{z},\\dot{r},\\dot{\\theta},\\dot{\\phi},t)", + "4455dfdb338dd645.png": "E[S_{1}+...+S_{\\lambda}]", + "445bee39deba3149.png": "U(S)\\ge d(1-2\\epsilon)s", + "445c033f01ac0199.png": "det\\varphi_{w}^{\\prime}(0)=-1", + "44601dbb5243c17c.png": "f(y)=2+2y+y^{2}", + "446e2a07ecd8089c.png": "\\varphi(t,X)=t-\\psi(X)", + "446fc896c09d1986.png": "\\dot{Q}/T", + "447379c6a9777752.png": "\\sqrt[3]{b}^{2}", + "4477bf268fa6e3b5.png": "logq>(q-1)logb", + "4479532c2c17f934.png": "U\\subset R^{2}\\times R_{+}", + "447e4d5427d5c798.png": "\\sqrt{1-x^{2}-y^{2}}", + "448586a5957f6a31.png": "(z_{1it},...,z_{kit})^{T}", + "4485e4a0711c2de9.png": "T_{j}\\subseteq[t]", + "4486e67a9f404150.png": "C^{T}B\\le l_{W\\times L}", + "44902fe46c3b964e.png": "\\alpha=D\\tau/W^{2}h_{0}", + "44a7154544c7fd95.png": "\\varphi(r)=\\frac{sin(lr)}{lsinhr}", + "44b3fe1444d3e8dd.png": "(x^{2}+1)^{10}", + "44b87a207a42f888.png": "\\int x^{2}e^{x^{2}}dx", + "44b90ce7df07d68a.png": "O(nlog(log(n)))", + "44bb09af98e7ad47.png": "f^{\\prime}(g(p))=p", + "44bc77699ad0e24c.png": "\\sigma^{1}=g(r)dr", + "44bf0e6a4b9ddaad.png": "O(\\sqrt[4]{N})", + "44c715ce21ef322a.png": "h_{ii}=(H)_{ii}", + "44cdbe29819250ff.png": "(\\rho,\\rho\\dot{q}_{i},\\rho\\dot{p}_{i})", + "44d0ee3212a3cf2f.png": "\\frac{\\partial f}{\\partial{x^{\\prime}}^{i}}=\\frac{\\partial f}{\\partial x^{j}}\\frac{\\partial x^{j}}{\\partial{x^{\\prime}}^{i}}", + "44d245a84c3f68f7.png": "\\hat{D}=A(D)", + "44da4130d6137882.png": "\\psi^{u}(x):=\\pi_{x}u", + "44dd91187a5b6ba3.png": "I_{i}=\\partial S/\\partial E_{i}", + "44e30717754f03d5.png": "v_{max}-e^{-\\alpha t}", + "44e66c822a3dec99.png": "d=2mn(m^{2}-n^{2})", + "4504cdfd545aac39.png": "-\\phi(-x)R(\\pi)\\phi(x)", + "45066c0ee048f210.png": "lim_{n\\rightarrow\\infty}x_{n}-a_{n}=0", + "4507257b13307b4e.png": "\\frac{y_{n}}{x_{n}}\\frac{X}{Y}=\\frac{x/x_{n}}{y/y_{n}}", + "45121ff765beb153.png": "P(v=2)P(c=2)", + "452d76827fff6fc6.png": "\\sigma=|c|\\frac{\\Delta t}{\\Delta x}\\in N", + "452dee821bf3127f.png": "1,2,...n", + "452ed481c397cd11.png": "L_{P}^{\\sigma}=L_{P}\\cdot(1-k)", + "45465335ad9f2d79.png": "d_{e}(n_{e})=\\frac{c_{e}}{n_{e}}", + "454aeb8cbce4703f.png": "\\phi^{\\prime}(t)\\ne0(t\\in I_{1})", + "454cc60adde59ad4.png": "\\dot{G}(t-\\tau)", + "455175fffcb1c425.png": "cos(\\sqrt{z})", + "455352dab843427c.png": "log(|z|)+2n\\pi i+i\\theta", + "4555caa15fe42437.png": "P^{e-1}/P^{e}", + "455be0e5243fdf37.png": "\\hat{B}=\\hat{x}\\hat{y}\\hat{z}\\hat{v}=i\\hat{v}", + "456088796eabd1d5.png": "|h|^{\\frac{1}{2}}=r_{0}^{2}sin\\theta", + "4560dfa4b8d69da9.png": "y=e^{lnx+\\frac{1}{2}x^{2}-\\frac{1}{2}}", + "4563e22573da6238.png": "d=\\frac{\\pi}{4}\\times b^{2}\\times s\\times n", + "4569083cbe3805ae.png": "\\frac{1}{2}sin^{2}0=0", + "456b81ee152709d5.png": "e^{*}=(sign(e_{i}))_{i}", + "45737b656813c66e.png": "axmod2^{w}", + "4575ea67a0a83330.png": "y=x^{2}-x-2", + "4582a65c7e5b0e75.png": "\\epsilon^{\\prime}\\alpha_{0}=\\mu\\epsilon", + "458b4667b7210ee4.png": "k_{t}:id_{D}\\sim k_{1}", + "458bba9e750d7ee1.png": "U(t)=e^{-(i/\\hbar)tH}", + "45971cc051134947.png": "N(0)2^{t/10}", + "45aa38206fb6ac96.png": "\\tilde{x}^{\\prime}=R(\\tilde{x}-t)", + "45b17fc7dcc8431c.png": "M_{X}(t):=E[e^{tX}]", + "45be5ed6381f9250.png": "|sinx|\\le|x|", + "45c446a5ad23ca48.png": "Z_{in0}=\\frac{V_{1}}{I_{in0}}=Z", + "45c544cfb2fbc21f.png": "\\Theta_{div}\\simeq2\\frac{w_{0}}{z_{R}}", + "45c56ca31f651ca6.png": "\\hat{g}=\\frac{k}{T^{2}}", + "45c97bd7b7975a86.png": "\\frac{1}{g_{11}}[\\begin{matrix}1&-g_{12}\\\\ g_{21}&\\Delta[g]\\end{matrix}]", + "45d21e53a2053aba.png": "P(m_{t},x_{t}|o_{1:t})", + "45db74c60eea28a2.png": "\\bigcup_{i=1}^{n}B_{i}\\in B", + "45de32b27efdeacc.png": "M_{0}=\\Phi^{-1}(0)", + "45f7a03ebcab3ae0.png": "w=\\frac{F_{m}+vx}{x}(3)", + "45fa3a8eb3502bf9.png": "A_{m_{1}}\\cap\\cdot\\cdot\\cdot\\cap A_{m_{p}}", + "460cf83a1f0cb248.png": "R^{\\prime}(E_{0})=0", + "4625baf6a5b27b78.png": "\\sqrt{a_{1}x+b_{1}}", + "46261ef392aed8bc.png": "(\\frac{a}{p_{1}})=(\\frac{a}{p_{1}})=-1", + "462a0f82cdba1712.png": "P_{ij}=\\tilde{P}_{ij}logn/n", + "462b6c9bd8276500.png": "Spec(A/p)", + "4632ff743d314a34.png": "X_{t+1}=c+\\phi X_{t}", + "4634b35bd2eda936.png": "E_{l}=\\frac{\\hbar^{2}}{2I}l(l+1)", + "463c8598d58dad7e.png": "\\sqrt{10/[3(5-\\sqrt{5})]}", + "4643ec8ff27b3d36.png": "d[P]/dt=k_{1}[A][M]", + "464a03b1281e1174.png": "\\frac{\\partial}{\\partial y^{i}}=\\frac{\\partial x^{k}}{\\partial y^{i}}\\frac{\\partial}{\\partial x^{k}}", + "464af6017b11262a.png": "TT^{*}=T^{*}T", + "464b09ef9e92974d.png": "I\\subset1,2...n", + "464e689c6f94cc88.png": "\\prod_{k=1}^{\\infty}\\frac{1}{1-x^{k}}", + "464f3872435be824.png": "(16-8\\sqrt{2})r^{3}", + "4658d01445cea4a8.png": "\\dot{y}(t)\\in HY", + "46611d45c9c08fe6.png": "E_{n_{1},n_{2}}^{(0)}", + "4666908da8e7807c.png": "S_{m}-S_{n}>1", + "473d2af98a27e1a5.png": "\\forall n\\in N,|n|_{*}\\le1", + "474db2a36067fb40.png": "\\bigoplus_{i=1}^{n}X_{i}", + "4755690def555f70.png": "0<\\mu<\\frac{2}{\\lambda_{max}}", + "475fab7d6c53d98a.png": "S\\leftarrow S-\\{s^{\\prime}\\}", + "476eaa324c58fe2a.png": "C_{DGT}=\\frac{M\\Delta g}{DtA}", + "4775c9df26cbbbc5.png": "V=(10+2\\sqrt{5})a^{3}", + "4782403f73dccd40.png": "lim_{t\\rightarrow\\infty}\\hat{d}(w,t)=d(w)", + "47840e960f5c71ea.png": "\\overline{\\partial}_{j,J}f=\\nu", + "47881fb9214b670c.png": "(E^{\\dagger}(R),I-E^{\\dagger}(R))", + "478b37f310644368.png": "B=10log_{10}(b)", + "47a8e91185ff0664.png": "E=\\frac{e^{H}-1}{K-1}", + "47a9c8c6a95b9194.png": "\\frac{1}{n_{0}}=\\frac{16}{3}\\frac{\\pi ld^{2}}{4}", + "47aca02c54fc1fc0.png": "E=f(a)=f(-a)", + "47ae0d21e7e2f14d.png": "lim_{t\\rightarrow\\infty}\\frac{t^{\\alpha}}{ae^{t}}=0", + "47af52284d3eefcd.png": "0=E\\{(\\hat{x}-x)y\\}", + "47b82f2d7da083a5.png": "Eq\\alpha\\Rightarrow\\alpha\\rightarrow[\\alpha]\\rightarrow Bool", + "47d17ca206ced86b.png": "Te_{1}=0,Te_{g}=e_{g^{\\prime}},", + "47d227ff597d1e2b.png": "P=\\frac{W}{t}=\\frac{1}{2}\\frac{F^{2}}{m}t", + "47d8154662cdcc98.png": "F_{i}*\\frac{dV_{g}}{dT}=\\frac{dC}{dT}", + "47dffdd70d76bfb0.png": "0\\notin S", + "47e56de17a438841.png": "F(t,x(t),\\dot{x}(t))", + "47e685a94c7ef963.png": "\\frac{4}{3}\\pi p_{f}^{3}(\\vec{r})", + "47e7515080a2658a.png": "ee=|F_{+}-F_{-}|", + "47e7ea7d32a78be3.png": "0=-\\nabla p+\\rho g", + "47ebe9ce403c5568.png": "Y_{12}=\\frac{-2S_{12}}{\\Delta_{S}}Y_{0}", + "47ec23f046d02f8d.png": "u_{min}=min\\{u_{i}\\}", + "47f45747636496a5.png": "a,a+2,a+4", + "47fcba10735f2d22.png": "|\\psi_{A,B}^{\\lambda}\\rangle", + "48048f70a2cab8ec.png": "\\{a,...,b\\}\\subset Z_{n}", + "4808257be147e9ba.png": "\\hat{\\theta}_{1},\\hat{\\theta}_{2},...,\\hat{\\theta}_{k}", + "480d10e03e82569b.png": "U\\leftarrow U-s^{\\prime}", + "4811d4a4d363f8e2.png": "Q(q)=\\frac{\\hbar^{2}}{4m}\\{S;q\\}", + "48127ed1235cf98b.png": "lim_{s\\rightarrow\\infty}e^{-st}(t)", + "48212d290f1f51e3.png": "||\\hat{r}||^{2}", + "482806e0b3528a19.png": "(x^{n})^{\\prime}=nx^{n-1}:", + "482b7248b959e748.png": "x_{1}[n]*x_{2}[n]", + "483f4ef706f7f1b6.png": "X\\cdot F_{i}\\subseteq F_{(h(i))}", + "4841b61cf9f94004.png": "\\zeta_{i}(s)=\\sum_{\\lambda_{j}>0}\\lambda_{j}^{-s}", + "48427e4a5bc03a10.png": "I_{i,j}=I_{j,i}", + "484a4fe12ef6af1b.png": "\\omega+\\omega_{i}\\gg\\omega-\\omega_{i}", + "4855283c62b6c874.png": "w[N/2-1]=w[N/2]<1", + "485a6f3787a5df9e.png": "M=S^{T}AB^{-1}A^{T}S", + "485daf32efe90481.png": "J_{\\hat{n}}", + "486a6ac05e5661f2.png": "(\\vec{0},\\vec{0})", + "486f221d772a8bb7.png": "\\omega_{H}^{2}=\\omega_{p}^{2}+\\omega_{c}^{2}", + "487863fe3dfa5127.png": "(q_{t}^{i}-\\Gamma^{i})\\partial_{i}", + "487cee65f4dc6afd.png": "\\overline{x}_{n+1}", + "4887ba6f8c260e79.png": "I_{SH}=\\frac{V_{j}}{R_{SH}}", + "489301ba52dea12d.png": "exp(-\\sum d_{i})", + "4895f97afd7a2dfa.png": "P=(1-\\frac{d}{a})^{2}Q", + "489a4e7556c54914.png": "Lu=u|_{\\Omega\\\\ \\omega}", + "489a927d2ac7d712.png": "\\kappa_{s}=\\kappa(T_{s})", + "489ad1338918ddff.png": "P^{\\mu},J^{\\mu\\nu},M", + "48a46d2e5bc3baba.png": "Q=Y/2+T_{3}/2", + "48a58500dfcd21d9.png": "X=[\\begin{matrix}A&B\\\\ B^{T}&C\\end{matrix}]", + "48b9f889c7af2cb5.png": "lim_{x\\rightarrow2}\\frac{x-2}{x-2}", + "48c9261b23a8537f.png": "[wz+h+j-q]^{2}-", + "48cc036bc06e04ff.png": "W_{n}=n\\cdot2^{n}-1", + "48cf64d584a8d708.png": "I(z)=I_{0}\\propto|E_{0}|^{2}", + "48d08913c81d4b75.png": "\\partial\\{(I^{2},\\varphi_{\\lambda},S_{\\lambda})\\}_{\\lambda\\in\\Lambda}", + "48dc39d2e91e7de6.png": "\\Delta t=0.1\\Delta x^{2}", + "48e795255008655b.png": "\\sum_{n}", + "48eff2753aabedbb.png": "T^{1}(R)\\subset G(p,1)", + "48f623cbf8b3929a.png": "\\sigma(T)-B(\\overline{R})", + "4907ff4b8277f9fa.png": "\\kappa_{2}=\\mu_{2}^{\\prime}-{\\mu_{1}^{\\prime}}^{2}", + "490f9e349ce7ddb7.png": "n=\\frac{r_{1}\\times r_{2}}{|r_{1}\\times r_{2}|}", + "491eb049b1d64287.png": "min\\{\\lfloor a/2\\rfloor,\\lfloor b/2\\rfloor\\}", + "491f8f65183f0644.png": "F=S/S_{P}", + "492ed026f56961f1.png": "\\Omega=arg(-z_{2},z_{1})", + "492f50b4c67991fc.png": "A_{1}=\\frac{P}{\\sqrt{2}}", + "4935bc7b5abef55a.png": "\\Omega=\\beta A_{m}^{fp}", + "49423329af6ab62a.png": "e^{-ax}x^{ax}", + "4947424fb93683d8.png": "D_{ij}\\subseteq(\\frac{1}{2})D_{i}", + "4950cfad374497fa.png": "\\frac{x_{1}+x_{2}}{2}>\\sqrt{x_{1}x_{2}}", + "495656f5f8144244.png": "H^{1}|_{E}", + "49598452eb547f8b.png": "n^{3}log(n)^{3}", + "495c734a7dfe3951.png": "\\prod_{i\\subseteq\\Sigma}M_{i}/U", + "4982818423f3a5dc.png": "a_{1}+a_{14}", + "4994dce06e8f96bb.png": "\\frac{2m-\\mu}{\\mu}", + "499df2ffd0eeab3a.png": "\\dot{Q}(t)", + "499fa1ac984269e7.png": "F(t,(t,y))=t^{3}-y", + "49a35435304cb3d6.png": "0-(-1)=1", + "49c331de0e7fb5f9.png": "[,)", + "49c961f7d758c8b4.png": "\\frac{v_{l}}{v_{a}}=\\frac{v_{l}}{v_{i}}\\frac{v_{i}}{v_{a}}", + "49d53ae85310b020.png": "C^{\\infty}(R^{n},R^{m})", + "49e381de7f284050.png": "C=[\\begin{matrix}0&A\\\\ A^{t}&0\\end{matrix}]", + "49e9b646c9fb7088.png": "\\frac{1}{a}+\\frac{1}{b}+\\frac{1}{c}<\\frac{s}{T}", + "49fd365e98f6896e.png": "\\omega\\times v=\\dot{Q}Q^{-1}v", + "49fff358a1a5ea2b.png": "1^{5/4}", + "4a08a2468cc206f7.png": "(O_{X})_{p}", + "4a19d0eae02bdb72.png": "\\frac{480}{0.9}=533.3\\approx534", + "4a220010b39c17f8.png": "\\sigma_{kl}\\equiv\\frac{i}{2}[\\gamma_{k},\\gamma_{l}]", + "4a25c92b3229c5f4.png": "n(\\frac{m-1}{m})^{n-1}", + "4a27036517e3e83f.png": "F_{snake}(\\overline{v}_{i})", + "4a2ba5710af87f73.png": "d^{n}y=f^{(n)}(x)(dx)^{n}", + "4a328717aee4d9e2.png": "\\pi_{X_{4}}-1", + "4a376b1ae0ca5003.png": "K=n_{;a}^{a}=2/r_{0}", + "4a3f7c335e2aeb2a.png": "y\\sim(\\nu t)^{1/2}", + "4a5a27900d7bc5f4.png": "f(y)=2+2y+y^{2}", + "4a68ad285dcbd0bd.png": "sin^{2}(x)=sin(sinx)", + "4a6dd175b1bb69b1.png": "-1^{n}", + "4a73348375a30766.png": "d_{e}(n_{e})=\\frac{c_{e}}{n_{e}}", + "4a8029f4e4ee49b2.png": "\\overline{i}\\equiv I=q\\mu n_{q}EA", + "4a83343230e34553.png": "\\sum_{\\{i|e_{j}\\in S_{i}\\}}x_{i}\\ge1", + "4a84acb39bdee2bd.png": "f=x^{2}-y^{2}-1", + "4a872ab19f19f78a.png": "\\frac{d^{2}\\psi}{dz^{2}}=\\kappa^{2}\\psi", + "4a8b36e15d23f340.png": "v^{\\rho}:=(\\dot{\\gamma})^{\\rho}", + "4a8e214919455956.png": "cos(2\\pi\\cdot F_{bfo}\\cdot t)", + "4a92809ab24497a2.png": "3V=kba(\\frac{Tn}{P})", + "4a945e0baf897925.png": "U\\subset R^{2}\\times R_{+}", + "4a97d8d9be7ef7e1.png": "\\sum_{k=1}^{n}\\frac{1}{k}-ln(n)", + "4aa0613638f4d10b.png": "\\psi_{0}\\rightarrow\\psi_{1}...\\psi_{m}", + "4aa07ca3fd0fc4cf.png": "x=(bg-cf)", + "4aa5968a47c3c0ac.png": "\\int_{0}^{\\pi}x^{n}sin(x)dx", + "4aa72e8b6f23a721.png": "V(+\\infty)", + "4ac3471d0efd837a.png": "(x^{2}+y^{2})^{2}=ax^{2}y", + "4ad01f218482faac.png": "\\frac{1}{a_{11}}[\\begin{matrix}a_{21}&-\\Delta[a]\\\\ 1&a_{12}\\end{matrix}]", + "4ad1791c3ac4e823.png": "a_{1}\\frac{r^{n}-1}{r-1}", + "4ad57d7b3b5540a1.png": "Z_{bus}={Y_{bus}}^{-1}", + "4ad6fdefa81234ac.png": "c\\ge12]", + "4ae0b6047792b53e.png": "[d,r_{o}d,\\delta]", + "4aeb55bb03bc400e.png": "f(x)+\\frac{h(x)^{2}}{4}", + "4af3454a8c8f711e.png": "\\begin{matrix}2&2&4\\\\ 3&5\\end{matrix}", + "4afd2b13ca51b1e7.png": "v_{p}=E/p=c^{2}/v", + "4b02c13d1402a342.png": "A\\cap B=\\overline{\\overline{A}\\cup\\overline{B}}", + "4b0de7f9b7d3926d.png": "E=\\frac{-\\mu^{2}}{2}", + "4b28c9c924a7dd9e.png": "A_{0}\\bigcap A_{1}=\\{2\\}\\ni2", + "4b2e924afae0b356.png": "\\vec{e}_{0}=\\sqrt{2}\\omega\\partial_{t}", + "4b39602b0c40b635.png": "R(\\theta,\\delta^{*})\\le R(\\theta,\\delta)", + "4b3c89ea6bd3c2a3.png": "\\sum_{i=1}^{20}i=210", + "4b4356bc9f512e0b.png": "\\{F_{i};i\\in I\\}", + "4b4721e82fb87b50.png": "\\frac{d^{2}y}{dx^{2}}=f(x,y)", + "4b4d6f1157464ba7.png": "\\forall n\\in N,|n|_{*}\\le1", + "4b5364e764d3aaf9.png": "\\exists x,\\exists s,(x^{2}=4", + "4b63ff781047749d.png": "q=q(0)+j\\frac{p(0)}{\\omega L}", + "4b6ab33cadd0e609.png": "e_{\\alpha}=-ln(\\alpha)", + "4b731187d5e9bf73.png": "k=\\pm4,\\pm2,-1", + "4b77a523d1dba4b1.png": "\\int_{0}^{\\infty}f_{k}e^{-x}dx", + "4b7aa4879d863a71.png": "[F_{k}:F]=k", + "4b7c18a99dd34048.png": "K_{z}*K_{z^{\\prime}}=K_{z+z^{\\prime}}", + "4b84a3d88102fcdf.png": "2^{n}\\le(\\begin{matrix}2n\\\\ n\\end{matrix})", + "4b8a35c11b66f030.png": "n_{i}^{\\prime}=\\sum_{j}w_{ij}n_{j}", + "4b9412378f7b6c2c.png": "\\overline{\\psi}(x,t)=[\\psi(x,t)]^{\\dagger}", + "4b9b822acfa16697.png": "\\frac{A*B}{B+C}+D", + "4ba51d2df73ba398.png": "(E_{2+})-(E_{2-})", + "4bb2331fcc0bf2a7.png": "\\frac{v_{i}(x)}{v_{j}(x)}\\ge\\frac{w_{i}}{w_{j}}", + "4bb2428df9f1591d.png": "\\gamma_{\\tau}(t)=\\gamma(\\tau+t)", + "4bb4950edf8454e3.png": "\\frac{1}{g_{11}}[\\begin{matrix}1&-g_{12}\\\\ g_{21}&\\Delta[g]\\end{matrix}]", + "4bc6970334e665c7.png": "B_{\\lambda^{j}}(x_{0})\\cap\\Omega^{c}", + "4bd2756128b355b5.png": "(it)^{r}\\psi(t)", + "4bd41ed344100b2d.png": "(\\begin{matrix}101\\end{matrix})(\\begin{matrix}42\\end{matrix})(\\begin{matrix}361\\end{matrix})", + "4bfab5fea89c4189.png": "\\frac{PV}{T}=\\sqrt{k_{P}k_{V}k_{T}}", + "4bfcf7146f472cf2.png": "\\pi r(r+\\sqrt{r^{2}+h^{2}})", + "4c0882bd2643a87c.png": "\\approx\\int_{\\partial N}f^{\\mu}ds_{\\mu}", + "4c22df26854d1660.png": "R=|Z|cos\\theta", + "4c24662eb81626ce.png": "(ax^{2}+2bxy+cy^{2}", + "4c2b2d9e5e5acd04.png": "\\pm z_{1}^{c_{1}}...z_{n}^{c_{n}}", + "4c39892d0ae32a19.png": "X^{i}Y^{n-i},0\\le i\\le n", + "4c462b6f79a7c504.png": "\\alpha_{i}\\rightarrow\\alpha_{i}e^{-i\\omega t}", + "4c4fc5a2c2715ee1.png": "K_{i}=\\frac{n-i+1}{i}K", + "4c5684b284f5663f.png": "y=e^{lnx+\\frac{1}{2}x^{2}-\\frac{1}{2}}", + "4c614ce1427e6ac2.png": "\\hat{\\Omega}_{OLS}", + "4c643cb06984cb14.png": "r_{Q}^{2}=\\frac{Q^{2}G}{4\\pi\\epsilon_{0}c^{4}}", + "4c7481f3ed441e06.png": "**", + "4c7680151b17f37b.png": "(A^{-1})_{ji}=|A|_{ij}^{-1}", + "4c76a3afac1cf940.png": "\\overline{v}=\\frac{\\overline{q}}{\\overline{k}}", + "4c79d96d6fcf2e30.png": "M_{v}=U_{1}\\Sigma V^{*}", + "4c804fc339cc88d8.png": "(\\rho=1000\\frac{kg}{m^{3}})", + "4c8f1a47442916f0.png": "\\frac{q^{k}}{k^{2}}\\rightarrow0", + "4c92016b10cdbb05.png": "F_{X/S}=(F_{X},1_{S})", + "4c971c403ce56111.png": "(14-x)\\times4", + "4c990cc9c0c5574a.png": "\\dot{q}_{2}=\\frac{R-r}{r}\\dot{q}_{1}", + "4c99985a909134db.png": "-\\frac{50}{\\sqrt{\\pi N}}\\approx log(P)\\approx P-1", + "4ca0386b7c760729.png": "y=x(n^{x}-1)", + "4caac15d44ecdf91.png": "x\\in[0.5,1]", + "4cab5cf85f6868f2.png": "x(t+t_{0})=x(t)", + "4cac2c44c2b165b7.png": "B_{k_{1}}^{\\alpha_{1}}\\cap...\\cap B_{k_{r}}^{\\alpha_{r}}", + "4cb41a9fe4b6ac54.png": "lim_{\\theta\\rightarrow0}\\frac{1-cos\\theta}{\\theta}=0", + "4cbb69a329776a7b.png": "\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}-\\frac{z^{2}}{c^{2}}=0", + "4cbc882b25f2e91e.png": "\\phi(g_{j})^{-1}", + "4cbde527b21e6141.png": "\\{F_{i};i\\in I\\}", + "4cbf1f5b46c3d5fd.png": "y:[x_{0},x_{1}]\\rightarrow V", + "4cc07ced343c1a48.png": "|\\tau|=-mglsin\\theta", + "4cc4083e780f4d2e.png": "Y_{t}=f(t)+e_{t}", + "4cd6813f8e4b8455.png": "\\frac{-G*M}{r^{2}}", + "4cd8065aad4db780.png": "P=(T_{1}-T_{2})v", + "4cd86cc1f6d7fa2f.png": "n^{\\prime}\\ge sn^{\\frac{s-1}{s}}", + "4ce86c06acdfe6f9.png": "A\\cong k[[x_{1},...,x_{d}]]", + "4d06c51da948904a.png": "\\prod_{n=1}^{\\infty}(1-\\frac{p}{p^{3}-1})", + "4d0e5d1a9af060b7.png": "\\frac{ds}{dy}=T_{0}\\frac{\\sqrt{2g}}{\\pi}\\frac{1}{\\sqrt{y}}", + "4d1192b42c43e5a5.png": "(E,\\vec{p}c)", + "4d1f8f99b9972d77.png": "y^{3}+y^{2}=\\frac{ca^{2}}{b^{3}}", + "4d4d814de20835ab.png": "Z_{\\epsilon}=\\frac{1}{\\dot{\\epsilon}\\epsilon_{0}}\\frac{l}{S}", + "4d4fe02fcd4cebe9.png": "\\psi=(\\begin{matrix}\\psi_{L}\\\\ \\psi_{R}\\end{matrix})", + "4d5cb73879766a6d.png": "\\pi_{j}=\\sum_{i\\in S}\\pi_{i}p_{ij}", + "4d685f360ea38c23.png": "2^{2^{n}-n-1}\\prod_{k=2}^{n}k^{(\\begin{matrix}n\\\\ k\\end{matrix})}", + "4d6b1cd993ac7ee5.png": "Q\\otimes_{Z}G=0", + "4d792e9565336844.png": "\\sum_{j=1}^{n}x_{i,m+j}=b_{m+j}", + "4d7f646816dc3d89.png": "f_{d}\\approx2v\\frac{f_{t}}{c^{\\prime}}", + "4d8a9a5d7fb48496.png": "\\frac{\\partial u}{\\partial\\tau}=\\frac{1}{2}\\sigma^{2}\\frac{\\partial^{2}u}{\\partial x^{2}}", + "4d8b7434694f5172.png": "4arctan\\frac{1}{5}-\\frac{\\pi}{4}", + "4d928a1e3226e323.png": "\\lambda_{1}=\\frac{3+\\sqrt{5}}{2}>1", + "4d9c7af57aa69776.png": "(\\alpha+1)\\frac{\\sigma_{0}}{E}=0.002", + "4db0805fd8764ff9.png": "S_{ijk}\\rightarrow S_{ij}(\\omega_{k})", + "4db8e5992ace49af.png": "t_{ik}=\\sum_{j}c_{ij}c_{jk}", + "4dbdb7d31133342c.png": "\\{F_{i},F_{j}\\}=s_{ij}\\circ F", + "4dc03ae41371f1cf.png": "00:X(t)<0\\}", + "5063380efcde89ce.png": "Z/l\\times Z/l", + "50712cdf9220189f.png": "N!/(6!(N-6)!)", + "5076e89ffd6b6ac6.png": "(\\frac{\\partial}{\\partial x^{1}},\\cdot\\cdot\\cdot,\\frac{\\partial}{\\partial x^{n}})", + "507d115984270582.png": "g(", + "507fbec2c9c25874.png": "F_{1}(x)=-x", + "509021ab8559f1df.png": "1-(0.95)^{2}=0.097", + "509124c1525e30c1.png": "q=q(0)+j\\frac{p(0)}{\\omega L}", + "5095b47707af1fac.png": "\\frac{2a}{2b},b\\le d", + "5095ef84257120f8.png": "F_{q^{k}}^{*}", + "509b4fe0e73f8e81.png": "F_{c}=Mv^{2}/R", + "50a1559488608034.png": "H=(\\begin{matrix}1&-1\\\\ -1&1\\end{matrix})", + "50ad31d3913139d9.png": "(\\begin{matrix}21\\end{matrix})(\\begin{matrix}21\\end{matrix})(\\begin{matrix}32\\end{matrix})", + "50aea53c706c7cc2.png": "\\hat{H}=\\hat{H}_{0}+\\lambda\\hat{V}", + "50c0104099d86562.png": "|\\begin{matrix}A&B/2\\\\ B/2&C\\end{matrix}|", + "50e280ad7593b59d.png": "h_{lm}^{(1)}(kr)", + "50fdb34557cbade7.png": "S=\\{\\rho_{i}\\}_{i=1}^{n}\\in\\tilde{H}_{S}", + "510324358cee91b8.png": "(dy,-dx)=\\hat{n}ds", + "510a369b7a9ff923.png": "E=\\frac{2.21}{r_{s}^{2}}-\\frac{0.916}{r_{s}}", + "510f9daaeb6ceb22.png": "e_{\\lambda}(f_{ij})=\\frac{f_{ij}}{\\lambda}\\frac{\\partial\\lambda}{\\partial f_{ij}}", + "511bc4747bc12fa3.png": "\\forall ij\\mu_{ij}\\in\\{0,1\\}", + "51203f11606aae03.png": "H=p_{a}^{i}\\partial_{i}y^{a}-L", + "512de584407e7661.png": "x=5+\\frac{14}{x}", + "514a43bd70334313.png": "p_{1}/\\pi_{1}40.74", + "5186b85e450a8e82.png": "S_{1}=S_{1}^{\\prime\\prime}", + "51993e8e493d2416.png": "\\frac{1}{(1-t)^{\\chi(X)}}", + "519af1c4197b8982.png": "SK^{n}=(K^{*})^{n}S.", + "519c4cf678b6a4f4.png": "C(n-1,k)", + "51a83d58727d5859.png": "\\frac{dy}{dt}=-0.1(y-70)", + "51b7aa9633cb67de.png": "b(\\theta)=-ln(-\\theta)", + "51baa0f44131fe26.png": "j(j+1)\\hbar^{2}", + "51c5d37971b46e86.png": "1,2,...n", + "51c706b056e40c67.png": "\\alpha=\\alpha(n)\\in(0,1)", + "51cda5e4e1745978.png": "\\partial_{v}f(x)=Df(x)v", + "51cfbe05aeb59de1.png": "Hom(X,-)", + "51ee2a4d113b9fcb.png": "\\dot{\\tilde{\\gamma}}(t)", + "5205dc951b0006e2.png": "n>log_{|z|}(\\epsilon)", + "52080e147261a5ee.png": "y_{t+1}=\\alpha-\\frac{\\beta}{y_{t}}", + "5208b02026731bfa.png": "k_{t}:id_{D}\\sim k_{1}", + "520a70abfbdef49d.png": "k_{i}-\\hat{k}=0", + "520d2387c7c07919.png": "\\int_{-\\infty}^{-1}\\frac{sin(\\pi x)}{\\pi x}dx", + "52102641b0298441.png": "0,(n-1)", + "5218d0820fc67e29.png": "1-4\\pi r^{3}/3V", + "5221d8881ec81954.png": "(1-\\delta(l", + "5222e65a1a75182d.png": "E[(X-E(X))^{2}]", + "52272b192f957d52.png": "F(x,y,z)-1.1=0", + "522877dddad3a1de.png": "\\sqrt{2}W+X", + "522b2e3d5b4f2b14.png": "a(\\rho,p)\\equiv\\sqrt{\\frac{\\partial p}{\\partial\\rho}}", + "523ef7a043a8c4b3.png": "ee=|F_{+}-F_{-}|", + "524358f8e15130ad.png": "(\\mu_{ab}^{*}(t))", + "524792017ecd3237.png": "[F_{k}:F]=k", + "52554326a85e94f0.png": "\\sum_{k=0}^{m}(\\begin{matrix}m\\\\ k\\end{matrix})(\\begin{matrix}n\\\\ r+k\\end{matrix})", + "5261daa6e5bf0796.png": "\\sigma:=-m^{b}m^{a}\\nabla_{a}l_{b}", + "526a5f3626271dcd.png": "\\Sigma=\\prod_{i\\in N}\\Sigma^{i}", + "527a93adbb05cfe8.png": "V=\\sqrt{2.67x}", + "52874e8630e74c26.png": "i_{*}i^{-1}G", + "52882de94428d6ca.png": "(-1)^{2}=1", + "528df69464e12113.png": "M:=\\bigcap_{n\\in N}M_{n}", + "528fccc6189085c7.png": "tr^{2}H>4", + "529520d65e35279d.png": "B=b-\\frac{a}{RT}", + "5295fa8e95ce6747.png": "A\\mapsto\\frac{1}{n}tr(A)\\cdot I", + "5299f7af7714622f.png": "(x-a)^{2}H(x-a)", + "52a1673c599b58a8.png": "f(x)=(x,x,x,\\cdot\\cdot\\cdot)", + "52a45d864cf8401e.png": "V_{t}=a_{0}\\cdot M\\sqrt{\\frac{T}{T_{0}}}", + "52b4508b24125849.png": "e^{\\pi\\sqrt{163}}", + "52c36b17440da205.png": "K_{1}\\frac{q}{2}", + "536b2837fe31df73.png": "\\sigma(X^{*},\\hat{X})", + "536ca615174588bc.png": "=A\\cap(A\\cup A^{C})", + "53a66730a39fdb9f.png": "\\overline{\\Psi_{0}}=\\sqrt{\\frac{m}{\\pi}}e", + "53a7f46bfb4ad53e.png": "<1", + "53b50f2014480731.png": "(\\delta^{k}F)(0)", + "53cdf23bebeb8a1c.png": "(uv)/2=q/4", + "53d2515be5167ef4.png": "P=[I|0]", + "53f09cbbf56d796c.png": "(x-a)^{2}H(x-a)", + "53fdc77a398fb315.png": "c_{t}=y_{t}+(1+r)b_{t}", + "5401968c0d9ebacb.png": "g(y)=y-\\overline{y}", + "540e190aac2b5113.png": "2^{112}(=2^{2*56})", + "540e5eafb0bf1dcd.png": "\\frac{2}{3}-\\frac{1}{2}=\\frac{4}{6}-\\frac{3}{6}=\\frac{1}{6}", + "540e828df5a38bc7.png": "\\Gamma(\\frac{1}{4})/\\pi^{1/4}", + "541676cb1d9e7349.png": "\\vec{F}=q(\\vec{B}\\times\\vec{v})", + "541818f2caaeacc2.png": "K=n_{;\\alpha}^{\\alpha}=2/r_{0}", + "54186eea4bcba8e2.png": "P_{t,t^{\\prime}}(x|x^{\\prime})", + "5419e9c44a73d015.png": "A=\\frac{\\partial v}{\\partial x}+\\frac{\\partial u}{\\partial y}", + "54218c0b341eec47.png": "\\Psi_{L}=\\overline{\\Psi}^{\\dagger}P_{3}", + "542246fc6bdb5019.png": "\\phi_{U}=-V_{\\infty}\\cdot n", + "542393c68fc2d32b.png": "B_{n}+C_{n}=B_{n+1}", + "5430050ec6b6c684.png": "I\\Delta_{0}+exp", + "54395c91b9210608.png": "v=\\{\\begin{matrix}1\\\\ -1\\end{matrix}\\}", + "5443c06ab3166c11.png": "d_{k-1}1", + "5ba2aa960116af3f.png": "a(x-x_{0})^{2}+y_{0}", + "5ba348b13d865219.png": "M_{x}=\\frac{u_{x}}{a_{x}}=\\frac{W}{a_{1}}", + "5bb0f4da40d7ad2c.png": "Be=\\frac{\\Delta PL^{2}}{\\rho\\delta^{2}}", + "5bb79d9254058d74.png": "10.2", + "5bbed317701d8c85.png": "C_{P}=\\frac{4}{27}C_{D}", + "5bc207ecc3fd136c.png": "q=q(0)+j\\frac{p(0)}{\\omega L}", + "5bcd5a1049b89dd5.png": "T^{4}-T_{s}^{4}\\approx u^{4}", + "5bd14b4cd5e6b575.png": "|\\prod(x-x_{i})|", + "5bdb2579c67db238.png": "H_{\\omega+1}(1)-1", + "5bdb3507cd92de64.png": "Z_{i,j}Z_{k,l}=Z_{i,l}Z_{k,j}", + "5be6f1fb944ca1c4.png": "j(j+1)\\hbar^{2}", + "5bee0ed5be6af037.png": "1-\\frac{x}{2}+\\frac{3x^{2}}{8}-\\frac{5x^{3}}{16}", + "5bf1228d2ab1b160.png": "J:V\\rightarrow\\overline{R}", + "5bf27aaecf12f252.png": "\\overline{16}", + "5bf49a5bb2cc91be.png": "\\varphi(r)=\\frac{sin(lr)}{lsinhr}", + "5bff826a64627d6b.png": "E[2n]\\backslash E[2]", + "5c15fb2e50ab9683.png": "K_{1}=K_{1}^{\\prime}\\cap K_{1}^{\\prime\\prime}", + "5c1f1c571e58fdf6.png": "I^{+}(S)\\cap T", + "5c25a22451cde96d.png": "P_{k|k-1}", + "5c353aa9389fd02d.png": "2=10^{0.301}", + "5c47cdabdcb318d7.png": "(q_{t}^{i}-\\Gamma^{i})\\partial_{i}", + "5c49b7042557de71.png": "U_{2n}=\\frac{2U_{n}u_{n}}{U_{n}+u_{n}}", + "5c4ab18d2ff6a034.png": "\\Delta F=T^{(n)}\\Delta S", + "5c4adb72da1797be.png": "\\pm z_{1}^{c_{1}}...z_{n}^{c_{n}}", + "5c4d39b703b99d15.png": "R=\\frac{1}{2\\sum is_{i}-1}", + "5c51adcb91c925ff.png": "\\varphi\\rightarrow\\frac{-\\nabla f}{|\\nabla f|}", + "5c5918f641ad4f51.png": "H_{cr}/H_{c}", + "5c63c8f550f3209c.png": "exp(-t^{1/\\theta})", + "5c644e396cb44081.png": "\\sqrt{a}\\cdot\\sqrt{b}=\\sqrt{a\\cdot b}", + "5c705606e915e610.png": "\\{C(a,b),c,d,e\\}", + "5c7bae392ebeab40.png": "P_{t}=100E_{t}/Y_{t}", + "5c7d2f804ce9e291.png": "\\kappa_{2}=\\mu_{2}^{\\prime}-{\\mu_{1}^{\\prime}}^{2}", + "5c92b1c71da86ff1.png": "\\frac{1}{2}+i\\frac{2\\pi n}{logn}", + "5c9d3b7867ac0854.png": "\\delta_{M,D}", + "5ca3c8ef1b78dcd6.png": "A(c)=-\\frac{u^{\\prime\\prime}(c)}{u^{\\prime}(c)}", + "5cc14ee691e182d0.png": "j\\mapsto(\\begin{matrix}-1&1\\\\ 1&1\\end{matrix})", + "5cc42545bc47fffd.png": "lim_{n\\rightarrow\\infty}|x_{n}-x|_{X}=0", + "5ccf4a18f25d17f4.png": "z_{n+1}=z_{n}^{2}", + "5cd24ccf0feb4638.png": "\\mu_{ij}=a_{i}a_{j}a_{i}...", + "5cda322d7c94d158.png": "\\frac{PV}{T}=\\sqrt{k_{P}k_{V}k_{T}}", + "5ce58fdb81839444.png": "\\delta\\omega=(\\omega_{+}-\\omega_{-})", + "5cfdf2c3b3a55dce.png": "r_{max}=\\frac{n_{0}+1}{2n_{0}}", + "5d009230f7d02890.png": "X=|X|e^{jarg(X)}", + "5d05d62a75e67b97.png": "f^{(m^{*}+1)}(b)=0", + "5d06f6547c32f08d.png": "(\\frac{\\partial H}{\\partial t}\\equiv0)", + "5d0d80669c4b5b3c.png": "\\lceil|k|/n\\rceil", + "5d18e12b7b15fc31.png": "y=x(n^{x}-1)", + "5d1b4dfb856263bb.png": "x^{2}-\\sqrt{x}=13", + "5d2d7845288b25d8.png": "CO=\\frac{VO_{2}}{C_{a}-C_{v}}", + "5d3492fdc5c1ff58.png": "M_{n}=M(i\\alpha)^{n}", + "5d3604436be57bb4.png": "\\delta g_{F}=\\frac{2g}{R}\\times h", + "5d3afef6f6bc1a1a.png": "f=a+bx+cp", + "5d3beefcdec477ed.png": "C=\\frac{8L^{3}}{E^{*}wt^{3}}", + "5d40f39a25aa2c8c.png": "X^{t=n+1}", + "5d4694e35e4ebad4.png": "ac", + "5d48acc4aff5296f.png": "P/A=\\sigma T^{4}", + "5d510c34b3ed1a8a.png": "x_{k+1}=x_{k}+\\frac{1}{m}", + "5d515540272b5dde.png": "M_{200}=M(3^{r}-r", + "5d832c366d517cd0.png": "D=\\sum_{j=1}^{n}e_{j}\\frac{\\partial}{\\partial x_{j}}", + "5d85d86027818186.png": "A=\\int\\lambda dE_{A}(\\lambda)", + "5d8819a4587dbe24.png": "t\\longrightarrow F(t,t_{0},x)", + "5d89a6386a8c4f41.png": "p(\\tilde{x}=1)=\\frac{\\alpha^{\\prime}}{\\alpha^{\\prime}+\\beta^{\\prime}}", + "5d89ae07b808d0f4.png": "\\mu_{2}=\\frac{4-\\pi}{2}\\sigma^{2}", + "5d8c140788c72331.png": "a-(+\\infty)", + "5da61ac5e006d34e.png": "d=0,1,2,...,2^{w}-1", + "5dac3477926d5d0c.png": "C_{\\beta}(s)=[\\begin{matrix}1&0\\\\ s&1\\end{matrix}]", + "5dafa629bd0a3c00.png": "G|_{R^{n}}=\\sum_{j=1}^{n-1}e_{j}R_{j}", + "5db079504fdd8acb.png": "(X,Y)=TrXY^{T}", + "5db3e85407360681.png": "1\\cdot a=a\\cdot1=a", + "5dc15fcb26d0e192.png": "10^{30}a^{2+2}", + "5dc96a86a6b19ea9.png": "U_{mn}T_{m}", + "5dca9e145f750c90.png": "(\\frac{ML^{2}}{T^{3}})", + "5dd4ba6dd548070c.png": "M(n,t)\\le B_{n-2t-1}", + "5de20bb4b8742171.png": "\\frac{2m-\\mu}{\\mu}", + "5df78071fdd9ce3a.png": "\\{L(u,v):u,v\\in X\\}", + "5e03c7c55ea53a17.png": "p_{n-1}(x_{i})", + "5e077c7669a2e3e0.png": "\\delta(\\alpha x)=\\frac{\\delta(x)}{|\\alpha|}", + "5e18674a7100f103.png": "-2\\le S_{CHSH}\\le2", + "5e237c70a13cc92e.png": "f=z\\sqrt{x^{2}+y^{2}}", + "5e243f43f21c9a56.png": "G=\\langle X|r^{n}\\rangle", + "5e2fc7863ae43982.png": "\\sum_{\\gamma\\in\\Gamma}n_{\\gamma}t^{\\gamma}", + "5e3226b8c5b5339d.png": "|f_{i}(x)-f_{i}(y)|<\\epsilon", + "5e3606ac6ed86bff.png": "\\lambda(G)=max_{|\\lambda_{i}|", + "5e52398631c20af1.png": "I(V+ksin(\\omega t))", + "5e536c8100d8479f.png": "\\sum_{i=1}^{n}iP_{i}=\\sum_{i=1}^{n}Q_{i}", + "5e5c9e5457b59a1e.png": "\\sum_{x}a=ax+C", + "5e77d1483b2d2429.png": "x=\\sum_{i=1}^{K}w_{i}P_{i}s_{i}", + "5e7a8fc3494612f1.png": "n,m=1,...,l_{\\mu}", + "5e861f914acf1dd9.png": "\\zeta(s)=\\prod_{p\\in P}\\frac{1}{1-p^{-s}}", + "5e88d30df6654f5f.png": "SL_{2}(R)\\\\ SL_{2}(Z)", + "5e8d2c9a56828a31.png": "\\frac{dV_{-}}{dt}=0", + "5e91c3fb6b6957f2.png": "E[2n]\\backslash E[2]", + "5eb910a8aee7bfbc.png": "a|c.)", + "5ebb8c94cc70828a.png": "\\mu_{ij}=a_{i}a_{j}a_{i}...", + "5ec1c2cd1a8ebe09.png": "l(U\\vec{v})=l(\\vec{v})", + "5ec52a5a1b67d69c.png": "\\{\\vec{x}:\\vec{y}\\}", + "5ed988bf446e7271.png": "N=\\frac{V_{s}\\times c\\times r_{s}}{n_{r}}", + "5ee5f00d11905e5a.png": "ds^{2}=\\lambda^{2}(z,\\overline{z})dzd\\overline{z}", + "5eea46a46c95fdcb.png": "0=P_{4}=P_{5}", + "5ef4db12df0cebea.png": "\\sum x*a^{i}=\\frac{x}{1-a}", + "5ef6e5cb6396aa07.png": "B\\subset P^{1}(k)", + "5ef75185958ad31e.png": "P=K\\rho^{1+\\frac{1}{n}}", + "5ef8814649e989ee.png": "A(t)=e^{W\\cdot t}A(0)", + "5f1f8926336b74b7.png": "\\Delta_{S^{n-1}}^{-1}", + "5f2081e79262c967.png": "\\dot{x}_{k}=h_{k}+g_{kl}\\xi_{l}", + "5f22826da1e581a2.png": "(\\prod_{i=1}^{n}(x-x_{i}))p(x)", + "5f24cc168af67b7e.png": "\\{a^{n}b^{n}|n\\ge1\\}", + "5f2d5025a66ade3f.png": "D(X)>0", + "5f4739040e73a24a.png": "X^{I}\\rightarrow X,\\chi\\mapsto\\chi(0)", + "5f4f81c2037f3487.png": "3^{(F_{n}-1)/2}", + "5f51ae4399177bc1.png": "P^{x}\\{\\tau<\\infty\\}", + "5f51f3a6f6140e3c.png": "2\\pi^{2}k\\delta(x)\\delta(y)\\hat{z}", + "5f5670fda53cfde8.png": "I(S;\\Omega-S)", + "5f59b5faf8286063.png": "v\\in R^{2^{n}-1}", + "5f5c4b1f7edd69f0.png": "\\sum f(T,c)=1", + "5f5db913047b4083.png": "y^{2}-x^{2}(a^{2}-x^{2})", + "5f715b8a113711e8.png": "\\frac{12}{5}\\pi a^{2}", + "5f787452f6fb45b3.png": "(CH_{3})_{2}C", + "5f7fb3d58ddc9423.png": "\\frac{q}{2}\\int_{-\\infty}^{\\infty}\\frac{z^{q-1}}{1+z^{p}}dz", + "5f833147566f1de9.png": "a=(\\alpha p_{0i})_{i=1}^{J}", + "5f83f74d3483bbaa.png": "\\frac{\\rho^{4}}{\\lambda^{4}}\\ll8\\frac{z^{3}}{\\lambda^{3}}", + "5f86d392aae35f52.png": "ax^{2}+by^{2}+c", + "5f8b24858d72f5bf.png": "O(V^{3}/2^{\\Omega(logn)^{1/2}})", + "5f9108950b15a655.png": "C\\rightarrow(B)_{k}^{A}", + "5fa8576909a629e0.png": "E_{t}u^{\\prime}(c_{t+1})=u^{\\prime}(c_{t})", + "5fadc78af7cc387b.png": "y^{2}=x^{3}-n^{2}x", + "5fb8bf5b8b812c12.png": "f(z_{0}(1+i\\epsilon))", + "5fbfb3784963095f.png": "t_{1}=X^{c}g_{1}^{s_{1}}g_{2}^{s_{2}}", + "5fc1006b8640baaa.png": "D_{\\mu}J^{\\mu}=0", + "5fc1a94047fbd3ac.png": "\\frac{R^{2}}{2}(\\theta-sin\\theta)", + "5fc5f22e048ba0d2.png": "f=a+bx+cp", + "5fcb0c562e0e89e7.png": "2^{k}2^{H(p+\\epsilon)n}\\ge2^{n}", + "5fddbc8e66040c87.png": "Z_{i,j}Z_{k,l}=Z_{i,l}Z_{k,j}", + "5fe14deda38619db.png": "\\overline{\\psi}D_{\\mu}\\psi", + "5fe292fe98d15547.png": "V=\\sqrt{-\\frac{R}{\\rho}\\frac{\\partial p}{\\partial n}}", + "5fe2c61dceb4d99d.png": "\\langle z\\rangle=e^{i\\mu-\\gamma}", + "5fe55806eeb77050.png": "\\Pi=-\\tau_{ij}^{r}\\overline{S_{ij}}", + "5fe89d3e36e5fadc.png": "t_{ik}=\\sum_{j}c_{ij}c_{jk}", + "5ff1d5a35f75920e.png": "S_{1}=V_{0}sin(\\omega t)", + "5ffa0abd2d08915e.png": "X_{>\\epsilon}:=\\mu^{-1}((\\epsilon,\\infty))", + "600aab93cfd23e48.png": "\\psi\\le\\frac{3}{\\sqrt{3}+1}", + "60190d6462802698.png": "V_{i}(X_{i})\\ge1/n", + "601a1ffac4fb1a80.png": "I\\subseteq\\bigcup_{id_{c}", + "605d4f66ac4124fc.png": "\\Delta U_{system}=Q", + "6061ed8431792377.png": "y:[x_{0},x_{1}]\\rightarrow V", + "60638f6374620406.png": "P(t)=\\frac{1}{1+e^{-t}}", + "60667a93dda92e2a.png": "\\overline{\\pi}:M(A)\\rightarrow M(B)", + "607518b96d1c799f.png": "t^{\\prime}=\\gamma(1-av)t", + "6077832d61005260.png": "d,d_{0}>d_{c}", + "607bede34d7beff6.png": "F\\hat{z}", + "60811b0ff3cda2d7.png": "|sinx|\\le|x|", + "608c9a6b6b1025c1.png": "|\\mu|(X\\backslash K_{\\epsilon})<\\epsilon", + "609362ffa2eb5fe7.png": "det\\varphi_{w}^{\\prime}(0)=-1", + "60a81aa26dc0ea35.png": "\\frac{dy}{dx}=\\frac{1}{5y^{4}-1}", + "60acb1f51b14bd9b.png": "t^{\\prime}\\rightarrow\\tau=t-t^{\\prime}", + "60ba466410f2b6b5.png": "z=a(2e^{it}-e^{2it})", + "60ba7e9136a03c60.png": "(v^{\\alpha})_{\\alpha=0,1,2,3}", + "60bc784dc62c5a2f.png": "y_{b}+\\epsilon=y(b)", + "60bcf869c1457cac.png": "L(r,\\theta,\\dot{s},\\dot{z},\\dot{r},\\dot{\\theta},\\dot{\\phi},t)", + "60c70b02648f97c2.png": "\\frac{1}{14}+\\frac{1}{21}+\\frac{1}{42}=\\frac{1}{7}", + "60c82c686ca61bd7.png": "U=\\hat{c}_{V}nRT", + "60c9554323f5130a.png": "R=(<_{1},...,<_{t})", + "60cb2a7cef8c8241.png": "d=2mn(m^{2}-n^{2})", + "60d691f1152c93d3.png": "const=\\lambda u.x", + "60dd3fcc5767c55f.png": "I(S;\\Omega-S)", + "60de264b9de62bd5.png": "E_{N,M}(Z_{1},...,Z_{M})", + "60f84adcd81536d5.png": "F(t,x(t),\\dot{x}(t))", + "60fbbb318faa6dd5.png": "M/P=L(i,Y)", + "610789ac43335f43.png": "?_{000}", + "610f61b910e6f45e.png": "Ax_{N-1}+Bu_{N-1}", + "612629fbed1e186e.png": "i-j|m", + "61396cbad8af71ca.png": "\\overline{Q}^{day}=0", + "613ab8bfda80df85.png": "GF(p)[x]/f(x)", + "61454d431eda87c2.png": "\\psi(\\psi(0))=\\omega^{\\omega^{2}}", + "61467f52d24bf155.png": "F(d_{1},d_{2},...d_{k},F)", + "61497ffe81823f82.png": "J_{ij},S_{i},S_{j}", + "61574f5c33dc6e98.png": "0^{2}+0^{2}=1", + "6178232b2aa92352.png": "\\lambda u_{g}=u_{g}\\lambda^{g}", + "617bab35240d0c9d.png": "-1^{n}", + "617bdef8ae921a1b.png": "\\sum_{k=1}^{n}k^{m}=nP(n)", + "618367b157f94a8a.png": "E[\\varphi(x)]", + "6185b4f0422540dc.png": "\\int_{0}^{\\infty}f_{k}e^{-x}dx", + "61868f9c11b09284.png": "B=\\frac{\\mu_{0}I_{enc}}{2L}", + "619a0a305af7768f.png": "\\int_{0}^{\\infty}x^{r}f(x)dx", + "619bead17f90ff03.png": "1-4\\pi r^{3}/3V", + "61b16fe4ad6cedd7.png": "\\Delta t=0.1\\Delta x^{2}", + "61bcaa925f10811b.png": "Eq\\alpha\\Rightarrow\\alpha\\rightarrow[\\alpha]\\rightarrow Bool", + "61c950f53477b920.png": "T=[0,\\infty)", + "61caac6b7ef3a8a1.png": "\\langle\\in,...,=\\rangle", + "61ccdfacce793158.png": "L=\\frac{-1}{4\\mu_{0}}F^{ab}F_{ab}", + "61d10a9fcd0ca4ad.png": "Lu=x,x\\in(0,\\pi)", + "61d1799e41b865b0.png": "\\{\\begin{matrix}n\\\\ k\\end{matrix}\\}=S(n,k)", + "61d1cdb0162ddcc5.png": "\\sum_{i=1}^{m}c_{i}x_{i}+\\sum_{j=1}^{n}d_{j}t_{j}", + "61e4938d0442f4f1.png": "i_{Q}^{*}(TE)\\rightarrow Q", + "61e9df32cfe58fda.png": "E[\\varphi(x)]", + "61ea3b14a08b1614.png": "S^{2}=\\sum_{j=1}^{n}X_{j}^{2}", + "61f169c579453412.png": "K_{W}=[H^{+}][OH^{-}]", + "61f29cd25c2dabab.png": "\\int_{0}^{\\infty}f(t)x^{t}dt", + "61fee81a43d0fe02.png": "N=[N_{x},N_{z}]", + "6206c1cd451c7f2b.png": "\\frac{m^{2}-n^{2}}{2mn}", + "6207cc0b0f20c4f2.png": "(\\prod_{i=1}^{n}(x-x_{i}))p(x)", + "62086df322d253b5.png": "[[", + "6209130d394a5cbe.png": "A_{\\infty}=lim_{\\omega\\rightarrow\\infty}A(\\omega)", + "620c08adcae1c7fa.png": "Ae^{0.077\\cdot2}=A1.08^{2}", + "622db979726eefe0.png": "R_{p,q}", + "62308b6f2da3c3f8.png": "G^{\\prime}=(V,E_{L}^{\\prime},s,t)", + "623cd10b1e132615.png": "x_{k+1}=x_{k}+\\frac{1}{m}", + "623ef871f63530cd.png": "\\sigma=(3/2)(\\rho_{s}/\\rho_{a})P", + "6240b5797336d2d2.png": "k=\\omega\\sqrt{LC}=\\frac{\\omega}{u}", + "6240bbeb20d17aec.png": "P_{\\theta}(S(X)\\ge\\gamma)", + "625b85611d44b60f.png": "\\pi r(r+\\sqrt{r^{2}+h^{2}})", + "626cbb2570b88975.png": "d[P]/dt=k_{1}[A][M]", + "627c2c76d8c3f05c.png": "A=(\\begin{matrix}0&1&0\\\\ -1&0&0\\\\ 0&0&1\\end{matrix})", + "6294aa1168264c35.png": "f\\in H^{k-2}(\\Omega)", + "62a50576c0c3567b.png": "\\omega\\mapsto inf_{b\\in K(\\omega)}d(x,b)", + "62ac8fa9679c4b9a.png": "\\Delta z=H(z)\\Delta\\chi", + "62c1bcabbd860d38.png": "nlog_{2}n-\\frac{n}{ln2}", + "62d7a070e4a70744.png": "\\frac{v_{0}^{2}}{gh_{0}}>1", + "62df210445fd8765.png": "\\varphi=\\frac{\\sqrt{5}+1}{2}", + "63015774cde071ed.png": "-|\\dot{p}|^{2}", + "630d01a89fb02bb5.png": "A_{i,j}=1", + "631666da5212ffe6.png": "50\\approx\\sqrt{30\\times77}\\Omega", + "63203ee0dd46016e.png": "V_{p}=0.5Sdln(\\frac{D}{d})", + "6321a7836044d0a6.png": "(G1+G2)/2", + "63308ebe9d9aa005.png": "\\frac{1}{n_{0}}=\\frac{16}{3}\\frac{\\pi ld^{2}}{4}", + "6334763c0a28d095.png": "\\lfloor ln(U)/ln(1-p)\\rfloor", + "633b377874acc294.png": "\\sigma_{ij}=\\frac{\\sigma_{ii}+\\sigma_{jj}}{2}", + "633b432be72a358f.png": "-x_{n}\\le\\cdot\\cdot\\cdot\\le-x_{1}", + "633d3df195581d68.png": "0\\Delta E", + "63f3b700a3a990af.png": "\\overline{T}", + "63fc58c64fdbbc8b.png": "C(x)=\\frac{1}{\\sum_{y}d(y,x)}", + "6408d139b7c69ae4.png": "\\frac{1}{|A|}\\sum_{a\\in A}f(a)", + "6408e4432a857cc9.png": "cos^{-1}(-\\frac{1}{3})", + "6416eb92f79e377b.png": "\\frac{(1-z^{3}/6)}{(z-z^{2}/2)^{2}}+c", + "64189e0e31327506.png": "A_{x}^{(12)}", + "6426470b7b4581f9.png": "\\tilde{p}(x)=n/N", + "643d32927d0d25ba.png": "f=a+bx+cp", + "6445666f60ec2724.png": "\\omega_{\\chi}(x,y)=\\chi([x,y])", + "644b0129aa3f31d6.png": "\\Delta x\\Delta p>h/2", + "644d7111f5aaa43a.png": "[x_{k-1},x_{k+1}]", + "6453e388c8f54231.png": "K_{x}Na_{1-x}Cl", + "646699373b059d4d.png": "X=A^{-1}(I-UY)", + "647116e568771736.png": "Q(a)v=(v\\cdot a)a", + "647ea133bf583ec4.png": "\\frac{1}{S_{1}}+\\frac{1}{S_{2}}=\\frac{1}{f}", + "64872448f3be104f.png": "f(\\zeta)=\\zeta^{-\\frac{1}{N-1}}", + "649c98ae271b444f.png": "\\prod_{i=1}^{s}x_{i}^{\\nu_{i}}=K", + "64a0a6ac29b4aca0.png": "\\omega_{1}(t):=sup_{s\\le t}\\omega(s)", + "64b311be6219498e.png": "p_{i}(q_{i},\\dot{q}_{i},t)=\\frac{\\partial L}{\\partial\\dot{q}_{i}}", + "64b5240d188fdc04.png": "Z_{p^{m}}[x]", + "64bde8ba6664010f.png": "-\\frac{1}{2}\\frac{1}{|\\xi|}-\\gamma\\delta(\\xi)", + "64bfc520ed673b9b.png": "\\overline{x}_{n+1}", + "64d7493b5d70b589.png": "\\omega_{T}=-lim_{\\Delta t\\rightarrow0}\\frac{\\Delta\\theta}{\\Delta t}", + "64d981e0d3378c23.png": "A\\cap B=\\overline{\\overline{A}\\cup\\overline{B}}", + "64df64945653e73b.png": "tr^{2}H>4", + "64ebc5be4ebdb647.png": "c=r_{i}^{2}+r_{j}^{2}+Z_{j}^{2}", + "650053034f12d8fe.png": "m=cos(\\phi)cos(\\lambda)", + "6507a4bfd90e1bfd.png": "\\frac{1}{16\\pi G}\\int d^{2}x\\sqrt{g}R", + "6514dfe7a4538725.png": "\\vec{r}\\rightarrow-\\vec{r}", + "6515559297cc4254.png": "-\\frac{6(n^{2}+1)}{5(n^{2}-1)}", + "6518713125b465a3.png": "E=\\frac{-\\mu^{2}}{2}", + "651adebdc075a06f.png": "G(i\\omega_{n})", + "652c48bb99522d33.png": "\\pm\\frac{1,2}{1,3}", + "6535599272d3f342.png": "p|q^{k}-1", + "653967fdd473838b.png": "M_{p}=(bd^{2}/4)\\sigma_{y}", + "654ae933a316489a.png": "sp_{2n}R", + "6554e8e8f019ffa7.png": "k=\\omega\\sqrt{LC}=\\frac{\\omega}{u}", + "655a762d939f5061.png": "\\overline{\\pi}:M(A)\\rightarrow M(B)", + "656902db2eb6c062.png": "a_{||m}=(a\\cdot m)m^{-1}", + "657f2bef207936ce.png": "I-B^{-1}Z", + "658400c4c8266ba4.png": "|h|^{\\frac{1}{2}}=r_{0}^{2}sin\\theta", + "6592754c6e6ef2a1.png": "2cos\\frac{\\pi}{3}=1", + "65a596b3d82cd6b0.png": "EL(\\Gamma)EL(\\Gamma^{\\prime})=1", + "65aa194ed720a5f0.png": "Z^{+}\\cup\\{0\\}", + "65b5b0a80a9cbdf0.png": "\\frac{n\\hat{\\sigma}^{2}}{\\sigma^{2}}\\sim\\chi_{n-1}^{2}", + "65d07ca909841059.png": "f^{(m^{*}+1)}(b)=0", + "65d70f5b9e2b0fb1.png": "\\hat{H^{\\prime}}=\\hat{T}\\hat{H}\\hat{T}^{-1}=\\hat{H}", + "65de9032829265ca.png": "-\\infty+x=-\\infty", + "65e52a36f6c963b5.png": "x^{\\prime}=\\frac{x-vt}{\\sqrt{1-\\frac{v^{2}}{c^{2}}}}", + "65e826b057ee9c3b.png": "(\\theta_{i})^{2}=0", + "660d9be1ee72e035.png": "xv\\alpha(x)^{-1}\\in V", + "6610c5b3059cb3af.png": "d=e^{-\\sigma\\sqrt{2\\Delta t}}=\\frac{1}{u}", + "661be550fe7b0ad8.png": "m=-\\frac{1}{2}\\pm i\\frac{\\sqrt{3}}{2}", + "6623b476f9b93641.png": "i_{C}=I_{S}exp(\\frac{v_{BE}}{V_{T}})", + "66268b688e140a75.png": "1-4\\pi r^{3}/3V", + "66295b1d6ad5e6f0.png": "|\\frac{cosh(x+iy)}{x+iy}|", + "662a530c78eea3cf.png": "A(c)=-\\frac{u^{\\prime\\prime}(c)}{u^{\\prime}(c)}", + "662f728f5c469f4e.png": "T_{t}=e^{t\\frac{d}{dx}}", + "66301234e693e949.png": "1+ln\\frac{\\sigma}{\\sqrt{2}}+\\frac{\\gamma_{E}}{2}", + "6654fdab3c80a5af.png": "a=p_{1}p_{2}^{k_{2}}...p_{l}^{k_{l}}", + "665d752a3554b6e7.png": "\\hat{A}_{1}=x[0]", + "665d75f166710dc3.png": ".d_{1}d_{2}...d_{n}0111...", + "6664a46a331700f9.png": "ACDA_{si}=\\frac{Vd_{hsd}}{V_{i}}", + "666bf092220a8878.png": "P=KG(W-W_{e})", + "666cf47b5d73d592.png": "\\rho\\frac{Dv}{Dt}=\\nabla\\cdot\\sigma+f", + "666d3f0896717d86.png": "f\\in H^{k-2}(\\Omega)", + "66740c7dedf9964f.png": "k=\\lfloor\\frac{x}{\\Delta}+\\frac{1}{2}\\rfloor", + "6678073283af471f.png": "\\frac{4}{\\nu-6}\\sqrt{2(\\nu-4)}", + "6696fb605cccbe25.png": "log_{2}(1.0)", + "66a2790c462d63d5.png": "D(>p,p,e)", + "66a9baf3479b7d11.png": "\\sum k^{3}={(\\begin{matrix}n+1\\\\ 2\\end{matrix})}^{2}", + "66ac253d0742b423.png": "\\frac{ln(1+c)}{2c}", + "66ada69a42e5fa94.png": "A/m=k", + "66b355f76ea872c9.png": "f(z_{0}(1+i\\epsilon))", + "66b9330ea8aa4a30.png": "I_{hkl}\\propto|F(hkl)|^{2}", + "66bbf8cc732331fc.png": "\\sum_{j=1}^{n}x_{i,m+j}=b_{m+j}", + "66c2c788e785829c.png": "Q(a)v=(v\\cdot a)a", + "66ccfeb183430dc4.png": "k=\\lfloor\\frac{x}{\\Delta}+\\frac{1}{2}\\rfloor", + "66daddf2a3c6a274.png": "R_{\\lambda,\\mu}=C_{0}J_{\\mu}(\\lambda r)", + "66dbd77705a90b90.png": "\\epsilon^{ijk}\\frac{\\partial v_{k}}{\\partial x^{j}}", + "66e3532a861da272.png": "|\\beta N|<2^{2^{\\aleph_{0}}}", + "66e9645bac5370fe.png": "\\tilde{\\phi}\\circ\\omega=\\phi", + "66eff7fd457f41c6.png": "B_{E}:X_{E}\\rightarrow X_{E}^{*}", + "66f234c626c735bb.png": "M_{n}=M(i\\alpha)^{n}", + "66f4f87766da3eef.png": "(0\\sqrt{x_{1}x_{2}}", + "671fdded15c54655.png": "(F_{0}+K)/2", + "672e9049400b4997.png": "1\\le p<\\infty,c\\in R", + "674033781a3e521c.png": ">T_{b}", + "6744d4673cfb04af.png": "|\\Psi|e^{i\\phi}", + "6746a02014deb857.png": "r=D_{K}[F(K,L)]", + "67477b10123b9109.png": "1/R_{c}=2L_{s}", + "6748e4bb8b3d6661.png": "\\gamma=\\frac{3}{\\sqrt{3+\\frac{v^{8}}{c^{8}}}}", + "674dbfc1ffed0334.png": "[q-1,k]", + "6751d90a5ae2bdad.png": "|\\langle\\psi_{i}|\\phi_{j}\\rangle|^{2}=\\frac{1}{d},\\forall i,j", + "675742838a2a08ad.png": "-|I|>I_{0}", + "675c8a363c5beb03.png": "x^{\\prime\\prime}\\in D(p,w^{\\prime\\prime})", + "6767702a66328398.png": "2sin(\\frac{108^{\\circ}}{2})=\\phi", + "676e19c9016b4c8f.png": "\\beta=0.92;0.57", + "6778741e3c1703dd.png": "lim_{n\\rightarrow\\infty}\\hat{S}(n)=0", + "677bae24b9bf1659.png": "(b^{3}-a^{3})/(b-a)", + "677f9d4f31528659.png": "Q_{n}=\\frac{\\pi}{ntan\\frac{\\pi}{n}}", + "678064e8a5cd07aa.png": "max_{X}E_{kl}(r_{k}^{B},r_{l}^{X})", + "6780daceac3aa267.png": "(n_{o}p_{o}=n_{i}^{2})", + "67879ffe266d6eed.png": "1(", + "6788243ed4f2d167.png": "=8\\sum_{i=0}^{n-1}(i)+1", + "6798938e25c0de9c.png": "|\\overline{x}-x|\\le M", + "67a877ea01b945af.png": "1-\\frac{\\lambda}{\\sqrt{1+\\lambda^{2}}}", + "67b34d9da1d941ff.png": "PI>40.74", + "67b8838782973fd0.png": "\\hat{t}:[0,\\hat{T}]\\rightarrow[0,T]", + "67c6befec99b8e68.png": "S_{2}=V_{0}sin(\\omega t-\\pi)", + "67d69f9b83cac250.png": "ln(4/3)/\\lambda", + "67d77e565d2d9bc7.png": "\\frac{d\\vec{J}}{dt}=\\vec{\\mu}\\times\\vec{B}", + "67d89a70068693be.png": "1-Q_{\\frac{k}{2}}(\\sqrt{\\lambda},\\sqrt{x})", + "67e01c07b91604bd.png": "g_{2}=g_{2}(x_{3},x_{4},x_{5})", + "67e173a3df235bf7.png": "\\frac{\\partial}{\\partial t}\\rho=\\frac{1}{2}\\frac{\\partial^{2}}{\\partial x^{2}}\\rho", + "67e6f558fdfa5d10.png": "U=(U_{t})_{t\\in[0,T]}", + "67ea2872aaa31e4d.png": "lim_{y\\rightarrow0+}\\frac{1}{y}", + "67fd1dfdc3fb850b.png": "2^{H(p+\\epsilon)n}", + "68019e3d9debf4f5.png": "\\omega^{2}=-U^{2}(\\frac{2k}{rd})\\theta^{2}", + "6801dc641ca707a5.png": "Z_{i,j}", + "680329821f01890d.png": "f_{+},\\varphi", + "68060e24aca9d0f7.png": "(x\\in[0,\\frac{1}{2}))", + "6809cf5687fc58d7.png": "S_{i}=-\\frac{Q_{H}}{T_{H}}+\\frac{Q_{a}}{T_{a}}", + "680ff4329ba1e590.png": "1\\mp2x+3x^{2}\\mp\\cdot\\cdot\\cdot", + "681c83aec75ec03b.png": "=|(I_{p}-2i\\theta I_{p})|^{-\\frac{1}{2}}", + "682336f563a15347.png": "\\tau_{1}=\\frac{K_{p}K_{v}}{\\omega_{n}^{2}}", + "68261115eade1cbb.png": "(\\alpha f)^{\\prime}=\\alpha f^{\\prime}", + "68261d26e588c34f.png": "\\Delta t=M+\\lambda_{p}-\\alpha", + "683965183b3da427.png": "(x,y)=(x_{n},f(x_{n}))", + "683972a236164f7e.png": "V_{T-j+1}(k)", + "6841eb891b2d65fe.png": "\\forall x\\exists y[\\varphi(x,y,z)]", + "685bbaa3dbbe2ecf.png": "0.082H_{s}^{2}", + "6880cc3e9db59c43.png": "2^{1,000,000}", + "6881d509cd3f2ca7.png": "1\\mp2x+3x^{2}\\mp\\cdot\\cdot\\cdot", + "6885aca0fc00d60e.png": "t_{ik}=\\sum_{j}c_{ij}c_{jk}", + "688a1e75f80bd86b.png": "2x_{1}=D+\\frac{r_{1}^{2}-r_{2}^{2}}{D}", + "68950c9a443dc23e.png": "E_{h}=\\alpha^{2}m_{e}c^{2}", + "689544a1296826bf.png": "A_{x}^{(12)}", + "689b8d56328a74cb.png": "\\overline{\\beta_{12}}=2[\\frac{1}{\\beta_{1}}+\\frac{1}{\\beta_{2}}]^{-1}", + "68ae43d607fe588d.png": "csc^{\\prime\\prime}(\\frac{1}{2}\\pi)=1>0", + "68c5cc1d75bc4bdb.png": "L(C)\\le L(T)", + "68cd1320b4665409.png": "V_{e}=I_{sp}*g_{n}", + "68eb4306d5cb84af.png": "F^{m}[x_{1},x_{2},...,x_{n}]", + "68edf4ecbbffdc26.png": "\\frac{1}{2}\\frac{mg}{L}x^{2}", + "68f3354d374aa590.png": "p_{j}(x)=j\\sum_{i=1}^{j}|x_{i}|", + "68f7d4ed6f54ecf7.png": "3A+2B+C=0", + "69003d67296fb834.png": "csc^{\\prime\\prime}(\\frac{1}{2}\\pi)=1>0", + "690143795821015c.png": "R_{1}\\in[0\\Omega,\\infty[", + "69022e69a39d75b8.png": "c_{d_{2}}>0", + "6904a74256473cde.png": "[a,b]\\rightarrow[az,bz]", + "6916d0b285b36def.png": "grR=gr\\hat{R}", + "691b25c8920392bc.png": "(L-K+1)^{2}", + "691bbdcb216c1c05.png": "E_{L}[u]=E_{M}[u]", + "694946c243e8820e.png": "|G|=|S_{21}|", + "6950ea2255519e9f.png": "+(1-f)", + "6953e36866fd4144.png": "Var(\\overline{x})=\\sigma^{2}/n", + "6957389468bdb470.png": "\\delta^{n-1}tr\\rho(\\sigma)", + "6958e3eef5800700.png": "\\forall_{x}\\exists_{y}G(x,y)", + "6959f008210dad2b.png": "(x^{2}+x+1)", + "695e917031fe182b.png": "e^{*}=(sign(e_{i}))_{i}", + "69689c53f1a7f95c.png": "f(z)=\\frac{e^{iz}}{z}", + "696ea2d36e366b53.png": "X[m]=FFT\\{x[n]\\}", + "697390215b060d85.png": "\\alpha\\dot{\\beta}", + "698ebfbbad14807a.png": "V=\\frac{1}{2}(3+2\\sqrt{2})", + "69984d1cc27cf069.png": "\\hat{\\rho},\\hat{\\phi},\\hat{z}", + "699cecfd16c84cbb.png": "f(\\vec{x},\\vec{e}_{i},t)", + "699ec5cfdc0943e2.png": "P=\\frac{I^{2}\\rho l}{A}", + "69a0fd011103ec00.png": "237/360=0.01034_{!}", + "69b014b0837eff42.png": "C=\\epsilon\\frac{A}{d}", + "69b18e1225acab82.png": "\\tilde{V}_{x}=|V_{x}|", + "69ba810b6a3097a7.png": "\\sqrt{a}\\cdot\\sqrt{b}=\\sqrt{a\\cdot b}", + "69bc838fadc73bc5.png": "P+\\frac{1}{2}\\rho v^{2}=P_{0}", + "69be8b97c5c71b33.png": "\\dot{\\rho}_{m}+3H\\rho_{m}=0", + "69d4483c1b807c36.png": "1+6(\\frac{1}{2}n(n-1))", + "69db3f7b0f5e95f2.png": "F(x)=E(1_{X_{1}\\le x})", + "69dd418cde23f3e4.png": "e^{i\\int_{\\gamma}A}", + "69deb7249bce0cd3.png": "(E,\\vec{p}c)", + "69e0a2e066447468.png": "(Dr=l^{a}\\partial_{a}r=1)", + "69e3f91d68572678.png": "[\\Omega]\\in H^{3}(M,R)", + "69e9be8cf42bd868.png": "\\frac{v_{1}^{2}}{2g}+y_{1}=\\frac{v_{2}^{2}}{2g}+y_{2}", + "69eb98711f3a5cea.png": "lim_{r\\rightarrow\\infty}\\int_{|x|>r}|f|^{p}=0", + "69ec85c44d988173.png": "\\mu_{n}(t)=E(X_{t}^{n})", + "69ee9aa8af303bc9.png": "\\hat{F}_{ab}^{i}\\dot{\\gamma}^{a}\\dot{\\gamma}^{b}", + "69f8dd4c067bd865.png": "\\frac{dx}{dt}=(x(t-1))^{2}", + "6a004b2f5e8fc5f9.png": "(t^{\\prime}-t)/\\epsilon", + "6a06032e15c13d3f.png": "|f^{\\prime\\prime}(p)|=0", + "6a0b60cef6fc3b1a.png": "Y", + "6a1d3b487c271676.png": "f^{\\prime}(a)>y>f^{\\prime}(b)", + "6a34d042cc10705a.png": "B=(T_{n}(s)=x)", + "6a3eff348bbe483d.png": "2^{km}e^{-\\epsilon\\alpha n/2}", + "6a4681757cb23503.png": "-y(\\gamma-\\delta x)=0", + "6a5c653a1d8f68b6.png": "H_{\\omega+1}(1)-1", + "6a5fdc6ded4f8ae8.png": "\\frac{1}{2}", + "6a61b09ded5b97cf.png": "\\langle\\Psi,s\\rangle=\\langle\\Psi,s^{\\prime}\\rangle", + "6a743eb024b65d81.png": "[\\hat{a}(t),\\hat{a}^{\\dagger}(t)]=1", + "6a889c8bddab2215.png": "g\\circ_{T}f=g^{*}\\circ f", + "6a8965554c20e5f0.png": "F_{k}(a)=\\sum_{i=1}^{n}a_{i}^{k}", + "6a8a97d2c1214f97.png": "Q_{1}+Q_{1}^{*}=0", + "6a9b0cac7e9c8f57.png": "3x^{2}+2x+1=6x", + "6aa0efcc0e5ff608.png": "\\lambda_{0}={(\\frac{k}{e})}^{2}\\sigma_{0}TI_{2}", + "6aa822abb1480821.png": "H_{0}^{1}\\subset H^{1}", + "6ab7bdc51a6fb804.png": "L_{0}^{\\prime}=x_{2}^{\\prime}-x_{1}^{\\prime}", + "6accb44d32728824.png": "1/r^{\\prime}+1/r=1", + "6ad50ae380f4322e.png": "(s,t)\\mapsto f_{1}(s)f_{2}(t)", + "6ad9218e394e4deb.png": "-2\\le S_{CHSH}\\le2", + "6adff3121db71072.png": "-\\frac{1}{12}\\pi^{2}", + "6ae1544bd6275379.png": "d=0,1,2,...,2^{w}-1", + "6af2d5d05656ecc9.png": "\\Omega_{X/S}=\\Delta^{*}(I/I^{2})", + "6afe72b4e30a4f3b.png": "t_{1}=X^{c}g_{1}^{s_{1}}g_{2}^{s_{2}}", + "6b00e12ccacb155f.png": "(h,q^{n}-1)=1", + "6b0496ed0d84a411.png": "8\\pi^{2}/105\\approx75.2\\%", + "6b05f49a49894a33.png": "(\\begin{matrix}22\\end{matrix}){(\\begin{matrix}32\\end{matrix})}^{2}(\\begin{matrix}401\\end{matrix})", + "6b16fbfc21338cf3.png": "\\bigwedge^{n}T_{e}^{*}G", + "6b35382fc12d0cb3.png": "A(x_{1},...,x_{n})\\rightarrow\\alpha", + "6b464a1b875f6b8d.png": "S[\\sigma]\\rightarrow T[\\sigma]V^{\\prime}[\\sigma]", + "6b5087464c6bf898.png": "X_{t}=N_{t}D_{t}^{-1}", + "6b50c9db67cc094b.png": "\\pi(0.99)\\times v(1000)", + "6b5516e00d5c2907.png": "(9.525,10.478)cm", + "6b5bad8aca64a8a3.png": "E[S_{1}+...+S_{\\lambda}]", + "6b680f0feb40cece.png": "1_{10}=0.\\overline{9}_{10}", + "6b6b1eae7e498d8a.png": "e^{*}=(sign(e_{i}))_{i}", + "6b6d48781a25ffca.png": "1_{10}=0.\\overline{9}_{10}", + "6b70757f93928d82.png": "D(a)=D(b)=0", + "6b7efcc0d0ab0485.png": "\\psi_{R}\\rightarrow(\\begin{matrix}\\psi_{11}\\\\ \\psi_{21}\\end{matrix})", + "6b856dac8e2cae90.png": "(\\nabla\\Phi)_{i}=\\nabla_{i}\\Phi", + "6b8d8562f963600a.png": "B(r)=B_{0}/r^{3}", + "6baf4de11b17d44d.png": "S_{2}=S_{1}-kln\\frac{c_{2}}{c_{1}}", + "6bb594424dd91946.png": "\\zeta_{i}(s)=\\sum_{\\lambda_{j}>0}\\lambda_{j}^{-s}", + "6bc6ba55c74f427a.png": "exp(-t^{1/\\theta})", + "6bc763653e4de324.png": "log_{2}3=m/2n", + "6bccb24be7ac1dcf.png": "Z_{r}=\\frac{N_{r}}{0.5(t-q)}", + "6bd35b6125a7f376.png": "|+z\\rangle\\otimes|-z\\rangle", + "6bd4c5b3f0967f34.png": "\\overline{X}_{n}\\rightarrow\\frac{1+r}{1-r}", + "6bd883946c2de24d.png": "=", + "6be17507587787ae.png": "abca^{-1}b^{-1}d\\sim?", + "6be4cddd73ef5fb8.png": "2^{1/p}>2", + "6bfc7df6b8760ea5.png": "S^{\\prime}=\\{s_{n}^{\\prime}\\}_{n\\in N}", + "6bfe3ec1cf7a3223.png": "f(\\sqrt[3]{2})=1", + "6c00f8eec7cc8f51.png": "2c>\\frac{q}{2}", + "6c05d76f1191a833.png": "00}w_{i}", + "6c9982b71a8916a1.png": "\\frac{F}{L}=\\rho vG", + "6ca41178f50a8d3e.png": "C_{N}=\\frac{h}{F_{1}}", + "6ca6c6eb650d51b8.png": "P(f", + "6cac206f2af918df.png": "H^{*}(X)\\cong H_{n-*}(X)", + "6cb1a7a7dfa6b624.png": "g_{\\mu,\\nu}^{\\lambda}(q)\\in Z[q]", + "6cc630fa7c40051f.png": "E_{d}>\\Delta E", + "6ccdbf1caca1c370.png": "a(\\rho,p)\\equiv\\sqrt{\\frac{\\partial p}{\\partial\\rho}}", + "6cd1face8d17a086.png": "(E_{1},\\hat{O}E_{2})", + "6cd2b1a77323d80d.png": "R_{01}=\\frac{W_{cu}}{3{I_{S}}^{2}}", + "6cd93ef09d88c3bb.png": "[\\begin{matrix}I_{l}&0\\\\ 0&0_{u}\\end{matrix}]", + "6cd9a959daa08bf0.png": "D=\\frac{2A}{2A+B+C}", + "6cec5f297e6823ec.png": "[a,a+r]", + "6cf42a7b01f97830.png": "DEP(T_{i})=[]", + "6cfd3fece2950537.png": "\\delta(v,v^{\\prime})\\ge0", + "6cff952436af09d5.png": "E=\\frac{-\\mu^{2}}{2}", + "6d032adca6747ebf.png": "[\\begin{matrix}s^{2}&psz\\\\ psz&z^{2}\\end{matrix}]", + "6d0c450c082a45b4.png": "\\lambda(A)^{\\prime\\prime}=\\rho(A)^{\\prime}", + "6d1042b9ee1c4c3e.png": "\\sum_{j\\in S}p_{ij}V(j)<\\infty", + "6d25f1d73d1ed050.png": "237/360=0.01034_{!}", + "6d27ef86adea9cbf.png": "\\dot{g}=-e\\cdot w(t)", + "6d2bc3a6e80542d3.png": "GF=\\frac{\\Delta R/R_{G}}{\\epsilon}", + "6d3d37365c39768f.png": "B^{n}xh/2", + "6f055b7a8761079b.png": "\\overline{v}=\\frac{\\overline{q}}{\\overline{k}}", + "6f1336ea1066eda8.png": "(ab)c\\ne a(bc)", + "6f27ca56ab40be18.png": "-\\sqrt{n},...,\\sqrt{n}", + "6f2c08cf55ed136f.png": "\\hat{w}=\\frac{dF(L)}{dL}", + "6f3c6d474b190565.png": "A_{\\lambda}:=\\bigcup_{\\alpha<\\lambda}A_{\\alpha}", + "6f3f14522953c34b.png": "log\\frac{\\overline{Y}}{1-\\overline{Y}}", + "6f40efdc44cb5e53.png": "R=\\frac{a}{\\sqrt{3}}", + "6f414dee7bb40778.png": "(\\overline{3},1,-\\frac{4}{3})", + "6f6336b71ee7be2d.png": "(\\frac{\\partial}{\\partial x^{1}},\\cdot\\cdot\\cdot,\\frac{\\partial}{\\partial x^{n}})", + "6f69c2fa8f71eee2.png": "j_{0}=f^{2}\\partial_{0}\\theta(t)", + "6f6c227c3f05f05e.png": "{\\epsilon_{1}}^{\\epsilon_{0}\\omega}", + "6f6fcd99e0fb777d.png": "T^{-1}x,x\\in Set", + "6f7758c335d1f8fe.png": "(a+t,b+t]", + "6f7ded137dab06d6.png": "\\overline{B_{1}(p)}=\\{p\\}", + "6f811cdee8b50fde.png": "x=(\\lambda-\\lambda_{0})cos\\varphi_{0}", + "6f83b1932a50c708.png": "\\frac{dy}{dx}=-\\frac{y}{x}\\frac{\\delta x-\\gamma}{\\beta y-\\alpha}", + "6f85fc54956f0806.png": "\\zeta\\equiv\\lambda+\\frac{2}{3}\\mu", + "6f886b938af71c79.png": "H^{*}(X)\\cong H_{n-*}(X)", + "6f89125c550ac905.png": "\\begin{matrix}\\times&c&d\\\\ a&ac&ad\\\\ b&bc&bd\\end{matrix}", + "6f8f5d7b6dc67e9f.png": "z^{-1}=z^{*}/||z||", + "6fac761bf79cb7fc.png": "\\tau=\\frac{(\\alpha\\Delta t)}{\\Delta x^{2}}", + "6fae5852b6c7cbf7.png": "(x+200)^{2}(x+58)", + "6faff511428e60f3.png": "2Rsin(\\frac{a}{2})", + "6fb964f91fb2f02b.png": "E_{1}\\cup E_{2}\\cup...=B", + "6fbb4d1ea6e8c1dd.png": "\\le^{-1}=\\ge,<^{-1}=>", + "6fbd5314633927a6.png": "\\sqrt{R}=\\frac{k_{1}-k_{2}}{k_{1}+k_{2}}", + "6fbf532ba7e47206.png": "\\approx(a+w)(e^{a}(1+w)-1)", + "6fcde8fefd12c645.png": "\\varphi(\\theta)=\\frac{1}{2}sin(\\theta)", + "6fceab63d07766c8.png": "2(L_{u}-L_{r})", + "6fd43824744cf5f3.png": "=0.28\\times10,000", + "6fd6b2f8a8402f02.png": "-\\frac{1}{sinx}d^{2}x=dt^{2}", + "6fd84d3cf78d4a69.png": "(\\frac{i}{2\\pi})^{n}\\delta^{(n)}(\\xi)", + "6fe1394ddf3fc44d.png": "\\prod_{i=0}^{n}p_{i}0\\}", + "7055dcf7e71f51ad.png": "n,m=1,...,l_{\\mu}", + "705f22537cdce1d2.png": "n_{1AU}\\approx\\sqrt{G}", + "70625560cc91e88e.png": "P_{t,t^{\\prime}}(x|x^{\\prime})", + "7078999683c4352c.png": "H_{1}=-\\vec{d}\\cdot\\vec{E}", + "707d17a9d2fb4522.png": "nlog_{2}n-\\frac{n}{ln2}", + "70863fbb1e3c9c95.png": "\\langle k\\rangle>1", + "70987253196e7c8d.png": "\\pi_{n}X=[S^{n},X]", + "709b1749e8a95a05.png": "(++++)", + "70abf99d5e744f38.png": "sp_{2n}R", + "70b5817b16ffa6a6.png": "c_{t}=y_{t}+(1+r)b_{t}", + "70b739d5248b71c6.png": "V_{e}=I_{sp}*g_{n}", + "70c199d5d852afe5.png": "t:=(e^{h}-1)^{-1}", + "70d999d7e68dd6a7.png": "R_{\\kappa\\nu}=\\Delta U\\Psi_{\\kappa}\\Psi_{\\nu}", + "70dc5ac3397c877f.png": "EV=g\\wedge\\bigcirc S_{0}^{2}V", + "70df5372362c0ad5.png": "E=rc^{4}/2G", + "70e2cb174037e3f6.png": "\\int x^{n-1}dx=\\frac{1}{n}x^{n}", + "70e45c19eec1ee65.png": "1-(0.95)^{2}=0.097", + "70e45f4d0123838f.png": "\\lfloor\\frac{i-1}{2}\\rfloor", + "70effa4ca79bd7e6.png": "D=S_{1},S_{2},...,S_{d}", + "70f79cb5197a53b4.png": "\\lambda\\sum_{t}||f||_{H_{k}}^{2}", + "70fad6b286fd5f3f.png": "L\\subset Fun(A,Ab)", + "71059506e3b1bca6.png": "j_{0}=f^{2}\\partial_{0}\\theta(t)", + "710b775679d7a89d.png": "I_{im+}", + "71140955c55285e0.png": "|f^{\\prime\\prime}(p)|=0", + "71162ed527bf82e1.png": "w\\in\\hat{C}\\backslash\\overline{D}", + "71266ca9762d5352.png": "\\sum_{n=1}^{\\infty}\\frac{1}{n}z^{n}", + "712ff3ed4a19458a.png": "1^{f(x)}", + "71334bbe0762d135.png": "\\chi^{-1}(-1)", + "7135d58cf454ba9a.png": "\\underline{T}(t)=\\frac{d\\gamma}{dt}", + "714b43352c902b7c.png": "|\\tau|=-mglsin\\theta", + "715d100b9a4fc282.png": "G(z)=E[z^{X}]", + "716187a861260d6b.png": "O(n^{\\lceil\\frac{d}{2}\\rceil})", + "7172393f10587cf6.png": "X=|X|e^{jarg(X)}", + "7175d6024b851a8e.png": "L^{1,\\infty}(H)", + "71a29dd4c941190a.png": "Li_{1}(\\frac{1}{2})=ln2", + "71adece80a10d3a4.png": "g(\\zeta)=f(\\zeta^{-2})^{-\\frac{1}{2}}", + "71b8bf5d8b8a9cef.png": "H^{*}(g)", + "71c50783ef9f3f8d.png": "O_{X}|_{U}", + "71c74cc8ee6295bc.png": "\\frac{1}{PM}=\\frac{AB}{AP\\times BP}", + "71cc747c0b66ffd1.png": "s=x_{1}+\\dot{x}_{1}=0", + "71cd104b64d76233.png": "\\int_{0}^{\\infty}\\frac{dx}{\\Gamma(x)}", + "71d73fb0e625220a.png": "m=\\frac{1}{2R}(y_{2}+y_{1})", + "71ed6a9dc6d9adb1.png": "1-\\delta+o(1)", + "71f456fa906b2975.png": "X(t)^{*}X(t)", + "71f6fe66b7bb8a0f.png": "f=z\\sqrt{x^{2}+y^{2}}", + "71f743ff55d040b7.png": "D_{P}\\cdot\\tau_{i}^{-1}H", + "71fd2f5281a858b7.png": "dete^{A}=expTr(A)", + "720ce1efedaa0b8a.png": "\\Delta Y=\\frac{\\Delta I}{(1-c)}", + "7210228f09650f42.png": "\\frac{d}{dt}|A|^{2}=2A\\cdot\\frac{dA}{dt}", + "721897d83799072f.png": "Q_{V}(\\vec{R}_{N},N|\\vec{R}_{0}.0)", + "7225202b6ebddc94.png": "d^{n}y=f^{(n)}(x)(dx)^{n}", + "722649576c43b38a.png": "\\tilde{f}=f+h", + "7237d5ca2a270d60.png": "W\\sim\\omega^{4}/m^{3}\\gamma^{4}", + "72385e90cb927478.png": "xv\\alpha(x)^{-1}\\in V", + "723ea452f7c25d11.png": "\\frac{1}{2}+\\frac{1}{10}\\sqrt{15}", + "724efbc7459f0f99.png": "(x_{i},x_{i+1})\\in E", + "7260913734b0d1a8.png": "f(k):=\\sum_{K^{\\prime}}\\tilde{u}_{k}(K^{\\prime})", + "7266d638ce05b5ca.png": "v_{e0}=\\sqrt{2q_{e}\\Delta V/m_{e}}", + "726c0eaaf7c95b4c.png": "F(y)=O(\\frac{1}{\\sqrt{y}})", + "7279a95195663930.png": "D(f)=[\\begin{matrix}0\\\\ 0\\end{matrix}]", + "7281dfac21bc6a0d.png": "\\mu(X)=\\frac{a+4b+c}{6}", + "728855ac96fa6bee.png": "\\langle a_{0},a_{1},...\\rangle\\in R^{\\omega}", + "728b672a3cb2c015.png": "\\frac{o^{+\\frac{j^{2}}{2\\sigma^{2}}}}{\\sqrt{2\\pi}\\sigma}", + "728bb2d5cf91ab7a.png": "nlog_{2}n-\\frac{n}{ln2}", + "728ca11359596e04.png": "OPL=\\int_{C}n(s)ds", + "729b394ef8f197c9.png": "\\nabla\\cdot\\vec{v}=3y+2yz", + "72a23e60f003d354.png": "Y(\\omega)=iB(\\omega)", + "72ac3851b4648b85.png": "g_{n}-B", + "7357df2f8a6429c2.png": "1991_{10}=7C7_{16}", + "735de302827fa6cb.png": "P/A=\\sigma T^{4}", + "73638d3d4b5bbcbd.png": "Z_{p^{r}}[X]", + "736a8a39124f0df7.png": "Z^{+}\\cup\\{0\\}", + "736c99a9450fadf4.png": "E:R^{n}\\rightarrow T_{p}M", + "7377abd601d41b02.png": "\\frac{1}{N}\\frac{\\sqrt{N}}{2}=\\frac{1}{2\\sqrt{N}}", + "73836907bfaaca9e.png": "H=-J\\sum_{[i,j]}S_{i}\\cdot S_{j}", + "73850ea62c5ba814.png": "\\hat{H}\\Psi=0", + "73885065247201f8.png": "t_{ik}=\\sum_{j}c_{ij}c_{jk}", + "738a498aecdd0ced.png": "(\\begin{matrix}101\\end{matrix})(\\begin{matrix}42\\end{matrix})(\\begin{matrix}361\\end{matrix})", + "7390a9edb6d95323.png": "\\prod_{c\\in g}a_{|c|}=\\prod_{k=1}^{n}a_{k}^{j_{k}(g)}", + "73b27b2542332438.png": "\\int_{E}f(x)\\mu(dx)", + "73c4c2636b836b9a.png": "s=\\frac{a+b+c+d}{2}", + "73cc27570a385767.png": "n\\approx\\sqrt{2m\\times p(n)}", + "73e199da50f02a8d.png": "v_{t}(w)=\\langle w,z_{t}\\rangle", + "73e709e685ffabbc.png": "\\theta=\\Theta sin(\\omega t+\\phi)", + "73ea551c11bbff97.png": "(\\begin{matrix}1\\\\ \\frac{c}{\\rho}\\end{matrix}),(\\begin{matrix}1\\\\ -\\frac{c}{\\rho}\\end{matrix})", + "73f1820d2a3c3f86.png": "\\sigma^{2}*(X^{\\prime}X)^{-1}", + "73f5f2ef7f26824d.png": "da^{T}\\cdot F=JdA^{T}", + "73f9b33e32b1d51a.png": "\\{x\\}=\\{X\\}e^{i\\omega t}", + "73faf62a1cf99130.png": "=n(c_{V}+R)\\Delta T", + "73fc6eb651d55e2f.png": "0=X_{0}\\le X_{t_{1}}\\le\\cdot\\cdot\\cdot", + "7411fb16166f300a.png": "x_{1},x_{2}\\in\\Omega\\\\ X", + "7422eb20f17ddef6.png": "\\frac{U}{T^{2}}=\\frac{\\partial\\Phi}{\\partial T}", + "74232175057916d5.png": "\\frac{\\pi}{180}M_{r}cos\\varphi", + "7428d6903c23fcb5.png": "\\pi(Y_{lm})=(-1)^{l}", + "742aa6bd4960819b.png": "\\sum f(T,c)=1", + "7441973d0afe5222.png": "J(x)\\in X^{\\prime\\prime}", + "7447a563ce90309d.png": "\\Delta U_{system}=Q", + "744f4107e4303229.png": "(p_{i},|\\phi_{i}\\rangle)", + "745a89e1e51a73ed.png": "(k+1)^{2}=k^{3}", + "7460f957062934f8.png": "\\nabla^{2}\\varphi=-\\frac{\\rho_{f}}{\\epsilon}", + "74720f93eb61e8e9.png": "(h_{1},\\cdot\\cdot\\cdot,h_{n-k})", + "7479581e40130dac.png": "\\overline{x}=1/2", + "747edd5fb2833687.png": "exp_{R}B(\\hat{R})", + "7481e870d2bf8917.png": "(b^{3}-a^{3})/(b-a)", + "74825e2158b369e9.png": "\\pi_{T}=a\\frac{n^{2}}{V^{2}}", + "7486ab2dbfa60fbc.png": "Y_{12}=\\frac{-2S_{12}}{\\Delta_{S}}Y_{0}", + "748a9946bdb97f33.png": "R_{ab}=g_{ab}R", + "74912c4b60f9151e.png": "a^{(b^{c})}", + "74937e4d8bd3e5be.png": "M/(N_{1}\\cap N_{2})", + "74951f6f5dbdaa5a.png": "f(x_{t},t)=x_{t}e^{\\theta t}", + "74ab6940c623e807.png": "\\rho_{1}=\\gamma_{1}/\\gamma_{0}=\\varphi_{1}", + "74bcafba93424203.png": "S^{2}C^{3}", + "74c500f223da1ec4.png": "\\phi^{\\prime}=(1-G)*\\phi", + "74ca72f813b3b64d.png": "2(1/1!)\\pi^{1}=2\\pi", + "74cef5327fb5edd8.png": "|S(\\alpha)|\\ll\\frac{N}{log^{A}N}", + "74d28a1e940fcef5.png": "\\int\\frac{\\delta Q}{T}=-N", + "74e67d00f982c837.png": "\\dot{x}(t)=F[x(t),u(t)]", + "74f2e03bb7d5fd2f.png": "(1-\\sqrt{2})^{n}", + "74f7bb282937c2e9.png": "\\int_{-r}^{r}\\sqrt{1+f^{\\prime}(x)^{2}}dx", + "75029b42ce027ffd.png": "0^{\\prime}", + "750634dc27e41cea.png": "(3+4i)^{*}=3-4i", + "75164fbc0597b6b1.png": "\\psi_{t}=\\frac{i\\hbar}{2m}\\Delta\\psi", + "7520f9c335667309.png": "GF(p^{t})", + "75294743fae9ec68.png": "1/e^{z}=e^{-z}", + "753eb3783be121a6.png": "\\Psi=\\Psi(r,s_{z},t)", + "753f9f4e6dd7b789.png": "K(x,x_{i})=x_{i}^{T}x", + "754614dba03a8c97.png": "h_{A}=Hom(-,A)", + "7564ddcd442e2571.png": "(a+t,b+t]", + "756d0091a508ca90.png": "T=\\frac{2}{s}\\langle K\\rangle_{t}", + "7586a88d0d497464.png": "F_{x}v=m\\dot{v}v", + "758c89196944e4ad.png": "indg:=min_{\\xi\\in g^{*}}dimg_{\\xi}", + "758dd33b0dfcd93b.png": "E=rc^{4}/2G", + "75921489a9442c9e.png": "2^{2^{\\cdot^{\\cdot^{\\cdot^{n}}}}}", + "7592f8a46a58f042.png": "\\sigma_{i}^{2}=h(z_{i}^{\\prime}\\gamma)", + "75a1395899792251.png": "(x_{n})_{n\\in N},x_{n}\\in K", + "75a2e83591d8d820.png": "q=\\lfloor\\frac{n_{1}}{n_{0}}\\rfloor", + "75ae6e1b8e5bf14a.png": "a_{n}-2a_{n+1}", + "75c050c0b20e5edd.png": "K_{1}=K_{1}^{\\prime}\\cap K_{1}^{\\prime\\prime}", + "75c7d3c4be5acfe8.png": "I_{B}<=N-1", + "76420eb535e4eb77.png": "y^{\\prime}\\in F_{q^{n}}", + "764d69f52b5cd1f9.png": "i_{C}=I_{S}exp(\\frac{v_{BE}}{V_{T}})", + "766381c7a4f8140b.png": "U^{\\mu}=\\gamma(-1,v)", + "766a44e49bd42baf.png": "\\Pi=\\sum_{i,j}\\Pi^{ij}\\partial_{i}\\wedge\\partial_{j}", + "766d806fe06dfbb4.png": "FDR\\le\\frac{m_{0}}{m}q", + "7673973cc7fb6e33.png": "a\\times b=[a]_{\\times}b", + "767565575655e2f9.png": "cosx=\\frac{1}{\\sqrt{2}}", + "76793219e2739d89.png": "H_{A}:\\rho<\\rho_{0}", + "768044457b6d74ac.png": "l/t^{2}=l^{1}t^{-2}", + "7698594a2f824c3c.png": "U=\\frac{d_{f}}{2}k_{B}T", + "76ae6f5772895616.png": "\\underline{\\underline{A_{\\epsilon}}}^{T}=\\underline{\\underline{A_{\\sigma}}}^{-1}", + "76b44b9e3aae1a96.png": "H_{x}+H_{p}\\ge ln(e\\pi)", + "76bdeb83720f8dac.png": "I(\\rho,N)", + "76cae72a2f4212cc.png": "s(r,E,\\hat{\\Omega},t)", + "76d5b6afd43e6d92.png": "cr+cs=a^{2}+b^{2}", + "76d700ca7282f663.png": "K(\\epsilon^{\\frac{1}{W}})/k", + "76d70896c0640ef0.png": "0\\le x\\le2^{2^{k}}", + "76e11eef861a7014.png": "\\vec{\\beta}\\cdot\\dot{\\vec{\\beta}}=0", + "76edaf842d90b3bc.png": "(s,t)\\mapsto f_{1}(s)f_{2}(t)", + "76fd9a41008a420c.png": "\\sum_{i=0}^{n}(\\begin{matrix}n\\\\ \\lfloor n/2\\rfloor\\end{matrix})", + "77027eec1ae1611a.png": "x=p_{i}(e^{t}-1)", + "770408abf5a80c3d.png": "A=(\\begin{matrix}0&-1\\\\ 1&0\\end{matrix})", + "77047498734195e4.png": "1000\\times9.5=9,500", + "7704b925f417bcf0.png": "\\phi(ln(x))=y(x)", + "7706eadef2f44cd4.png": "V_{d}=\\frac{\\pi^{d/2}}{\\Gamma(\\frac{d}{2}+1)}", + "7709d4d70e5854aa.png": "S={\\langle Q\\rangle}^{\\perp}", + "770c2aefc9974674.png": "(-3)!!=-1", + "772b948f866564da.png": "f^{-1}(y)=\\sqrt{y}", + "77314c5145f54d4c.png": "h=inf\\{\\frac{|\\partial V|}{|V|}\\}", + "77315341633b251b.png": "[I-A]", + "7732ef7a31613b05.png": "\\lambda\\in h^{*}\\\\ \\{0\\}", + "773b508dd606d1bd.png": "f^{\\prime}(x)=f(x)f^{\\prime}(0)", + "773fa5e0c265ce78.png": "E_{c}:z\\rightarrow e^{z}+c", + "77479df35d30fb39.png": "(m,u)=g_{m^{\\prime}m}(m)", + "774d71ace5e4bfd1.png": "R(x)=\\frac{R}{H}H(x)", + "774e7925bcf96a62.png": "b_{j}=\\int fv_{j}dx", + "7750a37d8e898cd4.png": "\\pi^{\\prime}0", + "7eae96bb51aee90a.png": "\\partial\\phi=:\\overline{\\psi}\\psi:", + "7ebb441a1cbb1810.png": "\\tilde{V}_{x}=|V_{x}|", + "7ebd798b0e6ce9ea.png": "\\hat{g}=\\frac{k}{T^{2}}", + "7ec4d70d72ed3dff.png": "A_{\\infty}=lim_{\\omega\\rightarrow\\infty}A(\\omega)", + "7ec6f82ff064700f.png": "M_{c}(x,y;t,\\gamma^{2}t)", + "7edbc2899d571143.png": "\\epsilon((-1)^{F})=1", + "7edc3884c5fa9601.png": "\\psi(r,\\theta)=\\frac{Q}{2\\pi}\\theta", + "7eee9f1f0fa79af4.png": "\\Delta b/b^{2}\\approx\\Delta f/f^{2}", + "7ef415f49faf7e8b.png": "\\sum k^{3}={(\\begin{matrix}n+1\\\\ 2\\end{matrix})}^{2}", + "7efb98f2a0f14c82.png": "max_{X}E_{kl}(r_{k}^{B},r_{l}^{X})", + "7f0462d58b680ca9.png": "V(s)=-J\\delta(s_{0},s_{1})", + "7f090bf53c5de339.png": "p_{i}(q_{i},\\dot{q}_{i},t)=\\frac{\\partial L}{\\partial\\dot{q}_{i}}", + "7f0fba8c33f335bd.png": "\\sum_{n=0}^{\\infty}\\frac{B_{n}}{n!}z^{n}=e^{e^{z}-1}", + "7f27b008e66b1123.png": "(CH_{3})_{2}C", + "7f2a80c4473262d3.png": "[Al^{3+}]=k_{G}[H^{+}]^{3}", + "7f2b67184f1fdc7f.png": "(-1)^{|a_{\\pi}|}", + "7f358b6060030277.png": "u_{i}=\\overline{u_{i}}+u_{i}^{\\prime}", + "7f4260b608df5cf9.png": "\\int\\sqrt{1-x^{2}}dx", + "7f47acb29da19934.png": "D(D):=D", + "7f4bff397a66bd50.png": "2(L_{u}-L_{r})", + "7f4fd504c1e929ec.png": "(it)^{r}\\psi(t)", + "7f649f5f0c2a1b06.png": "1\\le p/q<2", + "7f6bd3735a9b0469.png": "\\sqrt{S}=S\\cdot(1/\\sqrt{S})", + "7f716b627a496c9a.png": "f:R(X)\\rightarrow R(S_{R})", + "7f71bd2df9091c12.png": "\\angle P_{1}P_{2}P_{3}", + "7f74824c6f21c716.png": "100(1-\\alpha)", + "7f750b857ed52721.png": "(h_{1},\\cdot\\cdot\\cdot,h_{n-k})", + "7f7ac404ad906395.png": "r_{t}=ln(P_{t}/P_{t-1})", + "7f816479ad9b3f66.png": "\\frac{[HR]}{[H]}", + "7f9624df936d895e.png": "2^{k}0\\}", + "82e43cc8368ac337.png": "\\{\\begin{matrix}p\\\\ q,r,s\\end{matrix}\\}", + "82e9543d2fa22611.png": "\\oint_{C}\\frac{dz}{z}=2\\pi i", + "82f4f10c0d18dae7.png": "F(\\{a_{i}\\},\\{A_{j}\\})", + "82f6c9b08edc8817.png": "237/360=0.01034_{!}", + "82f8f53e7901d692.png": "(|x|^{p}+|y|^{p})^{1/p}", + "83171fb1ca8acb66.png": "\\Delta S_{int}-\\frac{Q}{T}\\ge0", + "831b6fddc4fa9914.png": "r_{2}=\\pm\\sqrt{p^{2}-4q}", + "832a40cba8d9894f.png": "x(t)=vt,y(t)=0", + "832ecfdcf27cb3ad.png": "\\{(x,y)|\\phi(x,y)\\}", + "832f696d17ddebfe.png": "y=a\\cdot x^{-b}\\cdot e^{-cx}", + "833cc44783bbf8c7.png": "H(E_{j})\\cong H(E_{j})", + "833fb4f82c208253.png": "\\int\\frac{\\delta F}{\\delta\\rho}(x)\\phi(x)dx", + "834f0650aec23e6b.png": "\\psi^{[-1]}", + "83518978ac0a9ad8.png": "\\sum^{\\infty}z^{n!}", + "8352c2acbe0d6067.png": "x^{\\prime\\prime}\\in D(p,w^{\\prime\\prime})", + "83560c24f5678159.png": "a<_{s}ce(ab)<_{s}b", + "835c2e579a04e0b7.png": "A=\\int\\lambda dE_{A}(\\lambda)", + "8363d1ef9796c607.png": "\\hat{b}^{i}=\\frac{b^{i}}{\\sqrt{g^{ii}}}", + "836564b2e4eda7b5.png": "\\{F_{i};i\\in I\\}", + "8367a3f4b7ee7c56.png": "E(sup_{T>t}W_{T}/T)", + "8370d5c6b1ff36c8.png": "\\int f_{n}\\le\\int f", + "8383bb547038b22b.png": "c(c-1+\\gamma)=0", + "8390d66107e882e7.png": "H_{0}\\lambda^{2}=-\\frac{\\hbar}{2m}", + "8391ed6f3f2b21e6.png": "f^{\\prime}(0)<0,f^{\\prime}(1)>0", + "8395a6228fb143d9.png": "P(E_{\\gamma},\\theta)\\rightarrow1", + "839a6ad8f20682ad.png": "Q=-10log_{10}P", + "839ac467093ae787.png": "2P_{\\frac{1}{2}}", + "839c642e9da0d8d0.png": "|\\psi(t)\\rangle=U(t)|\\psi(0)\\rangle", + "83abd56ea004ae15.png": "3=2^{m/2n}", + "83b2992d74d08bee.png": "\\tau_{t}^{s}\\dot{\\gamma}(s)=\\dot{\\gamma}(t)", + "83b5d4d6c6dbfa8a.png": "P=\\frac{1}{3}\\frac{U}{V}", + "83c9e649e28c0888.png": "ch(E)=\\sum e^{\\eta_{i}}", + "83d11baad823cf78.png": "a_{1}\\equiv a_{2}(modn)", + "83dd7c9c8f3bcf38.png": "20-\\frac{\\sum_{i=1}^{19}i^{n}}{20^{n}}", + "83df5282a5e91a96.png": "a_{||m}=(a\\cdot m)m^{-1}", + "83e1d65a3fbfcc9f.png": "-1+j0", + "83e99eac18cd0f31.png": "(\\delta^{k}F)(0)", + "83e9ea5145ad5954.png": "V=\\frac{IC_{l}}{PIC_{ij}(l)}", + "83eabfa53b0984b3.png": "P=\\frac{1}{3}\\frac{U}{V}", + "83edd9847099abd7.png": "\\frac{\\partial u}{\\partial\\tau}=\\frac{1}{2}\\sigma^{2}\\frac{\\partial^{2}u}{\\partial x^{2}}", + "83fd0dab05359c1a.png": "0,1,3,7,15,...", + "83ff54276992e59c.png": "H_{\\omega+1}(1)-1", + "8408e549c17c971d.png": "2Rsin(\\frac{a}{2})", + "840be764015c1189.png": "1+t=625t^{2}", + "840cf745e2a1b6f3.png": "a\\notin\\{0,1\\}", + "840ea36086401544.png": "m=\\hat{m}S^{-1}", + "841cdb6439bdd0a2.png": "\\frac{\\partial f}{\\partial{x^{\\prime}}^{i}}=\\frac{\\partial f}{\\partial x^{j}}\\frac{\\partial x^{j}}{\\partial{x^{\\prime}}^{i}}", + "841ff12755432c88.png": "c_{3,1}(\\hat{a},w(\\hat{\\epsilon},\\hat{b}c),\\hat{d})", + "84238ee9c2ef4377.png": "h=\\frac{6r^{2}}{r^{2}-9}", + "842a20981ab96673.png": "\\frac{hL(P-U)}{2PU}+\\frac{S}{L}", + "8430c60ee3585847.png": "\\frac{F_{p}}{F_{s}}=\\frac{M_{p}\\cdot d_{s}^{2}}{M_{s}\\cdot d_{p}^{2}}", + "843156b0ccb7273c.png": "x=f^{k}(y)", + "8465a0ffde7a2cbd.png": "F(x,w)", + "84664c9a231927a8.png": "C_{X}=C_{Y}=[0,1]", + "846754dfc8b16bf5.png": "\\mu^{-1}([\\epsilon,\\infty))", + "84786f8ce1c2cdbd.png": "\\alpha^{\\prime},\\alpha^{\\prime\\prime}\\in\\Phi^{+}(\\gamma)", + "8489b8a58f2dcdea.png": "L(G)=\\{a^{*}b^{*}c^{*}\\}", + "848a5735428e5e71.png": "(X,Y,Z,Z^{2},Z^{3})", + "8496f49f8334bf34.png": "(h,q^{n}-1)=1", + "8498a16776d3c2fc.png": "\\Sigma_{u}\\lfloor qu/p\\rfloor", + "84a58f23024197c7.png": "(\\begin{matrix}cos2\\theta&sin2\\theta\\\\ sin2\\theta&-cos2\\theta\\end{matrix})", + "84a66e55b53287c0.png": "s)", + "84a79143d07c97c7.png": "\\sum_{n=1}^{m}(a_{n}+|a_{n}|)", + "84b70cf2c6f1b094.png": "n_{Io}-2\\cdot n_{Eu}=0", + "84b8e283673cce2f.png": "\\frac{n}{m}+2m-10", + "85f7bb58125c3b11.png": "n^{x}+1>e", + "85fbaa06a3749fda.png": "Xe_{i}=\\lambda_{i}e_{i}+\\cdot\\cdot\\cdot", + "860b73b9da20a640.png": "\\sigma_{D}^{2}=\\frac{kT_{D}}{m_{D}}", + "8611e1d8aa844005.png": "E_{n_{1},n_{2}}^{(0)}", + "8616c435e2583bb8.png": "U_{p}=\\frac{F^{2}}{4\\omega^{2}}", + "8617ecb65be1d145.png": "t_{ik}=\\sum_{j}c_{ij}c_{jk}", + "862fd348fac5b039.png": "\\underline{T}(t)=\\frac{d\\gamma}{dt}", + "8635ca4589e37e4a.png": "W_{m}H^{k}(X;C)", + "86467d979ffb251f.png": "(z_{1it},...,z_{kit})^{T}", + "8655b0d19c4ed607.png": "\\psi\\mapsto e^{i\\epsilon^{IJ}(x)\\sigma_{IJ}}\\psi", + "866a27285ae6dff2.png": "(exp(M_{t}/2))_{t\\ge0}", + "8678796f3af5383c.png": "\\langle A_{\\alpha}:\\alpha<\\omega_{2}\\rangle", + "868e44bb8d050074.png": "K_{x}Na_{1-x}Cl", + "8694b52961bb5366.png": "(P+|P|)=0", + "869d940e237d001b.png": "\\dot{J}(t,t^{\\prime})", + "86a1aa83520bb4a2.png": "\\lambda\\gamma(\\sum_{g=1}^{G}||w_{g}||_{2})", + "86a7930a9ca85b4e.png": "Lu=u|_{\\Omega\\\\ \\omega}", + "86abe79ff6a65a14.png": "H^{*}(g)", + "86b1d977157442ef.png": "v_{1}(\\frac{1}{2})=v_{2}(\\frac{1}{2})", + "86c2ccf4ec72fc40.png": "\\{\\begin{matrix}q,p\\\\ r,s\\end{matrix}\\}", + "86c5d509efa29816.png": "\\overline{x}_{n+1}", + "86d843d46ed0d2ea.png": "y=x(n^{x}-1)", + "86dd32e0e8bda8e8.png": "T^{1}(R)\\subset G(p,1)", + "86ea6e6025d8769b.png": "C_{mnl}=\\frac{\\epsilon}{k_{mnl}^{4}V}", + "86ee94f96f425c9a.png": "\\frac{y_{n}}{x_{n}}\\frac{X}{Y}=\\frac{x/x_{n}}{y/y_{n}}", + "870475eb0bdc45f8.png": "10log\\frac{T}{t_{1}}", + "870b01e4feedd585.png": "k=\\omega\\sqrt{LC}=\\frac{\\omega}{u}", + "87169f1ef8ad596c.png": "F(y)=O(\\frac{1}{\\sqrt{y}})", + "871df28de8334e88.png": "\\sum_{a}\\sum_{b}\\frac{1}{|az+b|^{s}}", + "8729228d7b0a56cc.png": "\\frac{d}{dt}(\\frac{dt}{d\\tau})\\approx0", + "8731b9922723d87e.png": "\\Omega([\\rho(R)];\\mu,T)", + "873fa8dfb4a8e067.png": "P(x)=|\\langle x_{0},x\\rangle|^{2}", + "8743f0933ad59b0a.png": "C_{\\frac{1}{2}}", + "8748765789af1546.png": "A=10-20C_{N}", + "8748aba996c7cf8f.png": "v^{2}d\\overline{z}=|v|^{2}dz", + "874c4ce51948e50f.png": "R[t]/t^{n}R[t]", + "875895e9e97bb4f7.png": "X_{2i}\\epsilon R^{Q}", + "876eaf6aa99e56cf.png": "\\forall ij\\mu_{ij}\\in\\{0,1\\}", + "87764d54c518a806.png": "{L_{th}}^{2}=\\frac{D}{\\Sigma_{a,th}}", + "8782e345bb939e27.png": "(-\\infty,0]", + "878af89576585cc4.png": "\\frac{dV_{-}}{dt}=0", + "878fbc8a746f69ca.png": "(x-a)^{2}H(x-a)", + "879196f52f37c6f4.png": "Cl_{1,3}(R)", + "8796988d893d97fd.png": "F_{r}(t)+F_{cr}(t)=0", + "8799666a99413e6f.png": "T^{2},T^{3}", + "87a8118d12797bdd.png": "E=-\\frac{p}{3\\epsilon_{0}}", + "87aa38fdc9d3be37.png": "H_{n}^{(r)}=\\sum_{k=1}^{n}H_{k}^{(r-1)}", + "87aa741734fd0b50.png": "=\\frac{gt}{2v_{x}}", + "87b250fe93cc6d7f.png": "\\sqrt{R}=\\frac{k_{1}-k_{2}}{k_{1}+k_{2}}", + "87b419b307e84350.png": "E[E(f)]", + "87b819231f3fd124.png": "X-B_{k}^{1-\\alpha}", + "87b9171ae2fa9a14.png": "H^{\\dagger}B^{\\mu\\nu}B_{\\mu\\nu}H/\\Lambda^{2}", + "87c8aa4a3761075b.png": "E=\\frac{1}{2}mv^{2}", + "87ca68ca685cbab5.png": "\\frac{dx}{dt}=(x(t-1))^{2}", + "87d09e8a16600722.png": "\\Omega_{Y}^{\\bullet}(logD)\\rightarrow j_{*}\\Omega_{X}^{\\bullet}", + "87d51c290fae774a.png": "x=5+\\frac{14}{x}", + "87d9443541ce0873.png": "(0,1/2)", + "87dc40235ba0255d.png": "\\nabla\\times E=-\\frac{\\partial B}{\\partial t}=0", + "87e2f5168968f331.png": "|V_{0}|\\gg E_{f}", + "87f715c495a3e6a9.png": "2\\pi t/log(t)", + "87fda466366412d2.png": "lim_{t\\rightarrow0^{+}}f(t)^{g(t)}=1", + "88079723f9c4130e.png": "p_{1}/\\pi_{1}\\gamma_{ls}-\\gamma_{sa}>0", + "88814698f59003d9.png": "\\lambda=\\sum_{j}m_{j}deg(f_{j})", + "8887995a7cd94baa.png": "2cos(\\frac{5\\pi}{6})+6=4.3", + "888a320cd8f9c4fd.png": "x=(\\lambda-\\lambda_{0})cos\\varphi_{0}", + "888cac271bdf19d2.png": "L^{0}(F_{T})", + "888d0ad09c71e949.png": "\\Psi_{A}(1,2,...,N_{A})", + "888dd46012321a66.png": "P_{f}(N)", + "889160f2d67496ea.png": "2r\\sqrt{r^{2}-x^{2}}", + "88956e1dfee53f86.png": "B_{y}(t)=-B_{1}sin\\omega t", + "8898d02c9a4870ca.png": "w_{ij}=w_{ji}\\forall i,j", + "88a0630b67b0b18f.png": "|\\frac{d^{2}y}{dx^{2}}|\\approx\\frac{1}{R}", + "88aad69cf504c884.png": "f^{-1}(f(x))=x", + "88abda4af4c7b58c.png": "a^{n}a^{-n}=1", + "88b0f7fe50c4abdd.png": "a_{33}|a_{11}\\cdot a_{22}", + "88c8f543ccbffe66.png": "a^{n}a^{-n}=1", + "88cc9a7ea1134b03.png": "sinc(t):=\\frac{sin\\pi t}{\\pi t}", + "88dfed23291ee382.png": "J_{4}^{T}J_{4}=J_{4}J_{4}^{T}=I_{4}", + "88e0445a2b4ad752.png": "(3)Z(p^{\\infty})", + "88e717c143353860.png": "\\Psi<\\frac{2}{3}", + "88ea572f65f3935b.png": "\\hat{H}\\Psi[\\gamma]=0", + "89146ff7521ca7b8.png": "\\omega_{H}^{2}=\\omega_{p}^{2}+\\omega_{c}^{2}", + "89151813d59c9263.png": "X^{I}\\rightarrow X,\\chi\\mapsto\\chi(0)", + "891c7744ae04eacc.png": "\\nabla_{i}\\varphi=\\frac{\\partial\\varphi}{\\partial x^{i}}", + "89315947cb6f2f04.png": "\\int_{-\\infty}^{+\\infty}Dp^{\\prime}V_{W}^{+}(x;p^{\\prime})", + "89316cb7bda5475d.png": "\\beta_{(s)3}<0", + "8934d899e6beb2b8.png": "F=eEexp(-i\\omega t)", + "893a5f0b9ef0427a.png": "K(x,x_{i})=x_{i}^{T}x", + "893b2c60e3555c0d.png": "(\\theta-\\beta)=\\frac{\\theta H_{k}}{B+H_{k}}", + "8944bd6a6babb660.png": "\\int f_{i}^{\\prime\\prime}(x)f_{j}^{\\prime\\prime}(x)dx", + "894527bd33795766.png": "F=m_{1}m_{2}G/r^{2}", + "894779508f73a6fe.png": "|\\frac{4}{3}|>1", + "894c8460a46bd504.png": "a^{n}a^{-n}=1", + "895688f37a928de8.png": "FF^{\\dagger}=F^{\\dagger}F=I", + "8963372e5270afe5.png": "0,1,...r-1", + "897a5cf1f96bbc44.png": "H_{2}\\rightarrow2H^{+}+2e^{-}", + "8993ca8c87472bea.png": "m_{i,j}=x^{i}\\cdot x^{j}", + "899b9f3efb03f162.png": "\\frac{1}{n_{0}}=\\frac{16}{3}\\frac{\\pi ld^{2}}{4}", + "89a757bfe2bd5963.png": "x_{n}\\in C^{*}(\\theta_{n})", + "89b05c722fae7fb2.png": "\\epsilon_{S}^{v}=\\frac{K_{m}}{K_{m}+S}", + "89b45cce707baaf6.png": "\\partial_{v}f(x)=Df(x)v", + "89d6cd2a9bf1c72c.png": "D_{P}\\\\ G/H", + "89e069d269ac6255.png": "\\pi_{n}X=[S^{n},X]", + "89e2e2e20a6cb0a9.png": "tan(\\theta)=u_{y}/u_{x}", + "89e60e51f2bd3635.png": "a_{t+1}=k_{1}\\frac{a_{t}}{1+k_{2}a_{t}}", + "89edb85436a20515.png": "=J+\\epsilon_{0}\\frac{\\partial E}{\\partial t}", + "89f9b97a8eff8041.png": "\\tilde{G}_{f}(V,\\tilde{E}_{f})", + "8a0173b4d9b1416d.png": "P(E(s),E(s^{\\prime}),T)", + "8a02108f90cc5f39.png": "\\alpha=\\frac{T_{2}-T}{T_{d}-T}", + "8a065517d5b34b61.png": "K_{x}Na_{1-x}Cl", + "8a1159f6b4b29ee4.png": "f(\\vec{a},\\vec{b})=f(\\vec{b},\\vec{a})", + "8a16090d6c5049dc.png": "\\int_{x_{1}}^{x_{s}(t)-\\epsilon}w_{t}dx\\rightarrow0", + "8a1b1cf464e98049.png": "\\varphi(\\theta)=\\frac{1}{2}sin(\\theta)", + "8a2043516d3ec4e8.png": "|Y|=\\sqrt{G^{2}+B^{2}}", + "8a276970b3c8a04b.png": "O_{(\\begin{matrix}-1&1\\\\ 0&-1\\end{matrix})}^{-1}", + "8a2eb7b572e04d0f.png": "\\delta\\omega=(\\omega_{+}-\\omega_{-})", + "8a3472db0d33db5c.png": "f(g)=(gv_{0},v_{0})", + "8a360691094eec56.png": "\\frac{dD}{dt}=\\frac{1}{\\epsilon_{f}}\\frac{d\\epsilon_{p}}{dt}", + "8a36bb0eb339f5ad.png": "T_{j}\\subseteq[t]", + "8a509bb34130fa8d.png": "s=x_{1}+\\dot{x}_{1}=0", + "8a5102d942a6fbc4.png": "\\overline{i}\\equiv I=q\\mu n_{q}EA", + "8a517e771a4dd00c.png": "x=p_{i}(e^{t}-1)", + "8a66f089c942086b.png": "-a^{n}u[-n-1]", + "8a711a26472028aa.png": "\\underline{T}(t)=\\frac{d\\gamma}{dt}", + "8a723f90b084e4fe.png": "G|_{R^{n}}=\\sum_{j=1}^{n-1}e_{j}R_{j}", + "8a82175bb2fb4d72.png": "E_{1}^{\\dagger}E_{2}\\notin Z(S)", + "8a8475746bec613a.png": "c_{i}^{(-n)}", + "8a8c0c300568965e.png": "V_{max}=\\sqrt{2c_{p}T_{t}}", + "8a8db2c7e883dc24.png": "m\\frac{dv}{dt}=10m-kv", + "8a8dbd5387660cfe.png": "J_{k}\\equiv\\oint p_{k}dq_{k}", + "8ab2ce3ef81a2047.png": "J_{\\phi}=D_{\\phi}\\frac{\\partial\\phi}{\\partial x_{i}}", + "8ab44a5a237d40d6.png": "Z_{\\infty}^{p,q}=\\bigcap_{r=0}^{\\infty}Z_{r}^{p,q}", + "8abe44bf08a3fd08.png": "M=\\frac{1}{\\kappa_{1}},N=\\frac{1}{\\kappa_{2}}", + "8acbde0b9af3d5eb.png": "\\zeta_{i}=\\frac{m_{i}}{m_{tot}-m_{i}}", + "8ad5fc73da1dfda9.png": "A=0,B=1", + "8adec7e6e2a354a8.png": "x^{\\prime}=\\sqrt{1-\\frac{v^{2}}{c^{2}}}", + "8ae09871530bfc94.png": "x=10+2\\epsilon_{3}-5\\epsilon_{8}", + "8af900ef4d45d6f1.png": "r_{1}r_{2},...,r_{k}", + "8b09db2513483afa.png": "a_{i\\pm\\frac{1}{2}}", + "8b17ae8a85fe626a.png": "\\delta(q_{s},\\sigma)\\rightarrow q_{t}", + "8b182d16f5940425.png": "1-a_{i}z^{-1}", + "8b24c59ea78069f6.png": "\\phi^{\\prime}(t)\\ne0(t\\in I_{1})", + "8b25176b9b6f4d98.png": "T_{t}=e^{t\\frac{d}{dx}}", + "8b366352f1b00694.png": "f(y)=2+2y+y^{2}", + "8b442a6546476004.png": "\\rho:G\\rightarrow GL(d_{\\rho},C)", + "8b4573463088e5c2.png": "(9.525,10.478)cm", + "8b4886d54fb47ffe.png": "X[(p+m)\\Delta_{F}]", + "8b48ead58604507c.png": "2^{2}+2+1-1", + "8b4bdc276abc97ba.png": "H^{\\dagger}B^{\\mu\\nu}B_{\\mu\\nu}H/\\Lambda^{2}", + "8b5139c9928364ec.png": "\\frac{\\partial^{2}f}{\\partial x\\partial y}=\\frac{\\partial^{2}f}{\\partial y\\partial x}", + "8b57e5a921863cae.png": "\\sigma_{-}^{2}=\\frac{\\sum(m-x)^{2}}{n-1}", + "8b628c2543da6e1a.png": "m=\\Omega(n^{2\\gamma})", + "8b725448dc697d41.png": "\\{B^{(i)}\\}", + "8b92b807e64dddeb.png": "p(y|E(m))", + "8ba60d7df6c05ad2.png": "\\frac{9}{4\\sqrt[3]{2}}", + "8bab5f4851e0a0f5.png": "(\\Omega,F,P,\\vartheta)", + "8baffd90534d782f.png": "\\epsilon={c_{\\mu}}^{3/4}k^{3/2}l^{-1}", + "8bb1fabcd3857925.png": "f_{xx}(a,b)>0", + "8bb55d1f52e21830.png": "e^{-za}M_{X}(z)=\\alpha", + "8bd3fc7f1fe58a74.png": "(((ab)c)d)", + "8bd5ebcb7585f492.png": "-a^{n}u[-n-1]", + "8bd78ac93de37504.png": "\\{L(u,v):u,v\\in X\\}", + "8bd947db4f882534.png": "V_{0}\\oplus W_{0}=V_{-1}", + "8beb2c2006cd41d5.png": "H=\\frac{\\nabla\\psi^{\\dagger}\\nabla\\psi}{2m}", + "8befe8f477b0044f.png": "(-4)^{2k+1}\\equiv1", + "8bf1f986886e1498.png": "(\\frac{3}{F_{n}})=-1", + "8bfe9b44ce828408.png": "i_{*}i^{-1}G", + "8c00751f5fe84a8c.png": "\\frac{n!}{(n-k)!\\cdot k^{n}}=m", + "8c1f32923caf996e.png": "2^{\\frac{n(n-1)}{2}}", + "8c2f065f59174eac.png": "-1=e^{\\frac{2\\pi i}{2}}=e^{\\pi i}", + "8c36df7e3e503154.png": "W=\\int_{t_{1}}^{t_{2}}\\frac{dW}{dt}dt", + "8c379abad4cd7f29.png": "N[(1+K)^{M}-1]", + "8c3cf14eac9c6f06.png": "Q(\\sqrt[2]{2})", + "8c457f6d0dcd8eac.png": "\\Pi(\\sum\\frac{1}{n!})", + "8c4acd151571e39b.png": "n-(p+q)", + "8c53b8263ed8bfec.png": "fg-gf=i(f,g)", + "8c56a6666851bd9a.png": "Y=\\beta T_{8}+IX", + "8c579c0706006835.png": "A^{\\prime}=PAP^{-1}", + "8c5f189ed65b6260.png": "p(X,A|\\theta^{*})", + "8c5faee334b8b32b.png": "\\frac{R^{2}}{2}(\\theta-sin\\theta)", + "8c6b39bffab9c39c.png": "(0)(x^{2}+1)=0", + "8c6d7ccfc92152bc.png": "B=\\frac{\\mu_{0}I_{enc}}{2L}", + "8c6e8a88591deccb.png": "2sin(\\frac{108^{\\circ}}{2})=\\phi", + "8c79e3714196f6f0.png": "2^{2}+2+1-1", + "8c858f5da323e75f.png": "E[X]:=\\rho(-X)", + "8c89ce5e1e815a80.png": "A_{p}(\\kappa)=\\frac{I_{p/2}(\\kappa)}{I_{p/2-1}(\\kappa)}", + "8c90a0180370a07f.png": "a_{i}=\\langle\\tilde{\\Psi}|T^{\\dagger}\\hat{A}T|\\tilde{\\Psi}\\rangle", + "8c90aee7fc01dda2.png": "(a/a/a)/3:2", + "8c9ee8b75357854d.png": "3^{(F_{n}-1)/2}", + "8c9f94e8364e5920.png": "B_{k_{1}}^{\\alpha_{1}}\\cap...\\cap B_{k_{r}}^{\\alpha_{r}}", + "8cb0b205f4d9ff6f.png": "n=(\\begin{matrix}2r-1\\\\ 2\\end{matrix})", + "8cb1ae76fcf63532.png": "(S\\rightarrow S^{\\prime})", + "8cbe3f95c4e5d5f1.png": "v=A(1-e^{Bt})", + "8cc29e43253a846d.png": "I_{S^{i,z}}[f_{S^{i,z}}", + "8cc51f1d6afe2fd0.png": "\\{a^{n}b^{n}|n\\ge1\\}", + "8cd8fb22d03491da.png": "Z_{i,j}Z_{k,l}=Z_{i,l}Z_{k,j}", + "8ce48764d7befd66.png": "1\\le a_{\\mu(i)}d_{c}", + "8dcd795d528bb691.png": "\\partial_{v}f(x)=Df(x)v", + "8dd2bf0ae0d0c6fc.png": "E_{4}(x)\\propto E_{3}^{*}(x)", + "8dd3cf816fcd5934.png": "|V_{0}|+n/4^{k}", + "8dde60c651bc53af.png": "u_{1}=[\\begin{matrix}1\\\\ -i\\end{matrix}]", + "8de26247f3daaee4.png": "E=\\int\\vec{F}\\cdot\\vec{dx}", + "8df07bb647309a18.png": "\\frac{e^{4\\pi\\sqrt{n}}}{\\sqrt{2}n^{3/4}}", + "8df2897c0f8798b9.png": "\\frac{d^{2}\\theta}{dt^{2}}+1=0", + "8dfc74d40549044c.png": "0,1mod4", + "8e02dca6bed224fc.png": "\\pi^{\\prime}\\alpha>-1.6", + "8ece041da6dff6ec.png": "\\lfloor\\frac{i-1}{2}\\rfloor", + "8ed7bdbc72740357.png": "I\\Delta_{0}+exp", + "8efc86a85232c131.png": "(a_{1},a_{2},...,a_{n})", + "8f0b901087ee35d9.png": "\\sigma^{2}*(X^{\\prime}X)^{-1}", + "8f130b22ccd5acbd.png": "\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}-\\frac{z^{2}}{c^{2}}=0", + "8f139881daf406fa.png": "r^{(m)}(k)\\rightarrow r(k)", + "8f1c55aeba754e3e.png": "(E)-(G)-(H)", + "8f23bbf4f8a7f847.png": "E_{1},(E_{2}-E_{1}),...", + "8f3309e6ce8fea68.png": "w\\Vdash(A\\wedge B)[e]", + "8f4b5939ec5ab3f3.png": "1\\le p<\\infty,c\\in R", + "8f4e684129ae195e.png": "(x_{i},y_{j};x_{i+1},y_{j+1})", + "8f584844618e111e.png": "E(x_{i})=0", + "8f659003f2239741.png": "\\tau=inf\\{t>0:X(t)<0\\}", + "8f67e4b29c453b18.png": "Q_{Hur}^{1}(I)", + "8f6803ca508205f6.png": "Z(s)=\\frac{|Z|}{z_{11}}", + "8f7973b8a28cfbe2.png": "\\sum k^{3}={(\\begin{matrix}n+1\\\\ 2\\end{matrix})}^{2}", + "8f7d685c8fc55533.png": "\\nabla_{\\vec{\\theta}}=D_{d}\\nabla", + "8f7eca44f0a34b84.png": "\\pi=\\sqrt{10})", + "8f856771dc39c152.png": "R\\ge(2^{a-1}-1)", + "8f86c7afd1d3930f.png": "c_{j}=\\frac{c_{j-1}^{2}}{4a_{j}}", + "8f87467f18e1fa9a.png": "y=e^{lnx+\\frac{1}{2}x^{2}-\\frac{1}{2}}", + "8f884084d6e1362f.png": "\\hat{x}_{0|0}=[\\begin{matrix}0\\\\ 0\\end{matrix}]", + "8f9275a7bda0e1be.png": "|\\begin{matrix}A&B/2\\\\ B/2&C\\end{matrix}|", + "8f9c06c8c4a1ccfb.png": "F_{ii}F_{jj}-F_{ij}^{2}\\ge0", + "8fac1b4fe434c126.png": "G=\\oplus_{i}C_{d_{i}}", + "8fb3365612634b71.png": "|\\Omega^{-1}-1|", + "8fbb06b4ba5566c0.png": "[\\Gamma L,\\Gamma L]\\subset\\Gamma L", + "8fbbd0a424ffac4f.png": "T^{-}", + "8fc1b7ba01ed8b8e.png": "\\frac{1}{|G|}\\sum_{g\\in G}|(Y^{X})_{\\omega,g}|", + "8fc9ba71b6f1ac01.png": "0=f_{N}(s)", + "8fd9666cedcc32cd.png": "(\\Lambda(A):A\\in B_{b}(S))", + "8fdc8475c96c99f8.png": "\\langle G,S\\rangle\\rightarrow\\langle G^{\\prime},S^{\\prime}\\rangle", + "8fe159f4d5f35671.png": "H^{\\prime}|\\psi_{+}\\rangle=E_{+}|\\psi_{+}\\rangle", + "8fe5f245e58b01b5.png": "|y-\\rangle", + "8ffd7003f7e9e16f.png": "e(M)\\in H^{4}(M;Z_{2})", + "8ffe3505c86609b8.png": "J_{f}=(\\begin{matrix}2x&3y^{2}\\\\ 2x&-3y^{2}\\end{matrix})", + "900c1931460b764e.png": "E[c]=c", + "9016b83d2247dc6e.png": "1-4\\pi r^{3}/3V", + "9022e7298f19da56.png": "\\prod_{x}ax=Ca^{x}\\Gamma(x)", + "902f586b357b9ded.png": "m_{i}=[p_{i_{1}},...,p_{i_{k(i)}}]", + "903119dae7988d43.png": "I=C(dV/dT)", + "90320c048bb19cfb.png": "\\frac{q}{A}=h_{o}(T_{o}-T_{s})", + "90363fdf8c8e1c63.png": "\\nu=\\Gamma-\\lambda ln(p^{\\prime})", + "904bc8d486b2673c.png": "\\frac{b}{sin\\theta}=\\frac{r}{sin(\\frac{\\pi-\\theta}{2})}", + "90597f8677326d97.png": "\\frac{100}{0.96}", + "905a756c30ad12dd.png": "(x_{i},y_{j};x_{i+1},y_{j+1})", + "9061609183d17b5e.png": "(\\frac{3}{F_{n}})=-1", + "9070f9517370606b.png": "lim_{x\\rightarrow0}\\frac{f(x)}{g(x)}=\\frac{3}{2}", + "90763c1bc0ee11f7.png": "0=\\hat{x}_{1}-x_{1}", + "907d56a8b4aa143f.png": "0^{2}+0^{2}=1", + "907e557cf69cb93c.png": "(7)\\hat{B}_{ab}:=\\nabla_{b}k_{a}", + "907fbdc695734261.png": "x_{t}=1/(\\eta+w_{t})", + "90893a90ff824474.png": "D_{N}=A_{N}-A_{N/2}", + "908a75a9eb2c14ca.png": "\\gamma_{i}={\\phi_{i}}^{2}", + "908ee7e72b5f8097.png": "C_{D,0}=C_{fe}\\frac{S_{wet}}{S_{ref}}", + "90a9d0052f669cde.png": "\\frac{(n-2)\\pi}{n}", + "90bbe1df4e161164.png": "\\frac{d^{2}\\psi_{1}}{dx^{2}}=\\alpha^{2}\\psi_{1}", + "90c7deed08bc72ab.png": "J_{N(t)}\\le t0", + "93c67ddc15a82f47.png": "\\frac{logx}{x^{c}}<1", + "93cba47ac358d85c.png": "distance=tan(\\theta)\\frac{v}{u}", + "93d7e797674b5bff.png": "C_{4,n}=1+4T_{n-1}", + "93d84b7eed4044f5.png": "A\\cong k[[x_{1},...,x_{d}]]", + "93e973638a5265f9.png": "3=1+1+1", + "93ff45607e152215.png": "\\frac{d}{d\\tau}(Ie^{-\\tau/\\mu})", + "9411995d42ea93db.png": "H_{\\frac{1}{2},2}=4-\\frac{\\pi^{2}}{3}", + "942388fb39984cd4.png": ".d_{1}d_{2}...d_{n}0111...", + "943d8002b7ebbd6f.png": "[\\begin{matrix}a&b\\\\ c&d\\end{matrix}]\\rightarrow[\\begin{matrix}d&b\\\\ c&a\\end{matrix}]", + "943e1a85e9896ff4.png": "(x^{2}+y^{2})^{2}=ax^{2}y", + "9441ef1c0539de7e.png": "C\\rightarrow(B)_{k}^{A}", + "94530d725458d63e.png": "P[S_{0}=k]", + "94649d8980127ea4.png": "\\frac{v^{-\\frac{x^{5}}{5\\sigma^{5}}}}{\\sqrt{5\\tau}\\sigma}", + "9465325ebfa85850.png": "|\\phi_{i+1}\\rangle=G_{i}V|\\phi_{i}\\rangle", + "9465ba134929cdf3.png": "(a/l)(\\nu/\\omega_{0})", + "946d9d0d635a5f6b.png": "\\{x\\}=\\{X\\}e^{i\\omega t}", + "947751aa8aea8950.png": "u^{\\pm i}\\rightarrow e^{\\pm i\\phi}u^{\\pm i}", + "948609862033e3ec.png": "f^{n-1}(\\perp)\\sqsubseteq f^{n}(\\perp)", + "9488a322f94618d9.png": "\\alpha(f(0),f^{\\prime}(0))=1", + "9489719aaab3b81d.png": "A_{1}(f),...,A_{n}(f)", + "949f680a50d2c4a3.png": "E_{1},(E_{2}-E_{1}),...", + "94a05e1c5a9bc311.png": "\\tilde{p}(x)=n/N", + "94a6855a63095848.png": "\\{C(a,b),c,d,e\\}", + "94a810dfab55a252.png": "\\overline{n}=ne^{m\\pi/a}", + "94b52ffcd1fa9c37.png": "(\\frac{\\partial S}{\\partial T})_{P}=\\frac{C_{P}}{T}", + "94b71c97f1e2c4a0.png": "\\alpha_{0}n_{h}J(r)=\\frac{3S_{*}}{4\\pi r^{3}}", + "94d900cc2dc7e5af.png": "(\\begin{matrix}\\mu_{1}&\\mu_{2}&\\gamma\\\\ \\nu_{1}&\\nu_{2}&\\nu\\end{matrix})", + "94dc92c349452558.png": "A^{+}=(A^{*}A)^{+}A^{*}", + "94dfbf86bff17d2c.png": "P(\\overline{C_{1}},\\overline{S_{1}})d\\overline{C_{1}}d\\overline{S_{1}}", + "94ea360f30cd89ff.png": "\\frac{p_{02}-p_{01}}{\\rho u^{2}}", + "94ebc4cfc04c395b.png": "|\\Phi_{\\alpha_{1}}^{[2..N]}\\rangle", + "94f1ddf049c4fea5.png": "<1", + "9500c67ed201fb7a.png": "4sin^{2}(\\pi/10)", + "950b73924d2fe1fb.png": "\\frac{n-5\\pm\\Delta_{n}}{2-2n}", + "950d4d936f8f25d6.png": "\\hat{G}_{X}<1", + "951664816e056daa.png": "O(\\frac{d}{\\epsilon}log\\frac{d}{\\epsilon})", + "951a945225429315.png": "\\hat{H}=-m\\cdot B(t)", + "952aabf23e0814a6.png": "\\Delta S=\\Delta S^{\\prime}+\\Delta S^{\\prime\\prime}", + "95335cb858e8b6c1.png": "\\sqrt{a}\\cdot\\sqrt{b}=\\sqrt{a\\cdot b}", + "953a6ed9026cd9e7.png": "\\lambda(y_{i})(b,x)", + "96a81c4bea644f61.png": "logB\\in i[-\\pi,\\pi)", + "96aa535bed99ee8b.png": "2^{-1/4}\\approx0.841", + "96ad5eb8a3df5932.png": "B^{*}=\\{v^{i}\\}_{i\\in I}", + "96b01012f2053266.png": "\\int_{0}^{\\pi}x^{n}sin(x)dx", + "96b03333d786965e.png": "\\prod_{i=1}^{N^{2}}\\int_{R_{i}}\\Psi dA", + "96b5f1b5599036ab.png": "F_{ii}F_{jj}-F_{ij}^{2}\\ge0", + "96b97f42e948bd93.png": "-\\phi(-x)R(\\pi)\\phi(x)", + "96c32e6fc4efca48.png": "U=TS+\\frac{1}{2}\\sigma_{ij}\\epsilon_{ij}", + "96c4be9599ce5249.png": "X_{n}=\\sum_{v\\in T_{n}}1_{v\\in K}", + "96c6fe3075265a0f.png": "m=\\frac{5}{2}+\\frac{3}{\\gamma_{2}}", + "96d32c547704f664.png": "r=\\frac{1+i}{1+p}-1", + "96d6c0610c7c8545.png": "\\langle m|n\\rangle=\\delta_{mn}", + "96e6154ef6d6af72.png": "Li_{1}(\\frac{1}{2})=ln2", + "96f4dee2b838f616.png": "\\{\\begin{matrix}q,p\\\\ r,s\\end{matrix}\\}", + "970587856f3878cf.png": "J=A_{G}T^{2}e^{\\frac{-W}{kT}}", + "970b5469e746f0cd.png": "I_{K}(m_{K})/H_{K}", + "9710c394c5f86024.png": "\\phi_{0}(x)=f(x)", + "971451aaaeafe6f9.png": "b_{0}=\\frac{n_{0}}{n_{0}M_{0}}=M_{0}^{-1}", + "971ce0a5b65a9110.png": "C_{\\frac{1}{2}}", + "9724070beb5777b0.png": "1:\\frac{1+\\sqrt{5}}{2}", + "9724b9c3a2c459f2.png": "L^{1,\\infty}(H)", + "972650f93fe0d5f4.png": "E(X_{i})=\\frac{nK_{i}}{N}", + "973c154d38aaf7a2.png": "\\beta_{max}=(\\frac{R^{2}}{PQ})^{\\frac{1}{3}}", + "973c56753803f764.png": "(\\sigma^{2},\\nu,\\gamma)", + "97489c02025ab4e9.png": "(90^{\\circ}-z)", + "974bd7b1fa390c1a.png": "\\sum_{\\gamma\\in\\Gamma}n_{\\gamma}t^{\\gamma}", + "975277f0b4bff3af.png": "r^{2}+d^{2}=(r+h)^{2}", + "9756723885897ee8.png": "c_{i}^{2}\\sim\\chi_{n-i+1}^{2}", + "975778506f2a75ad.png": "[\\Gamma L,\\Gamma L]\\subset\\Gamma L", + "97816e187258528a.png": "Bm=\\frac{\\tau_{y}L}{\\mu V}", + "9794f7d721be5e0d.png": "S=\\{(0,1),(1,0)\\}", + "97a1189bcb01b7e3.png": "\\overline{n}=ne^{m\\pi/a}", + "97a6b973aedbe55a.png": "B_{\\mu\\nu}-B_{\\mu\\nu}^{(0)}", + "97ab753a068ce23e.png": "V_{t}=a_{0}\\cdot M\\sqrt{\\frac{T}{T_{0}}}", + "97bafd782c04c4d9.png": "(1+sin\\theta)", + "97c9e25d391339de.png": "p_{D}=\\overline{D}-D(\\overline{\\theta})", + "97cb2eb2d0cb894a.png": "(\\lambda,\\lambda+2\\rho)", + "97ce62183f38da1a.png": "ds^{2}=\\lambda^{2}(z,\\overline{z})dzd\\overline{z}", + "97d080f22bcdcc5d.png": "H_{1}=-\\vec{d}\\cdot\\vec{E}", + "97d2e818d52f304e.png": "\\eta=1-\\frac{1}{r_{v}^{\\gamma-1}}", + "97e1bcc7c93887aa.png": "\\delta V^{ext}(t)", + "97e3613b3e732012.png": "[\\dot{\\Omega}]=[\\begin{matrix}0&-\\alpha\\\\ \\alpha&0\\end{matrix}]", + "97f6240b89c8f5eb.png": "0\\frac{q}{2}", + "99062d0ecbe91a35.png": "(236c)^{11}", + "990c0bf69d69a0c7.png": "O_{T^{\\prime}}\\rightarrow f_{*}O_{T}", + "99127e5a69af6bad.png": "V_{T-j+1}(k)", + "9918efdf56bf9ee7.png": "(AB)^{\\dagger}=B^{\\dagger}A^{\\dagger}", + "99211c5143661844.png": "\\prod_{p}p/(p-1)", + "9923cd1658b53395.png": "En=\\{0,1,2,...,n\\}", + "99305fe3225bee38.png": "\\sum_{k=n}^{N(n)}\\alpha(n)_{k}=1", + "99356256aaa7cdfd.png": "(\\omega_{1},0,\\omega_{0}+\\omega_{r}/2)", + "9936b7c2d79763ca.png": "BG_{m}\\rightarrow P^{N}", + "9949a2b3d9a524fc.png": "\\vec{p}_{f1},\\vec{p}_{f2}", + "994ff8e299c69909.png": "f(x^{\\prime};s)\\ge f(x;s)", + "9977cd070adbcdeb.png": "e^{-t}\\ge1-t", + "9991e638df09f495.png": "P(\\theta|D,M1)", + "9995d3cb8565bf83.png": "|h|^{\\frac{1}{2}}=r_{0}^{2}sin\\theta", + "99a862440bb3787f.png": "\\hat{y}=\\hat{\\alpha}+\\hat{\\beta}x", + "99a8b1d5619d801f.png": "(\\hat{b}^{\\dagger})", + "99ae18602c195843.png": "\\int_{X}^{\\oplus}H_{x}d\\mu(x)", + "99b19cc13147a1ec.png": "2^{n}sin\\frac{x}{2^{n}}", + "99bac62954389725.png": "(-4)^{2k+1}\\equiv1", + "99be759f52801bb1.png": "p(z)=cosh(z)-1", + "99bea7b7e11c1382.png": "2^{S}", + "99d5dcc8cf2002fc.png": "(By+\\beta)^{n}-B^{n}y^{n}", + "99e271ada452ec85.png": "\\bigcup_{n\\in F}(S-n)=N", + "99e34a9f04e80311.png": "E\\le O(V^{\\frac{16}{15}-\\epsilon})", + "99e703cbd3300328.png": "du_{o}/ds(s)<0", + "99f519bdc5f57f62.png": "\\overline{\\nabla}_{X}Y=\\nabla_{X}Y", + "99f6f79b53b2b224.png": "\\mu\\in P(R^{k})", + "9a0134aa1c5e14bb.png": "0.5=E[X_{1}]", + "9a065a758ef748fb.png": "\\Gamma(\\frac{1}{4})/\\pi^{1/4}", + "9a0777d3d86f78fb.png": "1+x+\\frac{x^{2}}{2}", + "9a2c21610ecd284b.png": "\\frac{P_{f}}{P_{f}^{a}P_{m}^{1-a}}=\\theta", + "9a3187492a0cba3e.png": "[,,]", + "9a34c43f42a118bc.png": "\\langle\\Psi,s\\rangle=\\langle\\Psi,s^{\\prime}\\rangle", + "9a3e94cceb77f0bf.png": "|y|\\in O(|x|^{k})", + "9a3ebe0c0feb25cd.png": "\\tilde{F}_{\\mu\\nu}\\tilde{F}^{\\mu\\nu}=F_{\\mu\\nu}F^{\\mu\\nu}", + "9a50c6406e4a82df.png": "C_{\\Psi}=\\frac{16}{5}\\sqrt{\\pi}", + "9a5378f877bd33f7.png": "T^{j}f=f(\\cdot+j)", + "9a6f0bcce7487642.png": "\\overline{\\Psi_{0}}=\\sqrt{\\frac{m}{\\pi}}e", + "9a8673d1409e8b33.png": "(\\frac{a}{p})\\sum_{t=1}^{p-1}(\\frac{t}{p})\\zeta_{p}^{t}", + "9a92ef2268d40db1.png": "\\overline{R}=\\frac{1}{n}\\sum_{i=1}^{n}R_{i}", + "9a9340bc1ff9c3e5.png": "f^{\\mu}=x^{\\mu}L", + "9a9584bbd0bd0981.png": "A=k[[t^{a},t^{b}]]", + "9a9d0200279731c8.png": "\\prod_{k=1}^{\\infty}\\frac{1}{1-x^{k}}", + "9a9ed330d1fab3a2.png": "U(x_{0},t)", + "9aa90e90589fa9dc.png": "\\sum(-1)^{n}(lnlnn)^{-1}", + "9ab1bcba2102c6e2.png": "0=[\\tilde{L}]_{\\times}X", + "9ab2d7b4240c9750.png": "xN_{2}z\\phi_{1}=N_{1}\\phi_{2}z", + "9aba8dfe3d32589f.png": "\\psi^{[-1]}", + "9ac87b8bf7c6289c.png": "0<\\varphi n0", + "9ee5c334314b309b.png": "D^{*}=(\\mu^{*}E)^{2}\\frac{(\\delta t)^{2}}{16t_{0}}", + "9eeee93e6b34e55e.png": "\\delta V^{ext}(t)", + "9eef592e02b68ca3.png": "S[\\sigma]\\rightarrow T[\\sigma]V^{\\prime}[\\sigma]", + "9efe9635c703fc87.png": "BD=2x-\\frac{x}{4}q^{2}", + "9f116ccb240bbd34.png": "2,2+it", + "9f1cbcd3fd831d89.png": "A=0,B=1", + "9f3431d2037d413b.png": "D=\\epsilon_{0}E,B=\\mu_{0}H", + "9f36dd4a442fcec3.png": "P(x)=|\\langle x_{0},x\\rangle|^{2}", + "9f4c8318c686afc7.png": "\\forall x\\in R\\cup\\{-\\infty\\}", + "9f687a8742be5683.png": "uv=-\\frac{1}{3}p", + "9f68b1e0fe28b718.png": "O(klogk2^{O(log^{*}k)})", + "9f6b03932463060a.png": "(x_{n})_{n\\in N},x_{n}\\in K", + "9f6b52d017af0ac9.png": "P_{\\theta}(S(X)\\ge\\gamma)", + "9f9694caba630a25.png": "V_{100}-V_{0}=kV_{0}", + "9fb0e08030917326.png": "S_{2}=V_{0}sin(\\omega t-\\pi)", + "9fb85dbd5e24233d.png": "\\frac{d^{2}x}{dt^{2}}+\\frac{k}{m}x=0", + "9fbe022f9132d1d0.png": "\\epsilon,\\delta,K>0", + "9fc78b094828eae2.png": "\\Phi_{lm}=\\vec{r}\\times\\nabla Y_{lm}", + "9fcbb42df8aebd70.png": "H_{0}:\\hat{\\rho}_{XY\\cdot Z}=0", + "9fcfbc4fcb6cc443.png": "1,2,...n", + "9fe8f6c3584010a4.png": "(\\begin{matrix}1\\\\ \\frac{c}{\\rho}\\end{matrix}),(\\begin{matrix}1\\\\ -\\frac{c}{\\rho}\\end{matrix})", + "9feea5dd16576044.png": "x^{\\prime\\prime}=RxR^{-1}", + "9fef285d4b875ad8.png": "A/m=k", + "a002f1c2e51f34f8.png": "||\\varphi_{n}-\\varphi_{m}||_{d}<\\epsilon", + "a00546260e4537ef.png": "x^{\\prime\\prime}\\in D(p,w^{\\prime\\prime})", + "a00be8cc5fb8a903.png": "cdf_{y}(i)=iK", + "a00c5fa6b4ef6cf9.png": "\\upsilon_{in}=\\upsilon_{s}\\frac{R_{in}}{R_{S}+R_{in}}", + "a0140fe72cb405e7.png": "G=\\frac{2V}{j\\cdot1V}=-2j", + "a017d0106b4b9387.png": "|g,n\\rangle\\rightarrow|e,n-1\\rangle", + "a017ff3c82cd4b41.png": "X=|X|e^{jarg(X)}", + "a026fcad661f2155.png": "(X,A,\\mu,T)", + "a0277971369e2057.png": "(-1)^{x}", + "a028470336240d04.png": "E(S)=a_{1}M", + "a0355265f46ff0a3.png": "A()\\rightarrow aA()", + "a03c036fbc20f148.png": "E[F_{6}]=4", + "a03ef44cf397c55f.png": "X_{2},X_{2},X_{3}+aX_{4}", + "a04d06ef1907f60b.png": "|\\phi_{i+1}\\rangle=G_{i}V|\\phi_{i}\\rangle", + "a05e897df43aa1d4.png": "t^{\\prime}\\rightarrow\\tau=t-t^{\\prime}", + "a064a07253e1d34c.png": "A_{p}(\\kappa)=\\frac{I_{p/2}(\\kappa)}{I_{p/2-1}(\\kappa)}", + "a07e0a1d31332c6a.png": "H=\\frac{1}{N}+NV", + "a0810bc13068ca97.png": "\\Lambda_{0}^{0}=\\Lambda_{1}^{1}=cosh\\phi", + "a087033802d3e4f0.png": "P_{F}=\\sqrt{P_{P}\\cdot P_{L}}", + "a0a2aa6f452138ad.png": "SL_{4}/\\mu_{2}\\cong SO_{6}", + "a0a473cad64befa0.png": "A_{12}\\in R^{1\\times(n-1)}", + "a0a705bae43b3970.png": "2^{-1/4}\\approx0.841", + "a0b56738e5cec28a.png": "q-q_{i}=deg(v_{i})", + "a0c22d10e625feb1.png": "I=|U(P_{1})|^{2}", + "a0c66eaee3bda0f3.png": "W(\\cdot)\\equiv\\frac{f(\\cdot)}{f_{*}(\\cdot)}", + "a0c68a37e06c2b59.png": "J(f)\\le+\\infty", + "a0ca5bbb2e009e26.png": "x,\\dot{x},...,x^{(n)}", + "a0d2f40e88d31bf4.png": "\\frac{M-2G}{2M-2G}", + "a0dd2185ab93cdb9.png": "cos3\\theta=\\frac{3\\sqrt{3}}{2}\\frac{I_{3}^{\\prime}}{I_{2}^{\\prime\\frac{3}{2}}}", + "a0ddaca3f7fd092d.png": "\\overline{16}", + "a0e6cf50e5980169.png": "f^{(n)}(x)=\\frac{d^{n}f}{dx^{n}}", + "a0e6d2049ef41a18.png": "\\frac{1}{n_{0}}=\\frac{16}{3}\\frac{\\pi ld^{2}}{4}", + "a0ea03053a0539c0.png": "\\frac{\\nu_{a}\\nu_{p}}{\\nu_{0}^{2}}=1+2\\hat{\\alpha}\\beta^{2}", + "a0ea52913aeec96b.png": "p_{n+1}=2+\\sum_{i=1}^{n}g_{i}", + "a0eaf32131007e3f.png": "(H_{n})_{ij}=m_{i+j}", + "a0ebfcb601d42f14.png": "F^{3}(\\hat{f})=f", + "a0ed817b5aaecded.png": "sup_{t}|G_{n}(t)|", + "a0ee2d04be6a06f8.png": "V=\\frac{n_{d}-1}{n_{F}-n_{C}}", + "a0fa9411d78bd5ea.png": "||D_{n}||_{L^{1}}=O(logn)", + "a1024d97678d528a.png": "u_{2}^{\\prime}:=u_{2}-u_{1}", + "a11e6e32a6cda2bd.png": "P(x)=|\\langle x_{0},x\\rangle|^{2}", + "a12627ace5fcf585.png": "I_{B}<(b,x)", + "a4db608a807d90f5.png": "\\{\\begin{matrix}p\\\\ q,r,s\\end{matrix}\\}", + "a4dd0e2440ea41ce.png": "v_{p}=\\langle v\\rangle\\sqrt{\\pi}/2", + "a4e165c28ef8b7b8.png": "x=\\frac{i}{f}=\\frac{S}{f}\\sqrt{t}", + "a4e1dba06b4a09a7.png": "\\sum_{j}M_{j-1}^{*}/M_{j}^{*}=\\infty", + "a4e97ecb6eb6136a.png": "(-1)^{|a_{\\pi}|}", + "a4ee550108d4e689.png": "I\\propto\\frac{1}{r^{n-1}}", + "a4f6653ec2ef3cd1.png": "\\langle\\psi_{f}|\\psi_{i}\\rangle\\ll1", + "a5027e80d841e035.png": "WA_{k}=TH_{k}*FF", + "a51fab3b08bd4ccd.png": "\\eta_{k}(k=1,...,K)", + "a532bd1d433a36d7.png": "i_{*}i^{-1}G", + "a53b5eea9b0797d0.png": "[\\begin{matrix}1&\\lambda D\\\\ 0&1\\end{matrix}]", + "a5414fcd9e87020b.png": "\\langle A\\rangle_{\\psi}=||A\\psi||^{2}", + "a544f7dc42e38c84.png": "F:Z[x]\\rightarrow Z[x]", + "a547ba350c24610f.png": "g^{-1}\\mu(A)=\\mu(gA)", + "a572b6fcffdeb081.png": "\\frac{d^{2}\\psi_{2}}{dx^{2}}=-k^{2}\\psi_{2}", + "a582b4b325d6b162.png": "d_{e}(n_{e})=\\frac{c_{e}}{n_{e}}", + "a584061d70dd2922.png": "[\\begin{matrix}a&b&c\\\\ d&e&f\\\\ \\end{matrix}]", + "a5846b72abfc2b60.png": "T_{xuw}(J^{r}\\pi)", + "a596448554156b2c.png": "v_{i}\\in H_{0}^{3},i=1,2,3", + "a59b21e9bcdb11b6.png": "f_{N}-g\\in a\\backslash b_{N}", + "a59cc19898be93a6.png": "E=i\\hbar\\frac{\\partial}{\\partial t}", + "a5ae7469d7cd2b2b.png": "lim_{y\\rightarrow0+}\\frac{1}{y}", + "a5b87771da6e30e7.png": "n\\sqrt{n}+1", + "a5bab34ff5a94191.png": "\\Phi_{lm}=\\vec{r}\\times\\nabla Y_{lm}", + "a5d77c4e04220bb1.png": "V[x_{0},y_{0},z_{0}]", + "a5e621086662a59e.png": "\\frac{B(rc)^{2}}{2\\mu_{0}}=nmv^{2}\\Rightarrow", + "a5e700e2688b44ed.png": "P=KG(W-W_{e})", + "a5e782b5e3528c7d.png": "w_{x}logx+w_{y}logy", + "a5edf57bb75cafaf.png": "(logn)^{O(1/\\epsilon)}", + "a5ee89ba4405cc91.png": "C=\\epsilon_{0}\\pi\\frac{4800}{11}", + "a5f588c7aa3b8307.png": "196884/e^{\\pi\\sqrt{d}}", + "a5fbe374c5aec62a.png": "2^{n}\\le(\\begin{matrix}2n\\\\ n\\end{matrix})", + "a603a17cd37dd1af.png": "\\frac{\\partial c}{\\partial\\tau}=\\frac{\\partial^{2}c}{\\partial\\zeta^{2}}+\\frac{\\partial c}{\\partial\\zeta}", + "a6080bfad15715dd.png": "1(", + "a6085de1889e7a54.png": "\\Psi=\\frac{E^{*}h^{\\prime}}{\\sigma_{0}}>\\frac{2}{3}", + "a60b492730c8fb47.png": "\\frac{e}{p}=\\frac{w}{w+\\epsilon}", + "a60e5a8e94331813.png": "s(t)=\\int_{0}^{t}dt^{\\prime}v(t^{\\prime})", + "a613b927f4fdaebe.png": "x^{\\prime\\prime}\\in D(p,w^{\\prime\\prime})", + "a61f25ec64694630.png": "\\hat{B}=\\hat{x}\\hat{y}\\hat{z}\\hat{v}=i\\hat{v}", + "a6292d9eef66615e.png": "A^{+}P=A^{+}=QA^{+}", + "a62d148711185e34.png": "|\\phi_{2^{i}}\\rangle", + "a63d3cfa121854b2.png": "b_{k,i}=\\sum_{j=1}^{n}a_{kj,ij}", + "a64d03a9b473476e.png": "(sx_{0},sy_{0};s^{2}t_{0})", + "a65cfde176581add.png": "\\frac{1}{n+1}x^{n+1}+C", + "a66f9010f40ca546.png": "h_{lm}^{(1)}(kr)", + "a6894e5aa7ab31a8.png": "(\\frac{R}{M})^{j}P_{j}", + "a68a3382b9096bb2.png": "H=\\frac{\\Phi^{2}}{2L}+\\frac{Q^{2}}{2C}", + "a68a56137e808e1d.png": "P=(n-\\Delta/2)", + "a68eafd4b2c61fb8.png": "Q=U-W=H_{0}", + "a6a6b4ce10cee8d4.png": "T=(\\vec{\\omega},v+d\\times\\vec{\\omega})", + "a6a879076def816f.png": "X(u,v,w;z,x)", + "a6ad895437a074a5.png": "i=\\sqrt{-1}", + "a6b5bf17a0d8ce48.png": "d(-x)=-dx", + "a6b856c8dd0ff7f5.png": "\\frac{1}{a_{11}}[\\begin{matrix}a_{21}&-\\Delta[a]\\\\ 1&a_{12}\\end{matrix}]", + "a6b8de124a6a84d0.png": "Q(\\sqrt{1-p})", + "a6bc480da102e633.png": "f^{-1}(y)=\\pm\\sqrt{y}", + "a6be9cb660a337a5.png": "\\sum\\frac{1}{x_{i}}+\\prod\\frac{1}{x_{i}}=1", + "a6c04cda52a923b5.png": "O(log_{b}n+k)", + "a6c8920c20d56d3b.png": "F^{\\times}/F^{\\times2}", + "a6cefb8f0177bd92.png": "=x\\cdot(y\\cdot z)", + "a6ddb408e19429db.png": "q|p^{2}-p+1", + "a6e48c68dc631e84.png": "N_{1}^{c}=(\\frac{3}{4\\pi})^{1/2}", + "a6fdfac39a5c5084.png": "\\langle x^{*},x\\rangle", + "a70721489a1f3a9d.png": "1^{1^{1^{1^{1^{1}}}}}+3", + "a70e1aff72ea9667.png": "(\\phi^{\\Rightarrow x})^{\\Rightarrow y}=\\phi^{\\Rightarrow x\\wedge y}", + "a715b2e6a6e85cac.png": "C_{\\bullet}:Top^{2}\\rightarrow CC", + "a7167e0e4313363a.png": "E(sup_{T>t}W_{T}/T)", + "a71916a49d30765b.png": "S\\rightarrow c_{1,0}(\\hat{\\epsilon})", + "a720a0d28c780119.png": "\\Sigma_{i}P(i)=1", + "a7315bee3c9ba106.png": "P(Y^{k}=1|A^{kc})=1", + "a739b4433b0b309b.png": "L_{S}^{\\sigma}=L_{S}-M/a", + "a73cb2674e71d5a3.png": "y^{\\prime\\prime}-xy=0", + "a753e9c62c0a1b74.png": "E=i\\hbar\\frac{\\partial}{\\partial t}", + "a75f3805e3c04321.png": "-\\sigma_{c}=\\sigma_{1}", + "a7626088950ed74f.png": "D_{ii}=\\frac{\\sigma_{i}}{\\sigma_{i}^{2}+\\alpha^{2}}", + "a76371e2da58dcfd.png": "\\sum_{x\\in X}P(x)=1)", + "a770add3443a4630.png": "D(a)=D(b)=0", + "a777813f2e62ee4d.png": "|z|<1/(1-q)", + "a78d76c1d573e285.png": "a_{P}sini=", + "a78e56347fc51480.png": "[\\begin{matrix}1&\\frac{1}{sC}\\\\ 0&1\\end{matrix}]", + "a78fd1306fc93196.png": "ESR=\\frac{\\sigma}{\\epsilon^{\\prime}\\omega^{2}C}", + "a795c50563102426.png": "f(x)=A_{i+1}", + "a7979ae956f92505.png": "\\Phi_{e}=\\int\\frac{U_{e}}{T^{2}}dT", + "a7a958eb90ff3119.png": "\\frac{n!}{(n-k)!\\cdot k^{n}}=m", + "a7ca71d8f2321a23.png": "\\int_{0}^{1}\\frac{sin(1/x)}{x}dx", + "a7d89af8e00800ac.png": "Stk=\\frac{u_{0}V_{s}}{dg}", + "a7db7e289098aece.png": "\\sigma^{2}*(X^{\\prime}X)^{-1}", + "a7dc339692972371.png": "\\bigwedge_{i=1}^{n}p_{i}^{\\epsilon}", + "a7ec2f6b4be50eab.png": "V_{T-j+1}(k)", + "a7ee700114c39a15.png": "F\\hat{z}", + "a7f46fbadd1655fa.png": "P^{\\mu},J^{\\mu\\nu},M", + "a7f4dbec49c70b77.png": "(logn)^{O(1/\\epsilon)}", + "a7f6cb950b70b891.png": "A^{n+1}=A^{n}\\times A", + "a7ff9a736bdc3c9e.png": "\\frac{\\alpha}{\\alpha+n-1}", + "a8073a7c254fa13b.png": "\\sum_{d|n,d0,\\beta,\\delta>0", + "ac06cb420b37c748.png": "f(x_{1}^{|q|},x_{2}^{|q|},x_{3}^{|q|},...)", + "ac12ae921b4491b1.png": "=\\frac{2\\sqrt{2}}{3}\\pi r^{3}", + "ac13c0b40e3525d2.png": "R_{22}=R_{11}=-\\Delta p", + "ac246e40d860a9f0.png": "\\frac{vii^{ox}}{y}", + "ac537bd3f86303eb.png": "F_{jm}(t)<\\epsilon", + "ac5593697f921ea3.png": "M:F_{q}^{n}\\rightarrow F_{q}^{n}", + "ac5d66876511bfce.png": "\\tilde{f}=f+h", + "ac61fa454b18ecde.png": "\\mu^{-1}([\\epsilon,\\infty))", + "ac6785c020e09dfd.png": "y=5e^{2t}-4e^{t}", + "ac6be84b779cc7f2.png": "\\lambda\\ge2\\sqrt{d-1}-o(1)", + "ac7b07a24aa1159b.png": "E=\\frac{2.21}{r_{s}^{2}}-\\frac{0.916}{r_{s}}", + "ac85cbd699df83b1.png": "W_{E}=4\\int Y\\sigma^{2}dx", + "ac89b79f0dfd659d.png": "[\\begin{matrix}1&0&-\\overline{c}_{D}^{T}&z_{B}\\\\ 0&I&D&b\\end{matrix}]", + "ac8a1bc60623e58b.png": "\\frac{1}{pq}=\\frac{1}{N}\\times\\frac{N}{pq}", + "ac8d3a1bb55bf476.png": "2^{n}n!\\sqrt{\\pi}", + "ac985295b434109a.png": "D^{*}=(\\mu^{*}E)^{2}\\frac{(\\delta t)^{2}}{16t_{0}}", + "aca9c2dcb698fa96.png": "\\sqrt{1-\\omega^{2}r_{0}^{2}}", + "acacbed4b73e36fa.png": "r_{1},r_{2},r_{3},\\cdot\\cdot\\cdot,r_{n}", + "acaf671bf93de734.png": "f_{n}\\rightarrow\\chi_{[1,2)}", + "acb5e7b168d910bd.png": "\\Gamma=\\Gamma_{ab}+\\Gamma_{c}", + "acbca42a7fb4b63f.png": "\\sum F_{x}=0=R_{Ax}", + "acd8292ccc09f2d5.png": "SL_{n}(q)\\rightarrow PSL_{n}(q)", + "aceca317bd5b25fb.png": "\\frac{1}{\\tau_{M}}=\\frac{V_{0}\\Gamma\\omega^{4}}{4\\pi v_{g}^{3}}", + "acf00acf164ed14c.png": "-2\\omega^{2}r_{B}(t)", + "ad00fa3a03eb39f3.png": "\\frac{hL(P-U)}{2PU}+\\frac{S}{L}", + "ad05ca58df4f447b.png": "\\sqrt{1},\\sqrt{2},\\sqrt{3},\\sqrt{4},\\sqrt{5}", + "ad05f310c34b5205.png": "\\frac{1}{7}+\\frac{1}{14}+\\frac{1}{28}=\\frac{1}{4}", + "ad068c07be5a60e2.png": "DIV=\\frac{1}{L_{max}}", + "ad0e0c35b268106d.png": "U=D+(\\frac{wvkj}{w+v})", + "ad174abc859fc1fb.png": "v_{i}\\in H_{0}^{3},i=1,2,3", + "ad18e006c2d5f5e5.png": "c_{1}|\\psi_{1}\\rangle+c_{2}|\\psi_{2}\\rangle", + "ad1b6c36af87e58f.png": "\\psi=e^{\\frac{1}{2}(\\mu+\\beta i+\\phi)}", + "ad1b83e865dd33d4.png": "Q_{1}+Q_{1}^{*}=0", + "ad1e4d3456137383.png": "\\frac{dx_{i}}{dt}=x_{i}f_{i}(x)", + "ad3be0cd69f46c28.png": "2^{k}t_{0}", + "ad3f1381e1b01d56.png": "det(1-zL_{w})", + "ad407efca10480b3.png": "[p_{1}\\cdot\\cdot\\cdot p_{i}]", + "ad4a4399aab6e852.png": "|B_{i+1}-B_{i}|", + "ad55ea09f50591d0.png": "-27-20\\sqrt{2}", + "ad5c757e96fa591c.png": "\\sum(x_{i}-y_{i})^{2}", + "ad6692574c1d12ab.png": "Z_{in0}=\\frac{V_{1}}{I_{in0}}=Z", + "ad6ae2dfe5fa2d6e.png": "(0\\le m<2\\pi)", + "ad74f46081ea1f30.png": "[J_{\\pm},V_{0}]=\\sqrt{2}V_{\\pm}", + "ad7bf3a6599f1c56.png": "H_{eu}^{2}=\\frac{\\sigma_{a}^{2}+\\sigma_{d}^{2}}{\\sigma_{P}^{2}}", + "ad7e127ff61e871a.png": "GF(p)[x]/f(x)", + "ad7edfa358ef5c52.png": "1_{[N]}", + "ad82b7beefdaeed9.png": "y=\\frac{1}{Be^{2x}-2xe^{2x}}", + "ad8b14e0b20d9e05.png": "U(g,e)", + "ada12cdfed13b36e.png": "\\alpha+\\gamma=\\pi/2", + "ada2c115b01227dd.png": "80\\cdot10^{-2}=8\\cdot10^{-1}", + "adaf27569787a0b4.png": "\\langle A,\\wedge,\\vee,-,0,1\\rangle", + "adb2236e3dd7aa96.png": "P|", + "adbea5405091f83d.png": "\\frac{3x^{2}-2xy+c}{y^{3}-1}", + "adc19e02b5dc8f1a.png": "\\sqrt{1-\\omega^{2}r_{0}^{2}}", + "adcdb73d18da5800.png": "E(X_{i})=\\frac{nK_{i}}{N}", + "adcfddd2809f468e.png": "(sin(\\alpha))^{2}/2", + "add51ffc816b371d.png": "\\frac{210\\cdot196}{218+13}", + "add596cd5cd91758.png": "\\int e^{x}dx=e^{x}+C", + "add7eb1b11ad0260.png": "\\frac{x^{2}}{(p+q)^{2}}+\\frac{y^{2}}{q^{2}}=1", + "addd9790228b298f.png": "f^{\\prime}(x)=3x^{2}-1", + "adddb137251d110a.png": "P^{\\mu},J^{\\mu\\nu},M", + "ade2925b3e422b2b.png": "j(j+1)\\hbar^{2}", + "ade60f4d379b8b1b.png": "X^{2}+Y^{2}-Z^{2}=0", + "adeb2d45f0562322.png": "I=\\sum|\\varphi_{n}\\rangle\\langle\\varphi_{n}|", + "aded3aca689a804a.png": "(f(p_{1},p_{2},...,p_{j}))", + "aded54327890289c.png": "2\\sqrt[3]{x}=16", + "adf0c657cb533977.png": "1+x+\\frac{x^{2}}{2}", + "ae0291a31695429a.png": "6^{4}=(6^{2})*(6^{2})", + "ae059ce3105ade96.png": "L(G)=\\{a^{*}b^{*}c^{*}\\}", + "ae073c24f1bc2bda.png": "\\frac{1}{14}+\\frac{1}{21}+\\frac{1}{42}=\\frac{1}{7}", + "ae12797d2903e5b1.png": "2\\pi^{2}k\\delta(x)\\delta(y)\\hat{z}", + "ae24fc8fc20e470f.png": "(\\frac{a}{N})=-1", + "ae2ee645ef5e8676.png": "FL_{o}", + "ae3619c13abc5936.png": "V_{e}=I_{sp}*g_{n}", + "ae501b9bba8f4f98.png": "1991_{10}=7C7_{16}", + "ae513e3bde47e884.png": "X_{1}(\\frac{1}{z^{*}})", + "ae5140324e9c414a.png": "-1/\\xi\\le x\\le1/\\xi", + "ae54a54ebe541bfb.png": "E(k)=\\frac{\\hbar^{2}k^{2}}{2m^{*}}", + "ae60d740aad2d72c.png": "\\lambda\\gamma(\\sum_{g=1}^{G}||w_{g}||_{2})", + "ae63fbb2b5d68275.png": "\\tilde{K}(p;T)=\\tilde{G}_{\\epsilon}(p)^{T/\\epsilon}", + "ae673d7d3f733c52.png": "(\\frac{(210+4)}{9})^{\\frac{(7-57)}{9}}", + "ae7d7e48e22a0e32.png": "\\sigma_{ij}=(\\frac{\\partial f}{\\partial\\epsilon_{ij}})_{T}", + "ae7e632d8a2d379f.png": "\\sqrt[3]{b}^{2}", + "ae7f6610b5d198b0.png": "f=x^{2}-y^{2}-1", + "ae8464143969870a.png": "\\underline{\\underline{A_{\\epsilon}}}^{T}=\\underline{\\underline{A_{\\sigma}}}^{-1}", + "ae876dfd14482616.png": "(T_{A})^{-1}", + "ae9246b84acd7a90.png": "(-1)^{n}\\frac{d^{n}}{dt^{n}}f(t)\\ge0", + "ae9f10a9e81d73ce.png": "L^{1,1}=L^{1}", + "aea82c8d91c7093b.png": "-V_{0}\\cdot N\\ge0", + "aeb83a9c61032abe.png": "x\\in[-2,-0.5]", + "aec41a1951cd0218.png": "u\\cdot\\nabla u=-\\frac{1}{\\rho}\\nabla p", + "aec9cf13603e3c09.png": "f=a+bx+cp", + "aece90e5d8951bbd.png": "\\lambda_{3}=(\\begin{matrix}1&0&0\\\\ 0&-1&0\\\\ 0&0&0\\end{matrix})", + "aed3b9e3a11f0c41.png": "E_{n_{1},n_{2}}^{(0)}", + "aeded16daa5302f8.png": "\\hat{r}=\\frac{r}{|r|}", + "aee561ec06372fd4.png": "a_{n}=G^{-1}(1-\\frac{1}{n})", + "aeeb904ba8eed9a7.png": "\\Rightarrow x=\\frac{Pr_{2}}{r_{1}+r_{2}}", + "aef3491f19d33aa0.png": "A=SB\\overline{S}^{-1}", + "aef66cad84aa8d12.png": "f(y^{\\prime})=x\\odot y^{\\prime}", + "aefd0a5c0a2991fa.png": "I\\Delta_{0}+exp", + "af09b2947f43728c.png": "\\bigcup_{k}O(n^{k})", + "af0eee5615efdfd9.png": "T_{E}\\approx[\\frac{l}{R}]^{\\frac{1}{4}}T_{I}", + "af11f8fd34790b3f.png": "L=\\sum_{i=0}^{N-1}p_{i}x_{i}", + "af254bf06f44434f.png": "|f_{i}(x)-f_{i}(y)|<\\epsilon", + "af2559a15dc158cd.png": "C_{N}=\\frac{h}{F_{1}}", + "af2cd9154391d5f3.png": "0(1-\\epsilon)+2\\epsilon=2\\epsilon", + "af334f4f71c12205.png": "\\frac{m|v|}{|r|}=q|B|sin\\theta", + "af3c609045355620.png": "(d-r)^{2}=r^{2}-x^{2}", + "af4f02e47194cb83.png": "\\Gamma=\\Gamma_{ab}+\\Gamma_{c}", + "af54f462aede9468.png": "L=\\sum_{i=0}^{n}f_{i}(x)\\frac{d^{i}}{dx^{i}}", + "af708b3090d02f0f.png": "\\frac{d}{dx}y=t(x)y", + "af70a8433b46b2e9.png": "\\Psi=\\sqrt{\\rho}e^{iS/\\hbar}", + "af75ae24fa83ebb5.png": "x^{-1}\\in m_{R}", + "af8c24b2ce22d8f5.png": "10^{-12}\\frac{m}{s}", + "af8f0cba5e790d6b.png": "(J(x),\\nu(x))=0", + "af98704fe5b2796d.png": "F\\hat{z}", + "af9d8b463ab1af8d.png": "a^{2}-b^{2}=ab-b^{2}", + "afa69472bf88d37a.png": "A_{q}(n,d,w)", + "afa9328be6191b15.png": "\\Delta z=H(z)\\Delta\\chi", + "afadff222dbbbc0b.png": "\\xi_{i}^{(a)}dx^{i}", + "afae5369e3232014.png": "|\\beta N|<2^{2^{\\aleph_{0}}}", + "afb8c844edcfca76.png": "\\sum_{k1", + "b03fafec0332f85d.png": "u_{t}-u_{xx}=0", + "b04bf7a97f63bfe5.png": "\\gamma^{0}\\gamma^{0}=I_{4}", + "b04e27d2f1cddc68.png": "60=2^{2}\\times3^{1}\\times5^{1}", + "b04fb8f50d857a72.png": "\\frac{1}{2}mv^{2}=eV_{ion}", + "b065eecd076f7e06.png": "f^{m*n}x=(f^{m})^{n}x", + "b0674ce76f768ae4.png": "m_{i,j}=x^{i}\\cdot x^{j}", + "b07c03c085e0a520.png": "E[h(x,X_{1})]\\equiv0", + "b0affb17dbdea309.png": "M=-EI\\frac{d^{2}w}{dx^{2}}", + "b0bc258d5edad405.png": "f^{*}(d\\omega)=d(f^{*}\\omega)", + "b0bffb7e7aee36d9.png": "f=a+bx+cp", + "b0c164ba36c0596c.png": "K=\\bigcap_{n}E_{n}", + "b0c75590d6b9f9a6.png": "\\theta=\\frac{2\\pi}{\\phi^{2}}n,r=c\\sqrt{n}", + "b0db27c59a166de6.png": "S_{l}(t+", + "b0e2032a6a3297b8.png": "n=(\\begin{matrix}2r-1\\\\ 2\\end{matrix})", + "b0ebb346a5bb708d.png": "\\omega_{\\lambda}\\in H_{dR}^{1}(V_{\\lambda})", + "b0f9d8e2109f1b2f.png": "(t^{2},t^{3})A", + "b0fcdcd5056fdc4c.png": "(x+200)^{2}(x+58)", + "b10445f9b7b11d9a.png": "I_{s}=\\hbar c\\gamma k^{3}/12\\pi", + "b11b99c4af3d9f37.png": "\\frac{1}{2}+i\\frac{2\\pi n}{logn}", + "b11c1c8d21994037.png": "\\Delta E_{n}=\\frac{h}{T(E_{n})}", + "b12d058eb53c9bf1.png": "1/n=(n-1)_{-1}", + "b13889d176de9798.png": "(U(z),0,0)", + "b145186c5ab374ff.png": "\\sum^{\\infty}z^{n!}", + "b152acff025b0ecd.png": "(x\\in[0,\\frac{1}{2}))", + "b15686964788b9ce.png": "{(\\frac{d\\varphi}{d\\tau})}^{2}=\\frac{L^{2}}{m^{2}r^{4}}", + "b15999ea606e2ec0.png": "T_{j_{1}...j_{q}}^{i_{1}...i_{p}}[f]", + "b15ae852e6d4a0bb.png": "\\alpha+\\gamma=\\pi/2", + "b15c0a905710d0a9.png": "H_{dR}^{0}(M)\\cong R^{n}", + "b15ed4a2b7ec1de3.png": "H=0,t>0", + "b163554cc55b4bbd.png": "=\\int_{t_{0}}^{t_{1}}|a|dt", + "b167bc4e1c7e27e6.png": "\\delta(q_{s},q_{c})\\rightarrow q_{t}", + "b1707fb90d9a2a7b.png": "x-y+b^{n}-b^{n}", + "b175102a708a6132.png": "P=\\frac{Li}{1-\\frac{1}{(1+i)^{n}}}", + "b17d10ec555ef6ab.png": "R=\\frac{1}{r},\\Theta=\\theta", + "b185e046def7ae1a.png": "f^{\\prime}(x)=f(x)f^{\\prime}(0)", + "b18bf62dd05ea84e.png": "\\overline{\\nabla}_{X}Y=\\nabla_{X}Y", + "b1955a6596c985d3.png": "{\\epsilon_{1}}^{\\epsilon_{0}\\omega}", + "b1a09f9cd40f2bf3.png": "[0,0.5]", + "b1b64bb7d8857b34.png": "**", + "b1c0959b5d374ed7.png": "\\sum(f*g)(n)", + "b1c30f9f6ec95ce7.png": "A_{0}\\supseteq A_{1}\\supseteq A_{2}\\supseteq...", + "b1d6dc2366efdd95.png": "I=\\frac{P_{0}}{\\Omega|r|^{2}}", + "b1de6f253e967f44.png": "B_{i}=-\\frac{1}{2}\\epsilon_{ijk}F^{jk}", + "b1e2da2415ef1337.png": "d=2.9n^{2}a_{0}", + "b1e64c6ccdd1aadc.png": "\\partial(...)/\\partial\\theta=0", + "b1f3825d5a3e5d6f.png": "\\Delta u=u_{xx}+u_{yy}", + "b1f8799800df848e.png": "\\{|x+C_{2}\\rangle|x\\in C_{1}\\}", + "b239616e1e96abc2.png": "(0,1/2)", + "b2489557e1ff028c.png": "1/2\\sqrt{3}", + "b259cb887a8409d0.png": "(T-L_{m})", + "b26ae94493bf4669.png": "\\int dV|\\Psi|^{2}=N", + "b2731fa769e5a7d6.png": "\\{\\begin{matrix}n\\\\ k\\end{matrix}\\}=S(n,k)", + "b274acf8af6dacfb.png": "\\dot{Q}=U\\Delta T", + "b285555a570dd79d.png": "f_{transit}=0.45\\frac{v_{h}}{L}", + "b28ed3874aed60f2.png": "Z_{n}=Z/nZ", + "b2aca2ef5dad3db4.png": "M=S^{T}AB^{-1}A^{T}S", + "b2ae0ac0f631273c.png": "q_{ii},q_{ij}q_{ji}", + "b2b2cb8a115bad97.png": "\\eta(e_{\\mu},e_{\\nu})=\\eta_{\\mu\\nu}", + "b2ce79f71a91c8b1.png": "\\frac{dW}{dt}=F(t)\\cdot f^{\\prime}(t)", + "b2d7b30b4f864269.png": "O(klogk2^{O(log^{*}k)})", + "b2db6c201aa5e158.png": "\\dot{x}_{k}=h_{k}+g_{kl}\\xi_{l}", + "b2de86e57139cd9f.png": "f(x)=(x,x,x,\\cdot\\cdot\\cdot)", + "b2dfd93e2f3a2607.png": "S_{i}^{z}|0\\rangle=s|0\\rangle", + "b2f603658092219c.png": "2s=-(\\frac{1}{\\tau_{1}}+\\frac{1}{\\tau_{2}})", + "b30f3140462d1756.png": "\\bigoplus_{k=1}^{\\infty}b_{k}", + "b31fa9570adde70b.png": "|q\\overline{q}\\rangle", + "b327da73cc2bd567.png": "(u,v),(v,u)\\in S_{n}", + "b3310daa8e81a66a.png": "2^{\\aleph_{0}+n}", + "b36ffb972f17b82c.png": "\\sum_{i=0}", + "b3732af0c1f62a8b.png": "A=(\\begin{matrix}0&X\\\\ -X^{t}&0\\end{matrix})", + "b38180da0f147ead.png": "\\sqrt[2]{x^{3}}", + "b384ce28b7f606ae.png": "F(t,x(t),\\dot{x}(t))", + "b384d1f35abf25a6.png": "\\alpha^{-1}W_{\\alpha^{2}t}", + "b38a2dc775e39d44.png": "H=h_{1}h_{2}h_{3}", + "b38bd0ba28778e8e.png": "\\vec{m}\\in M", + "b396715e8e981876.png": "\\frac{\\pi}{180}M_{r}cos\\varphi", + "b39a8a148e026fac.png": "A=G_{0}V", + "b3a00c0665afd4c3.png": "\\frac{dx_{i}}{dt}=x_{i}f_{i}(x)", + "b3b07b207c4d6d5f.png": "\\hat{b}=b/|b|", + "b3b20bc3b91b708d.png": "\\delta=\\frac{3\\sigma(1-\\nu)}{E}\\frac{L^{2}}{t^{2}}", + "b3b233cfab80b14e.png": "C^{\\Delta[2]}\\rightarrow C^{\\Lambda^{1}[2]}", + "b3b2acfaa7e8eca7.png": "V:=L(\\underline{a}_{1},...,\\underline{a}_{r})", + "b3c55813c13e955f.png": "f(n)=\\prod_{i}f(p_{i}^{a_{i}})", + "b3c6e2daa3cc11b2.png": "gw=\\frac{\\alpha w+\\beta}{\\overline{\\beta}w+\\overline{\\alpha}}.", + "b3ca61fd2b50e554.png": "W_{n}\\le h^{n}\\frac{(n-1)!}{4}", + "b3d8aad9aedd4fcd.png": "O(\\lambda^{(d-1)/2}log\\lambda)", + "b3ddac1c8e435e28.png": "m(\\Omega)\\le\\alpha^{-1}||f||_{1}.", + "b3df1bc30298a57d.png": "f^{n-1}(\\perp)\\sqsubseteq f^{n}(\\perp)", + "b3e08eb02c98240a.png": "\\Pi=\\sum_{i,j}\\Pi^{ij}\\partial_{i}\\wedge\\partial_{j}", + "b3e80cc648916e9c.png": "\\gamma_{\\tau}(t)=\\gamma(\\tau+t)", + "b3ea8b12745e846a.png": "2^{1/p}>2", + "b3f6b5450aba32c3.png": "f_{+},\\varphi", + "b3fd654f9492f7de.png": "\\hat{p}_{x}=-i\\hbar\\frac{d}{dx}", + "b40c1e5733bc2e8b.png": "H=h_{1}h_{2}h_{3}", + "b40d42d6c7aedb3d.png": "I_{i}=\\partial S/\\partial E_{i}", + "b4117e32b2a4b613.png": "\\sigma(p_{n}^{\\prime\\prime})=p_{n}^{\\prime}", + "b411bc82b71b7719.png": "(x^{2}+y^{2})^{2}=ax^{2}y", + "b4138e25ed3a73df.png": "\\overline{f}(0)=\\langle\\rangle", + "b4252ac2470d0d46.png": "\\alpha_{0}=\\gamma^{-1}\\alpha", + "b426830ce2ea5609.png": "\\hat{\\rho},\\hat{\\phi},\\hat{z}", + "b42fdb8ed3d909f8.png": "v=\\dot{x}=[\\dot{p},\\dot{r}]", + "b4446cd08720ef92.png": "-\\frac{1}{12}\\pi^{2}", + "b4496d2f638c9eb2.png": "S_{z}=\\hbar(s-a^{\\dagger}a)", + "b44ad0a0d2dca27a.png": "\\epsilon,\\delta,K>0", + "b44ba6961f07ad30.png": "(Div)P^{(0)}=0", + "b44e47eff907e5d5.png": "k[X]=\\bigoplus_{\\lambda}k[X]_{(\\lambda)}", + "b45393440e34d20c.png": "|f_{i}(x)-f_{i}(y)|<\\epsilon", + "b456f068a0a81aa1.png": "C_{X}^{-1}=0", + "b45f4c7e62e84027.png": "H\\Phi_{0}(x)=E_{0}\\Phi_{0}(x)", + "b46caaf025791766.png": "(U,R_{\\delta_{\\Phi,\\epsilon}})", + "b47a019043f70f24.png": "=J+\\epsilon_{0}\\frac{\\partial E}{\\partial t}", + "b495aec291acccd4.png": "V_{p}=0.5Sdln(\\frac{D}{d})", + "b4a594f25756bda2.png": "t_{1}=X^{c}g_{1}^{s_{1}}g_{2}^{s_{2}}", + "b4a810542bd3b153.png": "\\sum_{i=1}^{d}(d+1-i)b^{i}", + "b4aa19360dd96320.png": "\\nu=\\nu(q)=\\frac{1}{\\sqrt{1-q}}", + "b4ac460771b0762f.png": "s(t)=\\int_{0}^{t}dt^{\\prime}v(t^{\\prime})", + "b4c90dbafd85af3c.png": "M=\\frac{1}{9}[\\begin{matrix}1&1&1\\\\ 1&1&1\\\\ 1&1&1\\\\ \\end{matrix}]", + "b4cbb8229c37bbe6.png": "M=\\rho V=\\rho\\frac{4}{3}\\pi a^{3}", + "b4cf948124235b9c.png": "CO=\\frac{VO_{2}}{C_{a}-C_{v}}", + "b4d7f8ca395f8b3c.png": "\\sqrt{a+b\\sqrt{c}}", + "b4d943cddfe56d86.png": "grR=gr\\hat{R}", + "b4daa46b559ff987.png": "\\rho_{i}=\\alpha_{j_{i}}/\\alpha_{i}", + "b4e1fbfbd0897fa5.png": "(m^{d})^{e}modn=m", + "b4f141b868beb52c.png": "X^{2}-X+1", + "b4f2da3c7ace46c3.png": "R\\ge(2^{a-1}-1)", + "b50596168b81d784.png": "\\frac{Ax}{Bx^{n}+C}", + "b505ab7ec8b0581e.png": "f(n)=x^{(n+1)}-1", + "b50a999af6e55155.png": "r\\vee r^{\\prime}\\equiv max(r,r^{\\prime})", + "b50c953a15c4ccd4.png": "\\overline{G}=\\{\\overline{g}:g\\in G\\}", + "b515316d92278346.png": "f_{2}(q,\\dot{q},t)", + "b518b443186927ae.png": "V_{z}=\\frac{2\\Omega l}{(k_{+}+k_{-})}", + "b51bed533fd6fdd8.png": "\\alpha=\\frac{\\sigma_{1}^{2}}{\\sum_{i}\\sigma_{i}^{2}}", + "b539a20bcf70ca48.png": "x^{-1}\\in m_{R}", + "b53c899711ae46c4.png": "W^{k,p}\\subseteq W^{m,q}", + "b53caaa1d5786cd7.png": "|T_{0}^{L}|+|T_{0}^{R}|", + "b5542c61c6ffee01.png": "X_{*}P=P(X^{-1}(\\cdot))", + "b55600c35f6eb81b.png": "\\mu^{X}:F\\mapsto\\int_{F}X", + "b55b1a6cf136b8b1.png": "G(-z)=-G(z)", + "b55bf50c3459ceda.png": "\\sigma^{1}=g(r)dr", + "b55ec54058921928.png": "|\\frac{q}{p}|=1", + "b56e0a45704fff64.png": "-\\frac{\\pi}{|\\nu|}-2\\pi\\gamma\\delta(\\nu)", + "b570667f4f4d6917.png": "H(Y|X)", + "b571f7ae4462bc76.png": "\\overline{\\psi}D_{\\mu}\\psi", + "b57e27b877f675bc.png": "\\vec{m}\\in M", + "b58300696a9be79c.png": "-csc^{2}(\\frac{\\pi}{2})=-1", + "b5a82071eb1f1e09.png": "lim_{\\Delta x\\rightarrow0}g(\\Delta x)=0", + "b5aef0cb818ce0b1.png": "|g(x)-b|>0", + "b5afc9fa57783ac4.png": "1!+4!+5!=145", + "b5b2845b048df183.png": "D_{x}=\\frac{1}{i}\\frac{\\partial}{\\partial x}", + "b5b59dd7c21c29d4.png": "A_{0}\\bigcap A_{1}\\ne\\emptyset", + "b5c603accc811a50.png": "\\frac{1}{1-\\delta}\\epsilon", + "b5ef99a601a6833a.png": "A=\\int\\lambda dE_{A}(\\lambda)", + "b6028d39d0fd6585.png": "\\sum_{k=0}^{n}(q+1)^{k}", + "b605a09065df3680.png": "2^{log^{*}n}", + "b608a22e8d2f93e4.png": "D_{\\mu}J^{\\mu}=0", + "b611ae1351440128.png": "\\alpha_{2}=\\frac{4\\alpha_{0}+1\\alpha_{1}}{5}", + "b6323b51f9bf2a17.png": "f(x_{t},t)=x_{t}e^{\\theta t}", + "b635bf05a8f94b59.png": "f_{0}(x):R^{n}\\rightarrow R", + "b64830ccd4043464.png": "\\tilde{N}^{0}\\rightarrow\\tilde{l}^{+}l^{-}", + "b64d3c66438686cf.png": "F\\hat{z}", + "b64f2de2fe794277.png": "\\pm z_{1}^{c_{1}}...z_{n}^{c_{n}}", + "b6511cde5624d58e.png": "v_{1}(\\frac{1}{2})=v_{2}(\\frac{1}{2})", + "b65719942eb4fa2a.png": "\\frac{x}{4}+\\frac{1}{x^{2}}", + "b65a9636f12afee7.png": "v(x,t)=\\dot{u}(x,t)", + "b662a13d856f192d.png": "\\int f_{n}\\le\\int f", + "b6647926eac977b5.png": "-\\sqrt{n},...,\\sqrt{n}", + "b66aaa8d05f7e4e2.png": "V(s)=-J\\delta(s_{0},s_{1})", + "b681f6b476cef34d.png": "|f_{i}(x)-f_{i}(y)|=1", + "b68585a6fec9f4ab.png": "\\hat{\\theta}=\\frac{1}{kN}\\sum_{i=1}^{N}x_{i}", + "b68c50ace7073d58.png": "X_{i}-\\overline{X}", + "b691875cda989154.png": "DM(x)[h,v(x)]", + "b6a4c3272a9e22df.png": "2^{10,000}", + "b6aa48e2ea740ac0.png": "J(f)\\le+\\infty", + "b6bc10c86d4c61a7.png": "\\frac{n!}{(n-k)!\\cdot k^{n}}=m", + "b6ca0d319e3a32ce.png": "2^{2}+2+1-1", + "b6eae35361cd1b2d.png": "I_{2}=D(b)f(b)b^{2}", + "b6f1d25452e6e627.png": "=\\sqrt{cosh^{2}(t)}", + "b70b0f9add0c3a84.png": "p_{n+1}=2+\\sum_{i=1}^{n}g_{i}", + "b716928e95050503.png": "A\\cong k[[x_{1},...,x_{d}]]", + "b7241a7c978e3701.png": "\\Sigma_{e\\in T}d(e)", + "b7256abbe0503e84.png": "t^{(k)}\\leftarrow t^{(k)}/t_{k}", + "b745ef7b73c89fb5.png": "\\alpha^{-1}W_{\\alpha^{2}t}", + "b748a87b1be992e9.png": "H_{n}^{(r)}=\\sum_{k=1}^{n}H_{k}^{(r-1)}", + "b74b43feb912c725.png": "\\rho_{A}=|\\psi\\rangle_{A}\\langle\\psi|_{A}", + "b750df48b8effdb0.png": "C:(x(t),y(t),z(t)", + "b755457a09da1367.png": "1+2x+x^{2}", + "b7580aeb5fcce94f.png": "\\{\\hat{Z_{s}}|s\\in F_{d}\\}", + "b76424cb919d3f22.png": "P[X_{n}\\in A]=\\mu(A)", + "b76aaf326e448261.png": "2P_{\\frac{1}{2}}", + "b776b27801d9a5ad.png": "I_{\\mu}(f):=\\int_{X}fd\\mu", + "b7819d8bc6855518.png": "I_{b+}=4I_{0}", + "b78a583bc5ac6a39.png": "P=KG(W-W_{e})", + "b79d5060a9e98cec.png": "X\\cdot F_{i}\\subseteq F_{(h(i))}", + "b7b9a248f191723f.png": "\\tau=\\frac{\\tau_{1/2}}{log(2)}", + "b7c9b8c9a2f50613.png": "\\frac{dL}{dt}=-k_{1}L+L_{b}", + "b7d5f9a52e6a556c.png": "{(\\begin{matrix}4\\\\ 1\\end{matrix})}^{7}=16,384", + "b7d795177227fee7.png": "A=C[S]", + "b7e1036a719a8de9.png": "r^{2},\\sqrt{r},exp(r)", + "b7ee9c5dea9930c2.png": "(1+4)^{2}=5^{2}=25", + "b7fde14704cee87a.png": "-|\\dot{p}|^{2}", + "b80b42639f321be1.png": "-\\omega\\propto-2\\vec{\\nabla}\\cdot\\vec{Q}", + "b822e37bdc3475a0.png": "1,x+x^{2}+x^{3}", + "b8244aca01f3c780.png": "C^{++}=C^{oo}=C", + "b82d5cf9c79f5887.png": "\\int d^{d}x\\overline{\\psi}iD/\\psi", + "b83fb7dd0ad9105e.png": "R=Hom(\\pi,G)", + "b841d233095ec4cb.png": "-2\\pi\\frac{J_{2}}{\\mu p^{2}}\\frac{3}{2}cosi", + "b8475f8b9b5539e8.png": "[L_{ij}^{\\prime},H^{\\prime}]=0", + "b84bd66165443d48.png": "1+3=4mod13", + "b8530540a10bbdb1.png": "X^{\\perp}=\\overline{X}^{\\perp}", + "b856076283ae6942.png": "\\sum_{k}(n)", + "b863259765dc6242.png": "(i\\hbar\\partial/-mc)\\psi=0", + "b86563cd4f090628.png": "[\\begin{matrix}S/I&S/I\\\\ 0&S\\end{matrix}]", + "b8784b1fb3aa2c89.png": "m=p^{T}\\nabla f(x)", + "b8838f58f38c5265.png": "\\hat{T}(0)=\\hat{I}", + "b8893091914c8191.png": "lim_{t\\rightarrow\\infty}\\hat{d}(w,t)=d(w)", + "b88a5c3a9b5edeed.png": "I_{K}(f)/H", + "b88cab01c52188d8.png": "Q=[\\begin{matrix}T\\\\ N\\\\ B\\end{matrix}]", + "b8940f1646c45c65.png": "\\tau=\\mu_{eff}(\\dot{\\gamma})\\dot{\\gamma}", + "b89cf48f1974243d.png": "A-x", + "b8a163c573bdfb78.png": "[00,i]=\\frac{1}{2}\\epsilon\\gamma_{00|i}", + "b8a5bd570462dc50.png": "F^{3}(\\hat{f})=f", + "b8adcd4d36a9444e.png": "lim_{x\\rightarrow0}\\frac{O(x)}{O(x)}", + "b8aea54084086627.png": "Q=U-W=H_{0}", + "b8baed6ab07fbd06.png": "[n]_{q}=\\frac{q^{n}-1}{q-1}", + "b8bba31f8c485d03.png": "i\\hbar|\\dot{\\psi}\\rangle=H|\\psi\\rangle", + "b8bf08b5bc596351.png": "WA_{k}=TH_{k}*FF", + "b8c40bb25056a444.png": "H(x,y)=(x-y)^{2}", + "b8d4c46e1cd7e441.png": "OPL=\\int_{C}n(s)ds", + "b8d635f9415a189d.png": "S=R(X)+\\overline{R(X)}", + "b8d6ab000a1110ee.png": "D=\\sum_{j=1}^{n}e_{j}\\frac{\\partial}{\\partial x_{j}}", + "b8d7c65dbee30a02.png": "\\delta_{M,D}", + "b8eeefa16b09efdf.png": "(x-b)^{2}-c", + "b8efca414dab424c.png": "\\Delta n=\\lambda_{0}K|E_{0}|^{2}", + "b8f411db15fbb824.png": "a=(x-1)\\div0.005", + "b91356aeb54d330c.png": "O(\\sqrt{b-a})", + "b916c61b52417939.png": "M_{p}=(bd^{2}/4)\\sigma_{y}", + "b9221f69931f294e.png": "\\partial_{i}f=\\frac{\\partial f}{\\partial\\xi^{i}}:=\\frac{\\partial\\overline{f}}{\\partial\\xi^{i}}", + "b92667cc19812528.png": "(L^{T}L)^{-1}L^{T}I=kn", + "b92d49aaca55131f.png": "11=2^{0}+2^{1}", + "b92da6cc7d85ed45.png": "T=\\sqrt[4]{\\frac{(1-a)S}{4\\epsilon\\sigma}}", + "b936bdabe3555edf.png": "\\langle G,S\\rangle\\rightarrow\\langle G^{\\prime},S^{\\prime}\\rangle", + "b93e7312d2c5b171.png": "|\\mu|(X\\backslash K_{\\epsilon})<\\epsilon", + "b9505442ea9526bb.png": "I(S;\\Omega-S)", + "b95f3dc982137648.png": "1\\le p<+\\infty", + "b96648dd1688a8fb.png": "\\rho_{T-1}^{com}:=\\rho_{T-1}", + "b9666715e7707a7a.png": "\\frac{1}{2}*(\\frac{2006-2*x}{\\sqrt{2}})^{2}", + "b97b0ae21006e8c9.png": "\\frac{[A_{ad}]}{p_{A}[S]}=K_{eq}^{A}", + "b98a1b1b752b05cb.png": "V_{T-j+1}(k)", + "b9a1ec6a3e8addf5.png": "\\dot{\\tilde{\\chi}}=-i[\\tilde{H}_{BS},\\tilde{\\chi}]", + "b9a708ea0d6c0e9e.png": "D_{P}\\\\ G/H", + "b9b1cc928fc86827.png": "v_{(G;c)}(\\emptyset)=0", + "b9bddc8a557dca30.png": "(\\begin{matrix}c_{k-1}\\\\ k-1\\end{matrix})\\le N-(\\begin{matrix}c_{k}\\\\ k\\end{matrix})", + "b9bddf87be19385d.png": "ln\\tau,\\tau,\\tau x,\\tau x^{2}", + "b9ce0648e497c757.png": "\\{f_{X}(\\cdot;\\theta)|\\theta\\in\\Theta\\}", + "b9d7aba3edb52f3e.png": "f(x_{1}^{|q|},x_{2}^{|q|},x_{3}^{|q|},...)", + "b9edcf09d266e3b6.png": "P=(n-\\Delta/2)", + "b9f47e28c51eed79.png": "\\bigcup_{i=1}^{n}B_{i}\\in B", + "b9f90774498f2516.png": "\\overline{\\Psi_{0}}=\\sqrt{\\frac{m}{\\pi}}e", + "ba0347bd17c979d3.png": "O(n^{\\lceil\\frac{d}{2}\\rceil})", + "ba038b399cf813a9.png": "Y_{(II)}", + "ba0600ed081a56d3.png": "|\\omega_{\\Delta}^{free}|\\le\\omega_{l}", + "ba10fdc84059c9c7.png": "\\sum_{k}(n)", + "ba21e47fb18fb7c0.png": "PN_{1}=\\frac{N_{2}}{d}", + "ba271caf2b10b7ae.png": "\\tilde{T}_{i}:=T_{\\tilde{G},\\tilde{H}_{i}}", + "ba30e5d4714b7582.png": "P=P(C(Z))", + "ba3e4bab8af19705.png": "I_{2}=D(b)f(b)b^{2}", + "ba538a859e3bd229.png": "\\frac{||J(x)||}{||f(x)||/||x||}", + "ba587bbb10c23b45.png": "N_{v}(\\mu_{2}-\\mu_{1})=\\frac{df}{dc}", + "ba59f5c579509d55.png": "(s,t)\\mapsto f_{1}(s)f_{2}(t)", + "ba5a74ee558839b4.png": "\\overline{f}(0)=\\langle\\rangle", + "ba5bf764516949e9.png": "ts^{i}\\in D_{2p}", + "ba67b95d651081b8.png": "K_{m}=\\frac{1}{2}(k_{1}+k_{2})", + "ba891bb8922b4b96.png": "f(t)=\\frac{1}{t},t\\in[0,1]", + "ba8f99ecb8d17729.png": "1-\\sqrt{-5}", + "ba9a46be0bae0b9c.png": "P(w)=P(-\\frac{1}{w^{*}})", + "ba9ae7366f8ae9d2.png": "\\sigma_{kl}\\equiv\\frac{i}{2}[\\gamma_{k},\\gamma_{l}]", + "ba9de5c21c00631f.png": "E[S_{1}+...+S_{\\lambda}]", + "ba9fc921ee31358f.png": "|y|\\in O(|x|^{k})", + "baa49ed1fe210bc0.png": "L_{\\alpha+1}:=Def(L_{\\alpha})", + "bacd080130666c02.png": "\\phi(u):=d(\\tilde{u},u)", + "bacdaef52301e171.png": "M^{K}:=-D\\nabla^{2}w^{K}", + "baf4af9c1abaabf6.png": "\\neg(xd_{c}", + "bb4add55da2e9a4b.png": "0/x=0,x/x=1", + "bb4ee0fdc872b460.png": "\\psi_{2m+1}\\in Z[x,A,B]", + "bb50751322747b48.png": "1-k_{i}\\in U(R)", + "bb51584bbcab6a31.png": "A_{0}=\\frac{\\sqrt{3}}{4}a^{2}", + "bb516f29366ee73d.png": "f=2\\pi^{2}\\frac{\\mu Nr}{Pc}", + "bb5a1c0e855da4ae.png": "cosx=\\frac{1}{\\sqrt{2}}", + "bb5c6b7ec53c5dde.png": "m_{i,j}=x^{i}\\cdot x^{j}", + "bb5d3416d4306687.png": "\\frac{1}{P_{0}}\\prod_{i=1}^{c}(\\begin{matrix}m_{i}\\\\ x_{i}\\end{matrix})\\omega_{i}^{x_{i}}", + "bb66239b3420cbad.png": "F^{\\times}/F^{\\times2}", + "bb73b2c9e5bf27de.png": "\\{z|z\\overline{r}+\\overline{z}r=0\\}", + "bb9305e8f9bc6810.png": "y_{n}(x)=x^{n}\\theta_{n}(1/x)", + "bb9b02391fa739aa.png": "\\nabla^{2}\\varphi=-\\frac{\\rho_{f}}{\\epsilon}", + "bba580665aaff379.png": "||\\sigma(x)||_{2}", + "bbb952eea51765af.png": "f=2\\pi^{2}\\frac{\\mu N}{P}\\frac{r}{c}", + "bbcdb1feed41d609.png": "h(k)=kmod11", + "bbd7f6429bbd3814.png": "l_{n}=kl_{n}\\cdot\\frac{b_{n}}{b_{a}}\\cdot\\frac{s_{n}}{s_{a}}", + "bbf275d8bfe0e4a3.png": "(\\begin{matrix}1&2&...&j\\\\ a_{1}&a_{2}&...&a_{j}\\end{matrix})", + "bbf4ccdb4f7a2934.png": "Mf(s)=-\\frac{1}{s+a}", + "bbf539d2d3fd68d8.png": "\\sqrt{k}(l+\\frac{5}{2})=E_{l}", + "bbf637c202d3c166.png": "F_{P_{2}}\\circ f=F_{P_{1}}", + "bbfa6b30aa257d92.png": "=A\\cap(A\\cup A^{C})", + "bc0bb68a6314cf54.png": "f(\\zeta)=\\zeta^{-\\frac{1}{N-1}}", + "bc327f0b791843ec.png": "V_{t}=a_{0}\\cdot M\\sqrt{\\frac{T}{T_{0}}}", + "bc3f8e407ba01c85.png": "0,s(0),s(s(0)),...", + "bc44a525c8ad9945.png": "\\frac{P_{i}+P_{o}}{2}\\times\\frac{1}{P_{o}}", + "bc48c4ba43a57976.png": "P_{\\pi}^{-1}=P_{\\pi^{-1}}=P_{\\pi}^{T}", + "bc4ac0bde72e715a.png": "\\lfloor b_{i}x\\rfloor-b_{i}x", + "bc51ec8f4d81ed1e.png": "\\Delta t^{\\prime}=\\frac{2D}{c}", + "bc551651aec156c1.png": "\\langle\\phi(x_{1})\\cdot\\cdot\\cdot\\phi(x_{n})\\rangle", + "bc6d25f5595aecb6.png": "(d,w,y,y^{\\prime},\\tilde{k})", + "bc75e87788ac3bc5.png": "Z_{\\infty}^{p,q}=\\bigcap_{r=0}^{\\infty}Z_{r}^{p,q}", + "bc87d3a9bbb0367c.png": "x=x(\\xi^{1},\\xi^{2},\\xi^{3})", + "bc909bd3b50c6c00.png": "[a-bi]", + "bc92c2ed1fa66665.png": "[Q^{\\dagger},b\\}=\\frac{dx}{dt}+iF", + "bc9e0efb85651bc7.png": "N[(1+K)^{M}-1]", + "bca0e791e107c34e.png": "M_{x}=\\frac{u_{x}}{a_{x}}=\\frac{W}{a_{1}}", + "bcb34f18fd0eae83.png": "(a,b):\\Sigma_{(x:A)}B(x)", + "bcbb096de8d1e56d.png": "\\langle N,\\in_{M},...\\rangle", + "bce5271606d5b5f5.png": "\\delta(v,v^{\\prime})\\ge0", + "bce6f7f87024ce0a.png": "\\int dV|\\Psi|^{2}=N", + "bcee4f63f416fb88.png": "a_{n}=\\frac{a_{n-1}}{9}=\\frac{a_{0}}{9^{n}}", + "bcf1aa6fb1a60dc4.png": "\\epsilon=\\sqrt{1-(s_{a}^{2}+c_{a}^{2})}", + "bcfa687656e7ff58.png": "p^{!}k=k_{X}[n]", + "bd0104473c33583b.png": "0.3>\\alpha>-0.3", + "bd01b26eaeb66d38.png": "C^{T}B\\le l_{W\\times L}", + "bd0326a53e2277fd.png": "\\frac{d}{dt}\\gamma(t)=X_{\\gamma(t)}", + "bd19799698ca90cb.png": "1-e^{-1}=0.61", + "bd1b5b5ed360a843.png": "\\prod_{\\sigma\\in G_{F}}\\sigma(J^{a_{\\sigma}})", + "bd1b9708168f098b.png": "q^{*}/\\|q|^{2}", + "bd2fb05822842e9a.png": "G^{p^{k}}=\\{g^{p^{k}}|g\\in G\\}", + "bd3368a22b22b118.png": "20log_{10}(\\frac{d}{d_{0}})", + "bd38248cf07eb7cb.png": "\\partial_{v}f(x)=Df(x)v", + "bd3936caddaab1cc.png": "\\approx(a+w)(e^{a}(1+w)-1)", + "bd3c732c4126b84e.png": "(a/l)(\\nu/\\omega_{0})", + "bd435403157a70b7.png": "k=\\lambda^{2},\\lambda^{-2}", + "bd4532fd76472d2b.png": "(l^{k},r^{k})\\in Z^{k}\\times Z^{k}", + "bd4ac82bacedce52.png": "||Y|_{I}-U_{k}||_{1}\\le\\delta", + "bd509f53d362c0ba.png": "(\\Lambda(A):A\\in B_{b}(S))", + "bd56f9b68902a2be.png": "S(q)=\\frac{2\\pi}{q^{4}}", + "bd5ae0276f13baab.png": "E_{b}(r)=\\sigma T^{4}(r)", + "bd6c016a7eac7f42.png": "lim_{x\\rightarrow-\\infty}\\frac{4x^{3}+3}{5x^{3}-2}=\\frac{4}{5}", + "bd6cec0ebb369591.png": "(t^{2},t^{3})A", + "bd81ee012d836490.png": "J_{9-p}", + "bd8a84fd28d340a0.png": "-\\frac{\\pi}{|\\nu|}-2\\pi\\gamma\\delta(\\nu)", + "bd8cbb932577edbe.png": "\\sum_{i}r_{i}\\times m_{i}v_{i}=0", + "bd8cbbe30ebeed73.png": "||f||_{BV}=V_{f}(I)", + "bd92abcba79126cf.png": "2\\pi k+\\frac{\\pi}{2}", + "bdb58f14bf286f05.png": "1-(1-P_{1}^{k})^{L}", + "bdc0d0bd0b84a66d.png": "abca^{-1}b^{-1}d\\sim?", + "bdd02c071f28d883.png": "\\omega_{k}=\\pm\\sqrt{\\beta_{k}-\\frac{1}{4}}", + "bdd4a0fb4475cf6f.png": "\\frac{480}{0.9}=533.3\\approx534", + "bdd97a58fc81cc4d.png": "Pr(t|B_{i}^{-})", + "bddb716ad647464c.png": "b-(n-b)=a", + "bde198aaa31a3247.png": "U^{5}>10^{20}c", + "bde2da03f438d7ca.png": "e_{i}\\cdot e_{j}=[D]_{ij}", + "bde499b1ecd801d2.png": "\\frac{2m-\\mu}{\\mu}", + "bde5881ef1723bd7.png": "f_{0}(x)=|x|", + "bdf2eed87de89d74.png": "Nq=qKq=(Tq)^{2}", + "be0222fb51b5edd3.png": "*3=", + "be0756bb36841c8d.png": "n=f^{\\#}(m)O_{Y,y}", + "be1b66c9aeb8f8f5.png": "\\Delta L=\\frac{F}{EA}L", + "be1d0edb0222e783.png": "10^{-12}\\frac{m}{s}", + "be2419626bdba151.png": "W^{T}=W^{+}-W^{-}", + "be2d052754635ac8.png": "\\psi_{0}=\\psi_{1}+\\psi_{2}.(1)", + "be41606f977600e5.png": "\\forall\\theta\\in\\Theta,T(F_{\\theta})=\\theta", + "be4aafc1649411b6.png": "O(n^{2}log(r)log(q))", + "be5bcfb694a4634e.png": "v=\\frac{1}{\\hbar}\\nabla_{k}E(k)", + "be663192dcf7c8f1.png": "max_{F}trace(KF)", + "be72c6c6ae934b31.png": "R(\\theta,\\delta_{1})\\le R(\\theta,\\delta_{2})", + "be8ed4d61f0c3eb5.png": "\\hat{\\Omega}=\\hat{\\Sigma}\\otimes I_{R}", + "be9e65b1c8d6263b.png": "(c:a:b)\\cdot\\tilde{a}:2\\cdot m", + "bea4f4057fb09544.png": "|z|<1/(1-q)", + "bea6f8638dd3dbcb.png": "=C_{c}", + "beb192e956900c8b.png": "\\theta=(m_{0},\\mu,\\overline{\\sigma},b,\\gamma_{1})", + "bebab3783b20b958.png": "F_{i}*\\frac{dV_{g}}{dT}=\\frac{dC}{dT}", + "bec84803897211cf.png": "[a,b)\\subset R", + "bec9041a606dd590.png": "x^{\\prime\\prime}=Gm/4x^{2}", + "bec99a2c623c9353.png": "n\\approx2.5\\sqrt{\\frac{c}{2j+1}}", + "bee8a2a53415dd7b.png": "00:X(t)<0\\}", + "bf074945ee8f8719.png": "R=Z[x]/\\langle f(x)\\rangle", + "bf2129f65c22e665.png": "x_{ij}=(\\begin{matrix}z_{2}&z_{1}\\\\ -\\overline{z_{1}}&\\overline{z_{2}}\\end{matrix})", + "bf240c6c977953f9.png": "A_{1}(f),...,A_{n}(f)", + "bf244fe610124eb6.png": "(\\rho=\\rho(p))", + "bf2db5fc9de8d3d5.png": "H=\\sum_{k}\\dot{q}_{k}p_{k}-L", + "bf39c4472b10bf05.png": "[\\begin{matrix}0&1\\\\ 0&0\\end{matrix}]", + "bf5bfcea2b213f63.png": "P=K\\rho^{1+\\frac{1}{n}}", + "bf5c980dcd6aad32.png": "[A]_{p}\\subseteq cl(A)", + "bf62fdc2d93db340.png": "-\\rho_{b}=\\nabla\\cdot P", + "bf68f4475020f1e0.png": "E_{1}\\cup E_{2}\\cup...=B", + "bf6ac83030569efa.png": "n^{a}\\partial_{a}=-\\partial_{r}", + "bf6b3caf15c99d85.png": "A\\cong k[[x_{1},...,x_{d}]]", + "bf6cdda1bba6c28f.png": "lim_{(x,y)\\rightarrow(0,0)}x^{y}", + "bf717ddbd8beb9fa.png": "|z|<1/(1-q)", + "bf84bcbcc2ce5ea9.png": "\\frac{d^{2}x}{dt^{2}}+\\frac{k}{m}x=0", + "bf8c96aaf4b12ea9.png": "\\hat{x}_{k+1}", + "bf9d5f66ff595299.png": "\\hat{A}(k)=A(\\hbar k)", + "bfa59d944a68d30c.png": "\\nabla_{\\mu}\\nabla^{\\nu}\\Phi_{\\nu\\mu(s-1)}", + "bfa6d9667f25d0e6.png": "\\sum_{j}M_{j-1}^{*}/M_{j}^{*}=\\infty", + "bfb834fbd7faff26.png": "\\varphi(s(x)\\cdot g)=g", + "bfc7476f4c20c620.png": "U_{a}(z)=", + "bfd10a0419bbd100.png": "\\eta_{a\\mu\\nu}\\overline{\\eta}_{b\\mu\\nu}=0", + "bfd5bfa5d3d4ccb9.png": "1(", + "bfd645e2bcdba771.png": "v=1-\\frac{f_{m}}{N}", + "bfda504f311e7a33.png": "\\nu=\\Gamma-\\lambda ln(p^{\\prime})", + "bfef755f08086144.png": "|f_{i}(x)-f_{i}(y)|<\\epsilon", + "bfef8767d5614c27.png": "||Y|_{I}-U_{k}||_{1}\\le\\delta", + "bff753885b238eb9.png": "\\sum_{k=1}^{n}\\varphi(k)\\sim\\frac{3n^{2}}{\\pi^{2}}", + "c000ae1586a05298.png": "\\Delta t=\\frac{(R+A)l\\Delta h}{1-h}", + "c003422473254237.png": "\\sigma^{2}*(X^{\\prime}X)^{-1}", + "c00c3bb1635144e6.png": "1/(2q^{2})", + "c0102226e610327b.png": "exp", + "c014063b8463849a.png": "\\frac{2log(l-1)-logl}{2}", + "c018fcaf81d7cc87.png": "w_{1},w_{2},...,w_{n}=", + "c0192c8d64ec0a39.png": "D\\rightarrow D/m_{D}", + "c03196802d3d8bba.png": "g_{4}=-x+3x^{2}", + "c04639a7a48b6d62.png": "[p^{2}(1-f)+pf]", + "c05a63212de01366.png": "U(x_{0},t)", + "c07184ef9aeb6475.png": "E=\\oplus E_{i}.", + "c083aea94f245849.png": "X=[\\begin{matrix}A&B\\\\ B^{T}&C\\end{matrix}]", + "c099d6c2b4dce7f6.png": "uv=-\\frac{1}{3}p", + "c0a18aa5ecf1cd03.png": "2P_{\\frac{1}{2}}", + "c0a60d9bf3572506.png": "g_{j}\\in L^{d-1}(R^{d-1})", + "c0a62bc63a06c3d0.png": "\\sum_{i=1}^{n}i", + "c0b51ed478c414f0.png": "\\phi(x)=Ax+x_{0}", + "c0ba29ee83c61415.png": "c_{k}=\\frac{f^{(k)}(0)}{k!}", + "c0bb717c1cfac726.png": "s_{i}=(a_{i}-d_{i})^{+}", + "c0bc7d2dbf453257.png": "L=L_{f}(D)", + "c0c6fd3def475492.png": "-a^{n}u[-n-1]", + "c0d1c0f539d021b8.png": "I=|U(P_{1})|^{2}", + "c0d46bb399b19bff.png": "2)x^{2}+2x=2", + "c0d9014679dba563.png": "\\pi(0.99)\\times v(1000)", + "c0e11ab0df84a1be.png": "T_{n}^{p}I(x)=-x+n", + "c0ef9c88db34f49c.png": "B=P(UP_{\\ge1}(Z))", + "c0efa5a099d88fd0.png": "\\alpha^{-1}W_{\\alpha^{2}t}", + "c0f1657f7fb1df7a.png": "T_{j}\\subseteq[t]", + "c0f5a36762f5abaf.png": "\\lambda x.yz=\\lambda x.(yz)", + "c0faf66635c9472d.png": "2sinAcosA=2\\frac{ab}{c^{2}}", + "c102d411b567698d.png": "A_{proj}=\\pi r^{2}cos\\beta", + "c11586bfe8859cb7.png": "\\sqrt{S}\\approx6\\cdot10^{2}=600", + "c1178f443f274fa8.png": "w_{j}=\\frac{1}{l^{\\prime}(x_{j})}", + "c117d0c45bcbfa38.png": "\\pm\\frac{1}{\\sqrt{2}}=\\pm0.7071...", + "c1194dc5cc3556c5.png": "N_{1}^{c}=(\\frac{3}{4\\pi})^{1/2}", + "c1244e6956f585b6.png": "A^{+}P=A^{+}=QA^{+}", + "c12772d4274536a1.png": "r=D_{K}[F(K,L)]", + "c12cd9996649c6f3.png": "-y(\\gamma-\\delta x)=0", + "c12f98ec15023216.png": "L\\frac{d^{2}q}{dt^{2}}+q/C=E", + "c13311b9cd70b12f.png": "Q(a)v=(v\\cdot a)a", + "c1464e0cadf72116.png": "G(X)/G^{0}(X)=G", + "c1613edcad0e6781.png": "F_{0}:S^{0}\\rightarrow T^{0}", + "c16e8d87b6d2d21e.png": "\\Phi=e^{\\beta(\\epsilon_{i}-\\mu)}-1", + "c17892f28cbd88b0.png": "\\alpha=1-\\frac{D_{s}P_{n}}{D_{n}P_{s}}", + "c180a3cac181675f.png": "log(e^{x^{\\prime}}+e^{y^{\\prime}})", + "c1b0f3a71c0f5d2f.png": "q=\\frac{1}{6}\\sqrt{2\\pi}\\Delta P\\frac{d^{3}}{l\\sqrt{\\rho_{1}}}", + "c1bbe314bf746e4f.png": "\\hat{\\Pi}\\equiv I-\\Pi", + "c1c17b6e16147358.png": "1/x\\approx1-x", + "c1c6954c93df4b1f.png": "distance=tan(\\theta)\\frac{v}{u}", + "c1ccb1648b47e4aa.png": "(3+N)+1", + "c1ccf699d1febe67.png": "T+ATT=1+E", + "c1d834ad5a48145d.png": "\\dot{m_{c}=\\frac{H_{5}-H_{6}}{H_{6}-H_{7}}}", + "c1da9e59d6782124.png": "\\{f^{n}(x)\\}_{n\\in N}", + "c1e2373203972e69.png": "\\prod_{k=1}^{\\infty}\\frac{1}{1-x^{k}}", + "c1e84b2835297953.png": "\\chi^{2}=\\frac{(121-59)^{2}}{121+59}", + "c1f178922ee42977.png": "(-p/2)", + "c1f89aebe4903904.png": ">T_{b}", + "c1fa97107e6ad0f8.png": "y^{2}(1-y)", + "c203ea5fad90966f.png": "\\overline{U}D^{2}", + "c205d8d93fd34cb0.png": "e_{\\lambda}(f_{ij})=\\frac{f_{ij}}{\\lambda}\\frac{\\partial\\lambda}{\\partial f_{ij}}", + "c211facc6b264ec1.png": "K\\equiv\\bigoplus_{\\omega\\in\\Omega}A_{\\omega}", + "c215e93c77af6d2b.png": "\\mu=\\sum_{k=1}^{15}kp_{k}", + "c21693dc7e6ab6d9.png": "E_{k}=mc^{2}-m_{0}c^{2}", + "c22401f6edd6320f.png": "a+(180", + "c227426055f052fb.png": "\\Delta\\epsilon=\\int vd(\\Delta v)", + "c22d1c3d12298ff0.png": "lim_{(a,b)\\rightarrow(0,0)}\\frac{a}{b}", + "c24fed71385bc1c3.png": "S=\\frac{c}{4\\pi}E\\times B", + "c2523167f08d3718.png": "\\frac{3^{n}+1}{2}", + "c2569662a604d398.png": "g_{4}=-x+3x^{2}", + "c25ea73f57e68641.png": "1-\\frac{(m)_{n}}{m^{n}}", + "c2613b79ecbe43d6.png": "csc^{\\prime\\prime}(\\frac{1}{2}\\pi)=1>0", + "c267170d422d0b18.png": "P(r_{i})\\propto p(r_{i})", + "c26b513397e1de8d.png": "\\frac{n-5\\pm\\Delta_{n}}{2-2n}", + "c26b9b4fbac584dd.png": "X=|X|e^{jarg(X)}", + "c26bbaef2da1a90c.png": "(s_{i}(t_{i}),t_{i})\\in C_{i}", + "c26cf3f118493eac.png": "\\frac{1}{1}=\\frac{2}{2}=\\frac{3}{3}=\\frac{4}{4}", + "c2788beab489f34f.png": "\\Omega_{X/S}=\\Delta^{*}(I/I^{2})", + "c283d61d7d0cf65b.png": "e^{*}=(sign(e_{i}))_{i}", + "c284e3cc8ed9f1c9.png": "\\frac{hL(P-U)}{2PU}+\\frac{S}{L}", + "c28d339d5ef15ce1.png": "2^{k}t_{0}", + "c2988ad612f77dd9.png": "\\sum f(T,c)=1", + "c29b7fb723c5f412.png": "\\pi^{\\prime}y>f^{\\prime}(b)", + "c52993fdf29152bb.png": "\\Omega_{\\Lambda}\\simeq2/3", + "c529a62debc764aa.png": "1/\\sqrt{3}=0.57735...", + "c52d02b055cd8641.png": "\\alpha_{i}|\\alpha_{i+1}\\forall1\\le i0", + "c7457df7cdf1a055.png": "E[X]:=\\rho(-X)", + "c74bec83fe4d5dda.png": "f(s)=\\frac{s^{2}+1}{s}", + "c754aac1c6c0af54.png": "\\Rightarrow x=\\frac{Pr_{2}}{r_{1}+r_{2}}", + "c7580acd5426052b.png": "\\mu_{e}=\\frac{2\\epsilon_{r}\\epsilon_{0}\\zeta}{3\\eta}", + "c75b6e8ec590a046.png": "X_{>\\epsilon}:=\\mu^{-1}((\\epsilon,\\infty))", + "c75e8dcfafb309f2.png": "Be=\\frac{\\Delta PL^{2}}{\\rho\\delta^{2}}", + "c76b4831a746fe90.png": "\\{\\begin{matrix}3,4\\\\ 3,3,3\\end{matrix}\\}", + "c7851be7364ac75f.png": "s=\\frac{a+b+c+d}{2}", + "c786578228ddd158.png": "x(t)=\\Phi(t,x_{0})", + "c79bc3ccb6b8558f.png": "(\\begin{matrix}zId&D^{t}\\\\ X&\\partial_{z}Id\\end{matrix})", + "c7b276d55b13d866.png": "P_{\\nu\\mu}=\\sum_{\\alpha}P_{\\nu\\mu}^{\\alpha}\\frac{\\partial}{\\partial x^{\\alpha}}", + "c7b5abe7dc286c17.png": "x^{\\prime\\prime}=RxR^{-1}", + "c7c22dbfa06d2188.png": "\\alpha=c\\times\\omega^{\\wedge\\frac{k}{2}}", + "c7c7453379cada93.png": "(\\frac{m}{s^{2}})", + "c7ca73abe08721ea.png": "3^{t}-t>3^{r}-r", + "c7d0b84a1ff46a3d.png": "e^{i\\mu t-\\sqrt{-2ict}}", + "c7d7ce0e110744f3.png": "so(2n+1,C)", + "c7d83ddd653870a9.png": "|\\phi_{2^{i}}\\rangle", + "c7e2234c67e25be7.png": "(e^{z})^{n}=e^{nz},n\\in Z", + "c7ed6964bd6f6ccf.png": "(t^{2},t^{3})A", + "c7eeefe85da7fef4.png": "p(a/2)>2p(a)", + "c7fe734054c1a8e4.png": "|G|=|S_{21}|", + "c800b965c4f8b5b9.png": "\\frac{1}{1-\\delta}\\epsilon", + "c81625dd0adc08d3.png": "\\forall i:V_{i}(Y_{i})\\ge V_{i}(X_{i})", + "c82a0d2e2309a727.png": "\\overline{\\psi}(x,\\tau)", + "c82a918a4d48592a.png": "C_{X}=C_{Y}=[0,1]", + "c8375cf46431c5ee.png": "L=L(y^{a},\\partial_{i}y^{a},x^{i})", + "c83d62c99e97694e.png": "0\\le b^{\\prime}0", + "c9bd466272f4fef6.png": "E[(X-E(X))^{2}]", + "c9be3144516209b4.png": "\\Theta_{div}\\simeq2\\frac{w_{0}}{z_{R}}", + "c9c96bfee2741a7b.png": "\\hat{p}_{x}=-i\\hbar\\frac{d}{dx}", + "c9ccc1fba1747305.png": "h=\\frac{|R|+|A|}{n}", + "c9d75323af172b7e.png": "U=\\gamma(c,\\vec{u})", + "c9e00a12cd64da93.png": "I/I_{0}=e^{-m\\tau}", + "c9ee0cb545bf30fd.png": "(\\Theta\\subset R^{r},S)", + "c9f8b18d04eb3df0.png": "R_{q}=a\\sqrt{q_{p}/2}", + "ca04350a03af31d3.png": "\\frac{1}{2^{N}}(\\begin{matrix}N\\\\ k\\end{matrix})", + "ca0a825c737a1935.png": "D^{j}(G_{0})", + "ca0ed5191693c75d.png": "\\Lambda^{(m,m+1)}", + "ca2159fe3df8090c.png": "1-F_{Y}(q)", + "ca22862a99757980.png": "A_{0}\\bigcap A_{1}\\ne\\emptyset", + "ca2a92375f195cf4.png": "u_{t}-u_{xx}=0", + "ca2c16c9b6a92ad9.png": "M_{L/2}=\\frac{PL}{4}", + "ca2d3fd16ef9fe17.png": "E_{h}=\\alpha^{2}m_{e}c^{2}", + "ca3622f7e06843db.png": "\\frac{\\pi^{2}}{6}\\approx1.64493", + "ca3cab2a2a1b5c6b.png": "L^{1,1}=L^{1}", + "ca3e6fceb8e684c2.png": "D=D^{(0)}+\\epsilon D^{(1)}", + "ca51cc78ca79db66.png": "\\frac{1}{2}m\\overline{v^{2}}=\\frac{3}{2}k_{B}T", + "ca565288cadbb9b6.png": "w_{ij}=exp(-\\frac{r_{m}^{2}}{\\kappa})", + "ca5a3068bd071c64.png": "\\hat{b}^{i}=\\frac{b^{i}}{\\sqrt{g^{ii}}}", + "ca5d7a88efdbdcd8.png": "TT^{*}=T^{*}T", + "ca60c808c7574613.png": "\\alpha(f(0),f^{\\prime}(0))=1", + "ca6a5d2140c623e7.png": "\\underline{W}(\\mu,\\cdot)", + "ca6fddcc738a80ce.png": "(-1)^{2}=1", + "ca73196a25ec59bb.png": "1-(0.95)^{2}=0.097", + "ca7aa0a478b0e554.png": "\\int\\frac{\\partial}{\\partial\\theta}f(\\theta)d\\theta=0", + "ca84e160f3aadfe3.png": "\\alpha_{A}=\\sum w_{i}\\alpha_{i}", + "ca88dd6dc6935a97.png": "lim_{x\\rightarrow0}\\frac{x}{x^{3}}=\\infty.(6)", + "ca8a0f2d02c0dd74.png": "\\frac{a_{n}}{\\sum_{i=1}^{n-1}a_{i}}", + "ca8c75171f780705.png": "\\sum_{k=0}^{m}(\\begin{matrix}m\\\\ k\\end{matrix})(\\begin{matrix}n\\\\ r+k\\end{matrix})", + "ca95f7f55a07d331.png": "(f(t)*\\delta(t-T))", + "caa6ed1684646c16.png": "\\pi(k+\\frac{1}{2})", + "caa9c9a6c393610f.png": "\\beta=||b-Ax_{0}||", + "cab2833a2228e8f7.png": "I_{n}=[a_{n},b_{n}]", + "cac121534b2be17e.png": "\\gamma^{\\mu}\\gamma^{\\nu}\\gamma^{\\rho}\\gamma_{\\mu}", + "caca8565adf3d74b.png": "\\pm\\epsilon^{ijkl}e_{k}\\wedge e_{l}", + "caf63ae11512f033.png": "a^{n}a^{-n}=1", + "caf6619f3c559701.png": "\\frac{d^{2}w}{dx^{2}}=-\\frac{M}{EI}", + "cb01ee6ebdf38561.png": "D^{j}(G_{0})", + "cb07223759d8a987.png": "ds^{2}=\\lambda^{2}(z,\\overline{z})dzd\\overline{z}", + "cb21889018601cde.png": "{(\\hat{k}_{F})}^{\\kappa\\lambda\\mu\\nu}", + "cb21ff5682f0f18a.png": "\\int e^{x}dx=e^{x}+C", + "cb2488099e38e3db.png": "x=y^{3}+2z-1", + "cb25184c8600f7a9.png": "\\frac{v_{0}^{2}}{gh_{0}}>1", + "cb26eaaf24bb895d.png": "A_{peak}=\\Delta H_{vH}(T_{d})", + "cb3603e8ccb96c2e.png": "[\\hat{a}(t),\\hat{a}^{\\dagger}(t)]=1", + "cb4de2908f341dfc.png": "\\int\\frac{e^{x}}{x}dx", + "cb52b2a4ad197800.png": "\\int d^{d}x\\overline{\\psi}iD/\\psi", + "cb54d88e3d983186.png": "\\sum_{i=0}^{m}|\\Delta F_{i}|", + "cb5550740fc18b06.png": "|\\psi\\rangle^{A}", + "cb6dae1648005809.png": "p(a/2)>2p(a)", + "cb79746215ec2c43.png": "(pa+qd)", + "cb79f9e57deb16b6.png": "E_{n}^{(0)}-H_{0}", + "cb7bce67edeb522e.png": "E_{T}:=E\\otimes_{O_{S}}O_{T}", + "cb7fac6f6007ea31.png": "S=\\frac{h_{f}}{L}=\\frac{1}{\\rho g}\\frac{\\Delta p}{L}", + "cb84ed3cca6a516a.png": "\\frac{|x-3|}{|x|}<\\epsilon", + "cbb86359378850cd.png": "\\vartheta=[\\vartheta^{f},\\vartheta^{s},\\vartheta^{n}]", + "cbc42e3b6bc11cc2.png": "\\mu^{-1}([\\epsilon,\\infty))", + "cbce0323c5c763df.png": "f(x)=\\frac{b-x}{1+cx}", + "cbcfbd8696577084.png": "2x_{1}=D+\\frac{r_{1}^{2}-r_{2}^{2}}{D}", + "cbd1e68d5cdbaceb.png": "I_{n}=[a_{n},b_{n}]", + "cbd3b4c5e0c5bfa7.png": "\\dot{Q}=\\dot{m}C_{p}\\Delta T", + "cbd4addf6b570e52.png": "x\\ne0,[x:y]\\mapsto\\frac{y}{x}", + "cbd8f039e4ffde3f.png": "l_{n}=kl_{n}\\cdot\\frac{b_{n}}{b_{a}}\\cdot\\frac{s_{n}}{s_{a}}", + "cbd8f05d47db253c.png": "so(m-1,C)", + "cbdd13d5572f2523.png": "\\dot{\\phi}=L/r^{2}", + "cbe6e13131e399ec.png": "\\sum\\vec{a}(x_{i})=1", + "cc0ac7184ba3abc7.png": "\\overline{B_{1}(p)}=\\{p\\}", + "cc17f75dad86b0a9.png": "\\sigma(X^{*},\\hat{X})", + "cc1af326a46deb65.png": "Stk=\\frac{u_{0}V_{s}}{dg}", + "cc36346a6f4b5d05.png": "\\frac{y_{n}}{x_{n}}\\frac{X}{Y}=\\frac{x/x_{n}}{y/y_{n}}", + "cc42deb52b084174.png": "|\\frac{a_{n+1}}{a_{n}}|=1", + "cc457bd36a0da1c2.png": "I_{0},I_{1},I_{2}...", + "cc4a515b9d33bad9.png": "E(x)=f(x)-p(x)", + "cc52f56a291d4ebf.png": "2^{5}=32>26", + "cc53a7aaef749b32.png": "\\overline{B_{1}(p)}=\\{p\\}", + "cc57cb3742add42d.png": "|V_{0}|\\gg E_{f}", + "cc619d4965b2f740.png": "lim_{t\\rightarrow\\infty}\\hat{d}(w,t)=d(w)", + "cc62fc7919e64abf.png": "(1337;12,3)", + "cc6482a8f49d9ee5.png": "\\hat{u}^{2}=\\gamma_{0}+\\gamma_{1}x+v", + "cc6a4ae36d17a479.png": "\\vec{x}(t)=[\\begin{matrix}f_{1}(t)\\\\ \\cdot\\cdot\\cdot\\\\ f_{N}(t)\\end{matrix}]", + "cc70e60e9d3d5915.png": "-\\omega\\propto-2\\vec{\\nabla}\\cdot\\vec{Q}", + "cc79b5b35d9e559a.png": "H_{0}\\lambda^{2}=-\\frac{\\hbar}{2m}", + "cc7df10ad2b8905a.png": "\\varphi\\rightarrow\\frac{-\\nabla f}{|\\nabla f|}", + "cc80d2775e2b8314.png": "X_{n}=\\sum_{v\\in T_{n}}1_{v\\in K}", + "cc86f5ae52befe77.png": "a_{i}=\\frac{1}{N}\\sum_{j=1}^{N}y_{i,j}", + "cc87be6a29b9362f.png": "X_{1}(\\frac{1}{z^{*}})", + "cc89d323a4475d77.png": "\\overline{\\psi}\\mapsto(\\lambda\\psi)^{\\dagger}\\gamma^{0}", + "cc9f0f0965e89da7.png": "\\overline{X}+X_{\\xi}", + "cca8a03c2f292150.png": "\\frac{BO_{2}}{BE}=\\frac{1}{2}", + "ccad9deaac3f0cfd.png": "(e^{iax}-e^{-iax})/(2i)", + "ccb15f09cf6253ba.png": "N(d_{+})F", + "ccb81e48d50c77d6.png": "UNC=\\overline{x}(1-\\overline{x})", + "ccc6081a5376d827.png": "\\Theta=R\\times R^{+}", + "ccc6d799375f955d.png": "1\\leftarrow0.\\overline{1}=1.\\overline{0}", + "cccae6b38289eb0d.png": "C^{\\prime}\\rightarrow L=\\frac{1}{\\omega_{c}\\omega_{c}^{\\prime}C^{\\prime}}", + "ccd92d449bee596a.png": "\\hat{\\Sigma}_{j,/j}", + "ccdb45ea992a7a26.png": "Q_{1}+Q_{1}^{*}=0", + "cce231af30ac0f07.png": "=\\frac{1}{\\sqrt{2}}(|00\\rangle+|11\\rangle)", + "cceb53e1d6f44a87.png": "-R=P_{1}+P_{2}", + "ccecc67e234b15ee.png": "\\frac{\\partial}{\\partial y^{i}}=\\frac{\\partial x^{k}}{\\partial y^{i}}\\frac{\\partial}{\\partial x^{k}}", + "ccf8f454b391d198.png": "H_{\\epsilon}f\\rightarrow Hf.", + "ccfaa4c72510bac8.png": "\\sigma_{f}\\approx|a\\frac{\\sigma_{A}}{Aln(10)}|", + "cd000ccfbc8402c2.png": "-V_{0}\\cdot N\\ge0", + "cd01b3043e2a3232.png": "P_{i}\\propto\\frac{exp(-\\frac{E}{kT})}{Z}", + "cd06cc00c4fe1129.png": "\\prod_{x}ax=Ca^{x}\\Gamma(x)", + "cd081be1066b28bb.png": "1+2+3+4=10", + "cd1a286a779f8abb.png": "2^{1/p}>2", + "cd226cee297f5630.png": "(dy,-dx)", + "cd2420d1f9a16c51.png": "(a_{1},..,a_{n})", + "cd2ce99cb2712874.png": "\\begin{matrix}\\delta+x&=&x\\\\ \\delta\\cdot x&=&\\delta\\end{matrix}", + "cd3b08a263aea32f.png": "x^{\\prime}=-\\frac{1}{x}", + "cd4142264d350a4f.png": "V=\\frac{3\\pi^{2}}{16}R_{max}^{2}L", + "cd61479149da1efa.png": "(\\begin{matrix}n-1\\\\ 2\\end{matrix})", + "cd62a8ca2d4088f5.png": "(\\Sigma_{0}^{-1}+n\\Sigma^{-1})^{-1}", + "cd64a0e50607d8c5.png": "\\alpha:Id_{Id_{A}(a,b)}(p,q)", + "cd6e213e96e3d393.png": "\\mu=A\\cdot e^{Q/RT}", + "cd71b374c3e69d0c.png": "T_{n}^{p}I(x)=-x+n", + "cd8e9e74a7a6d868.png": "1-(1-P_{1}^{k})^{L}", + "cd8f98f27fe64049.png": "(1337;12,3)", + "cd8fa665d409ed98.png": "A_{proj}=\\pi r^{2}cos\\beta", + "cd94f40f36b072d2.png": "\\lambda=\\frac{ln2}{t_{1/2}}", + "cd998126ff42b0c3.png": "\\frac{d\\omega}{dz}=\\frac{\\omega}{1+\\omega}", + "cd9f75c1c828370d.png": "a_{G}=(\\frac{1}{n},...,\\frac{1}{n})", + "cda0ee40bf379c22.png": "R\\times R\\times(C-R)", + "cdab986f4300c986.png": "D=\\sum_{j=1}^{n}e_{j}\\frac{\\partial}{\\partial x_{j}}", + "cdb186ebffbb5494.png": "V=1096.7\\sqrt{H/d}", + "cdb51323319fc876.png": "\\Delta\\overline{\\nu}=0", + "cdbfb05467be8716.png": "log_{2}(n)", + "cdc0673ea205b2fc.png": "argmax_{x\\in X}f(x,s)", + "cdc3494916d18d99.png": "\\alpha=\\frac{\\pi}{4n}(2n-1)", + "cdc985529276c352.png": "\\tilde{f}=f+h", + "cdcb4fe1c04d95ec.png": "+(1-f)", + "cdd27f3cfeaeb59e.png": "\\sigma(T)-B(\\overline{R})", + "cdd37948ba4b5213.png": "F^{\\times}/F^{\\times2}", + "cde1b1412e17d440.png": "L_{10}=(C/P)^{p}", + "cde2eda9f1efe995.png": "1+2x+x^{2}", + "cdf16cd066c4787e.png": "\\tilde{M}=U\\tilde{\\Sigma}V^{*}", + "cdf3e6983712b4bc.png": "k=\\pm4,\\pm2,-1", + "ce027f3598d0fac6.png": "Z_{p^{m}}[x]", + "ce0dc1f1d214803a.png": "P_{e|H_{0}}", + "ce1fe7a395bad6c6.png": "f=T_{K}\\varphi+T_{K}^{*}\\varphi", + "ce2943d8d8726c54.png": "h(x)=\\frac{x_{i}}{|x|^{2}}", + "ce2b7c98714ff846.png": "(s,t,f(s,t))", + "ce31948c2080f0bd.png": "-2r^{-3}cos\\theta", + "ce33450be252a66a.png": "\\sum_{x}a=ax+C", + "ce3422256acbcfe5.png": "Nq=qKq=(Tq)^{2}", + "ce4045f1541b03bd.png": "E_{i}=C\\frac{M_{i}}{N_{i}}", + "ce4053e776691bc1.png": "1^{1/2}=-1", + "ce49f928e7280410.png": "X_{3}=(XX_{1}-1)^{2}", + "ce4a03a2e78b9c94.png": "\\omega_{\\{(k,i),(k^{\\prime},i^{\\prime}),(k^{\\prime\\prime},i^{\\prime\\prime})\\}}", + "ce5218f66e61558f.png": "-\\omega\\propto-2\\vec{\\nabla}\\cdot\\vec{Q}", + "ce63963f5f871a4c.png": "S_{n}/\\sqrt{nloglogn}", + "ce647cc91254a27c.png": "\\tau\\sqrt{\\frac{g}{h}}=9.80", + "ce64c96c16b25e08.png": "P^{\\mu},J^{\\mu\\nu},M", + "ce7d9698f56b71dc.png": "x^{\\prime\\prime}\\in D(p,w^{\\prime\\prime})", + "ce7f9d8bc3342d9b.png": "M_{X}(t):=E[e^{tX}]", + "ce83e8ac44de9314.png": "s_{max}\\sim|p-p_{c}|^{-1/\\sigma}", + "ce8f87a3812165c7.png": "F^{3}(\\hat{f})=f", + "ce911d1041af1adb.png": "1^{5/4}", + "ce95913487306977.png": "F_{n}=\\dot{m}v_{e}", + "cea3ff4e6c97a66d.png": "F_{q^{k}}^{*}", + "cea68e0977bb817c.png": "J_{(1)}=J_{(2)}", + "ceb7c11689c0c09e.png": ":c_{1}(z),...,c_{N}(z)", + "cec06f2d7eec7b3e.png": "0=f_{N}(s)", + "cec3909e4c68be19.png": "r_{2}=\\pm\\sqrt{p^{2}-4q}", + "cec3e5be4b0eeb5f.png": "3,2+5i,2-5i", + "cec97af8955e2f10.png": "24ms^{-1}=12s/23s", + "ced2ecfd14dd57f1.png": "|x-a/q|<\\frac{1}{q^{c}}", + "cee40554c3627c5f.png": "\\{f_{X}(\\cdot;\\theta)|\\theta\\in\\Theta\\}", + "ceea49d18c4f886a.png": "(\\Lambda(A):A\\in B_{b}(S))", + "ceebf728a3167bf7.png": "1+tan^{2}u", + "ceeee90e0907f9c1.png": "2^{2^{n}-n-1}\\prod_{k=2}^{n}k^{(\\begin{matrix}n\\\\ k\\end{matrix})}", + "ceefdcbdec685a3c.png": "\\sum f(T,c)=1", + "cef32fed945d95c9.png": "\\frac{T}{T_{i}}=\\sqrt{\\frac{M_{i}}{m_{e}}}", + "cef9724ff9acdd41.png": "H_{0}(\\langle\\vec{X}\\rangle_{m})<\\infty", + "ceff4c0ce1441e4e.png": "Z(z)=i\\sqrt{\\pi}w(z)", + "cf1146f50e72ce7a.png": "\\frac{1}{S_{1}}+\\frac{1}{S_{2}}=\\frac{1}{f}", + "cf226c9bb7fb8b84.png": "(G,q,g_{1},g_{2},c,d,h)", + "cf2378873fc61ebd.png": "w(\\neg\\theta)=F_{\\neg}(w(\\theta))", + "cf32f325cc99cf34.png": "1-\\frac{(\\begin{matrix}n-p\\\\ k\\end{matrix})}{(\\begin{matrix}n\\\\ k\\end{matrix})}", + "cf56b3cc6555f5f6.png": "B_{r}=-\\frac{2B_{0}}{R^{3}}sin\\lambda", + "cf64833c4a7fc1c0.png": "\\delta_{0}=\\frac{a_{P}}{A^{1/2}}", + "cf653b019fd59459.png": "d[P]/dt=k_{1}[A][M]", + "cf66a6636910e399.png": "\\frac{M-2G}{2M-2G}", + "cf6e21c670844c3f.png": "I=\\int_{-\\infty}^{\\infty}e^{-x^{2}/2}dx", + "cf75a41cd4efd338.png": "lim_{s\\rightarrow\\infty}e^{-st}(t)", + "cf76aff7858ebbf5.png": "af^{*}(\\frac{x^{*}}{a})", + "cf76f4fdae539eeb.png": "T=\\dot{m}V_{w}", + "cfc2e71c4f960eab.png": "S=R(X)+\\overline{R(X)}", + "cfce9bfa7d8c0e44.png": "H^{1}(X,O^{*})", + "cfd391323f3a7816.png": "U_{t}=e^{itA},t\\in R", + "cfd722f4ccb4ed7d.png": "f_{z}(x)=e^{ix^{t}Zx/2}", + "cfeb8ac034c8b7f9.png": "\\nabla^{2}L(x,y,t)", + "cfebd789fa7462b7.png": "[M]^{-1}", + "cfef0168817703b9.png": "f^{-1}(y)=\\frac{\\sqrt[3]{y}-8}{2}", + "d0008487c916e9e0.png": "\\delta\\omega=(\\omega_{+}-\\omega_{-})", + "d00b8952ce778234.png": "\\alpha_{t}\\leftarrow0.01L\\alpha_{t}", + "d00fb4844ed333bc.png": "(s,t)\\mapsto f_{1}(s)f_{2}(t)", + "d028ee64c6c979dd.png": "\\lambda(y_{i})0", + "d105ce8a753f8a7a.png": "O(\\frac{d}{\\epsilon}log\\frac{d}{\\epsilon})", + "d1069bb5d8b55ed8.png": "Q(a^{m})=Q(a)^{m}.", + "d10a80d93527506a.png": "4x^{2}+2xy-3y^{2}", + "d11b5ca751449a9d.png": "b-(n-b)=a", + "d11fa1ec9e8692aa.png": "y=\\frac{x}{g(x)};t=\\frac{1}{g(x)}", + "d127d9fc54152c09.png": "(n,Z_{p})", + "d13081d6009a3921.png": "A(\\omega)=\\frac{Z_{0}}{Z+Z_{0}}", + "d1344f10c384db13.png": "f(x_{t},t)=x_{t}e^{\\theta t}", + "d13a9f02fdef9925.png": "X_{j}=i\\frac{\\partial g}{\\partial\\xi_{j}}|_{\\xi_{j}=0}", + "d1599334e4eacdd3.png": "\\frac{e}{p}=\\frac{w}{w+\\epsilon}", + "d15ae3500dc6d2df.png": "L=\\frac{-1}{4\\mu_{0}}F^{ab}F_{ab}", + "d162a32aa7b5534f.png": "\\tau\\sqrt{\\frac{g}{h}}=9.80", + "d166bd6663e3e2d4.png": "x_{k+1}=x_{k}+\\frac{1}{m}", + "d167d25730898171.png": "\\pi(x)-\\pi(\\frac{x}{2})\\ge1", + "d17f966134b8733b.png": "\\phi^{\\prime}=\\frac{e\\phi}{T_{e}}", + "d18898af726dc139.png": "F_{y}=-T\\frac{y}{L}-Mg", + "d190c3aec67d72c0.png": "V\\approx\\sum\\pi y^{2}\\cdot\\delta x", + "d1b6184f9e8a88d4.png": "lim_{x\\rightarrow\\infty}\\frac{x!}{n^{x}}=\\infty", + "d1c67fa5273fe2d7.png": "\\oplus_{i=1}^{m}L^{2}(R,\\mu_{i})", + "d1ce7f622dea85c7.png": "V_{1}=Z_{11}I_{1}+Z_{12}I_{2}", + "d1d53e4d70bce15a.png": "A=-27q", + "d1da1667e391434b.png": "\\dot{q}_{2}=\\frac{R-r}{r}\\dot{q}_{1}", + "d1e550bbe3782b6a.png": "S_{i}=-\\frac{Q_{H}}{T_{H}}+\\frac{Q_{a}}{T_{a}}", + "d1e71100f86ef17b.png": ".d_{1}d_{2}...d_{n}0111...", + "d1e94b88c1c1a8bc.png": "\\Theta_{div}\\simeq2\\frac{w_{0}}{z_{R}}", + "d1ee5c0ea2129a65.png": "x,\\dot{x},...,x^{(n)}", + "d1f0a8a4d253af17.png": "x\\in[-2,-0.5]", + "d1f1a37d3d15c003.png": "\\phi(-a)=\\phi(a)=0", + "d1f8466552a61974.png": "\\pi=\\sqrt{10})", + "d1fa01f0ed45f2b0.png": "L(\\alpha)+\\alpha=K(x)", + "d1fd720360736137.png": "f^{\\prime}(x)=f(x)f^{\\prime}(0)", + "d204f7b4cf940ec2.png": "V_{max}=\\sqrt{2c_{p}T_{t}}", + "d20615bb65dd8c3e.png": "v\\in R^{2^{n}-1}", + "d20f61f6d32095fa.png": "[\\begin{matrix}1&0&0&2\\\\ 0&1&0&3\\\\ 0&0&1&-1\\end{matrix}]", + "d22a1376a74bde7b.png": "dw_{i}=\\frac{d\\Gamma}{4\\pi r}(6)", + "d25a772f71a25f86.png": "2^{f(|x|)}", + "d262280231842b36.png": "237/360=0.01034_{!}", + "d265767644bb6899.png": "t:=(e^{h}-1)^{-1}", + "d26a296895125f6b.png": "k_{i}-\\hat{k}=0", + "d2704283d0051f9f.png": "I=log_{2}2=1", + "d2743c4fc78a759d.png": "\\frac{d^{2}\\theta}{dt^{2}}+1=0", + "d277ffaa701cfaa6.png": "i_{C}=I_{S}exp(\\frac{v_{BE}}{V_{T}})", + "d27a462b612623aa.png": "(1-p+px)^{n}", + "d27eaf3fd6445333.png": "e^{-i\\epsilon H(p,q)}", + "d2943f3bfb4b2c34.png": "=\\frac{1}{\\sqrt{2}}(|00\\rangle+|11\\rangle)", + "d2a6c2777af171af.png": "\\sum k^{3}={(\\begin{matrix}n+1\\\\ 2\\end{matrix})}^{2}", + "d2ae4386a129b5e4.png": "\\pi(k+\\frac{1}{2})", + "d2be70cc72028785.png": "\\overline{T}", + "d2c5a5175ce962d2.png": "\\rho(r)\\propto exp(-Ar^{\\alpha})", + "d2d2bb2ef9c27824.png": "rank(\\tilde{M})=r", + "d2d313e52fe0e8cf.png": "=8x-15x^{2}", + "d2e010f11eb85b08.png": "4^{n}+2^{n+1}-1", + "d2e19f0eb32db3e4.png": "i,g\\in[0,1,...,n]", + "d2e37fdf5a0acadf.png": "\\gamma_{||}|A|^{2}L", + "d2e857b581fa7131.png": "\\frac{(N)_{i}}{(N-1)_{i-1}}=N", + "d2e8c9f97a2214ca.png": "V=f(t)=V_{0}e^{-\\frac{t}{\\tau}}", + "d2ea5583f3acd57e.png": "\\pm z_{1}^{c_{1}}...z_{n}^{c_{n}}", + "d2eace48448c2a72.png": "\\Omega=e\\Omega(e)e^{*}", + "d2ebb8762666149e.png": "S_{2}=V_{0}sin(\\omega t-\\pi)", + "d2fe1d93209a444c.png": "M=\\int_{V}\\rho dV", + "d30178fdaeccfdb8.png": "e_{i}\\cdot e_{j}=[D]_{ij}", + "d30272727c72c202.png": "\\overline{\\partial}_{j,J}f=\\nu", + "d303b34f2dfc217f.png": "\\chi_{f(x)>r}", + "d307915c1fbc614a.png": "B_{z}(x)=B_{0}e^{-x/\\lambda}", + "d30d2a9128eb0d94.png": "p_{q,x}:f\\mapsto q(f(x))", + "d31a189a8456da5a.png": "[q-1,k]", + "d32f26bda45c7109.png": "x=\\frac{d-bc}{1-ab}", + "d32f794c074c9f8d.png": "8.6.", + "d33bab97be05e30a.png": "y^{\\prime\\prime}=(y_{1}^{\\prime\\prime},...,y_{N}^{\\prime\\prime})", + "d3430a01c938aaba.png": "A\\cap B=\\overline{\\overline{A}\\cup\\overline{B}}", + "d348c14aec5feb5a.png": "P_{k}=\\eta_{0}\\frac{R^{2}}{Q\\beta^{3}}", + "d349c766fe692546.png": "E=1-\\tau_{pb}/\\tau_{pb}^{\\prime}", + "d34b0b8f9c7b80ff.png": "\\mu_{a}\\cap(A^{T}\\mu_{b}A)", + "d35b4c3a2862c36c.png": "g(t)=\\frac{1}{\\sqrt{s}}f(\\frac{t}{s})", + "d35f20e8dba26fea.png": "\\hat{\\rho},\\hat{\\phi},\\hat{z}", + "d360c1ba470d9828.png": "\\sqrt{\\rho}=\\rho=|\\phi\\rangle\\langle\\phi|", + "d36fcb8534d9b1fd.png": "OPL=\\int_{C}n(s)ds", + "d37f5569190ee08e.png": "(-1)^{x}", + "d391ac3a3738e2c3.png": "m=\\frac{1}{2R}(y_{2}+y_{1})", + "d394c872cdcecacd.png": "F^{m}[x_{1},x_{2},...,x_{n}]", + "d3a42b848d917f42.png": "(X,Y,Z,Z^{2},Z^{3})", + "d3a65ffcc8e8567e.png": "J(f)\\le+\\infty", + "d3b06f1eccd06fad.png": "-a^{n}u[-n-1]", + "d3c1deed70d8e2a5.png": "(\\phi_{\\tau}(\\omega)\\ne\\phi_{\\Gamma}(\\omega))", + "d3ce1a8e0940be0f.png": "\\rho_{i,i+1}=\\frac{2}{3}=0.66", + "d3dbb095382c7adb.png": "1/e^{z}=e^{-z}", + "d3f17bafcbd554e2.png": "D[f_{S}]", + "d3f18bfe4b3460b3.png": "\\frac{\\rho^{4}}{\\lambda^{4}}\\ll8\\frac{z^{3}}{\\lambda^{3}}", + "d3f326074f939f5d.png": "f^{\\prime\\prime}(x)<0", + "d3fb37d823e552de.png": "\\dot{Q}/T", + "d3fda9003b3fd1c0.png": "\\sum_{i=1}^{n}W_{i}\\times F_{i}=", + "d3ff4516c23cead8.png": "\\phi^{\\prime}=(1-G)*\\phi", + "d405749113664c4c.png": "Q(\\sqrt[2]{2})", + "d42280d48021a60c.png": "P(f", + "d42483a19aa85c7b.png": "U_{t}=e^{itA},t\\in R", + "d426582df89fc866.png": "H_{0}\\lambda^{2}=-\\frac{\\hbar}{2m}", + "d430280ca06e9cf0.png": "\\pm\\sqrt{\\frac{3}{7}+\\frac{2}{7}\\sqrt{\\frac{6}{5}}}", + "d43909532381cc08.png": "\\{|x+C_{2}\\rangle|x\\in C_{1}\\}", + "d43b6a37947ab13a.png": "I_{S^{i,z}}[f_{S^{i,z}}", + "d44028f4c1ba948b.png": "(u,y)\\in k^{d}\\times k^{n-d}", + "d442b6ab5f2a34ce.png": "F(t,x(t),\\dot{x}(t))", + "d44b17faa9913b51.png": "sin(\\alpha_{R})=1.22\\frac{\\lambda}{D}", + "d44b20bffd140daf.png": "\\Sigma_{k}^{P}=\\Sigma_{k+1}^{P}", + "d44cac55c42ef4f6.png": "(\\forall)\\frac{\\forall x.\\gamma(x)}{\\gamma(x^{\\prime})}", + "d44eeb25c0656901.png": "1-4\\pi r^{3}/3V", + "d44f2646732953fa.png": "R(t)=\\frac{R_{+}-gR_{-}}{1-g}", + "d45686e02d4409ff.png": "F_{P_{2}}\\circ f=F_{P_{1}}", + "d46c1ac87342b73b.png": "\\gamma^{0}\\gamma^{0}=I_{4}", + "d474e60fc2414c93.png": "m>\\varphi(m)", + "d47ccf5703452ac8.png": "|f_{i}(x)-f_{i}(y)|<\\epsilon", + "d47d7ac830a32731.png": "X^{\\{q\\}}=\\bigcap^{\\{q\\}}X_{i}", + "d490d5ba6406ac18.png": "\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}-\\frac{z^{2}}{c^{2}}=0", + "d491a3e8cfbd98b6.png": "\\frac{X}{X_{o}}=e^{-k}", + "d49b167a82f20ed1.png": "V_{i}[|R_{i}|=K]", + "d4aa6e3d9d35ae6c.png": "n_{\\perp}^{2}=\\epsilon(1-Q^{2})", + "d4af98dd8303534a.png": "L(r,\\theta,\\dot{s},\\dot{z},\\dot{r},\\dot{\\theta},\\dot{\\phi},t)", + "d4bc2c2ae30a53b2.png": "K_{x}Na_{1-x}Cl", + "d4c41b4f4c83f74e.png": "p(z)=cosh(z)-1", + "d4cb6f03c8489ca5.png": "\\sqrt{x}=-1", + "d4d114f38471e197.png": "S[\\sigma]\\rightarrow T[\\sigma]V^{\\prime}[\\sigma]", + "d4e476c5a37b6a2b.png": "x=10+2\\epsilon_{3}-5\\epsilon_{8}", + "d4e5e4f5c62249b4.png": "[u_{k}-\\hat{u}_{k}]", + "d4f135e5334f8cc1.png": "T(G)=T^{2}(G)", + "d505444a59965cf1.png": "a_{33}|a_{11}\\cdot a_{22}", + "d524b50742b65bf2.png": "N[u(x)]=0", + "d52efcc6034bffcb.png": "Dx-\\frac{1}{2}x=\\frac{1}{2}e^{t}", + "d533dd65ac8b699d.png": "S_{t+l}>H", + "d5345b6bf577d4b2.png": "0=-\\nabla p+\\rho g", + "d53e384e4febbd9a.png": "S_{w}=\\langle X|R\\cup\\{w\\}\\rangle", + "d53f77f1ad146310.png": "(\\frac{i}{2\\pi})^{n}\\delta^{(n)}(\\xi)", + "d5659d1c04c02468.png": "f(x)=|x|", + "d56a7802b784d944.png": "\\xi=\\frac{a^{2}\\omega_{0}^{2}}{2c}x", + "d5708776125229a5.png": "\\hat{x}_{0|0}=[\\begin{matrix}0\\\\ 0\\end{matrix}]", + "d576db66bd60c20a.png": "O(\\sqrt{b-a})", + "d57af58e75ecbb3d.png": "O(VElog\\frac{V^{2}}{E})", + "d57c50f49e70293e.png": "L^{2}(H^{2})", + "d5865e59a7800792.png": "\\sigma_{t}=\\frac{8\\pi}{3}(\\frac{\\alpha\\lambda_{c}}{2\\pi})^{2}", + "d58cc92659fdf9e0.png": "0t}W_{T}/T)", + "d8004456463d280a.png": "E(sup_{T>t}W_{T}/T)", + "d805ddaca266b836.png": "I(S;\\Omega-S)", + "d80fc0b526631ac4.png": "\\frac{\\partial f}{\\partial x^{\\alpha}}dx^{\\alpha}=0", + "d81ba37c3415c8cd.png": "X[(p+m)\\Delta_{F}]", + "d81e2e05766021c1.png": "\\sum_{d|n,dy\\Rightarrow x>\\sqrt{y}", + "d9bc556622d5d5b7.png": "1/n=(n-1)_{-1}", + "d9d17b134610a736.png": "\\sum k^{3}={(\\begin{matrix}n+1\\\\ 2\\end{matrix})}^{2}", + "d9dffc6dcfac8b8c.png": "\\frac{dx}{dt}=(x(t-1))^{2}", + "d9e8b8cfcb05045e.png": "h(k)=kmod11", + "d9ea0cef2ece85fd.png": "t_{2}-t_{1}:", + "d9fd249f59b38f23.png": "8.6.", + "d9fdc4d30b58ca2c.png": "(M,<,...)", + "da0cb149f26bdb1c.png": "\\sigma_{3}(n)=\\sum_{d|n}d^{3}", + "da33fc944877c2da.png": "p(a/2)>2p(a)", + "da36339db0d7954a.png": "V(s)=-J\\delta(s_{0},s_{1})", + "da3821e63651c2e7.png": "\\theta_{n}:=I_{[-N,N]}\\frac{\\nabla f}{|\\nabla f|}", + "da3e2d38fb679b50.png": "h=Nu_{c}\\frac{k}{d}", + "da4196ea56518618.png": "dy/dt(0)=y_{0}^{\\prime}", + "da4252ab74e41c37.png": "X^{\\perp}=\\overline{X}^{\\perp}", + "da4d408410f207b1.png": "\\frac{M}{13}=n+\\frac{r}{13}", + "da594836bf58352f.png": "y_{i,1}=x_{i}^{T}\\beta_{1}+\\epsilon_{i,1}", + "da7088cabc64e179.png": "Z_{\\epsilon}=\\frac{1}{\\dot{\\epsilon}\\epsilon_{0}}\\frac{l}{S}", + "da716594039c28e1.png": "\\exists!x_{n}A(x_{1},...,x_{n})", + "da860fb7bcbaba89.png": "\\sum_{\\gamma\\in\\Gamma}n_{\\gamma}t^{\\gamma}", + "da8a7b6fdda80346.png": "f(x)=|x|", + "da943ddb54efb04d.png": "1-\\epsilon log_{2}n", + "da9f4797f51c9070.png": "\\sqrt{x^{2}}=x", + "dac43f233b70ede3.png": "\\prod_{n=1}^{\\infty}(1-\\frac{p}{p^{3}-1})", + "daca179ad10e4364.png": "f(\\vec{a},\\vec{b})=f(\\vec{b},\\vec{a})", + "dacbf5f88addfd66.png": "y^{2}=x^{3}-n^{2}x", + "dacdadbc124b90b0.png": "P_{ij}=\\tilde{P}_{ij}logn/n", + "dacebc8e068369fa.png": "[n,n-m]_{2}", + "dad5a3c2a65fe43e.png": "A_{s}/A_{cef}", + "dafcf51353d3385c.png": "E=\\frac{2.21}{r_{s}^{2}}-\\frac{0.916}{r_{s}}", + "db08ce40d8da475f.png": "Q(\\sqrt{d})/Q", + "db1647565c2ec7d9.png": "(c,\\vec{v})", + "db1854f4245c2563.png": "DM(x)[h,v(x)]", + "db1a860bc347bf80.png": "\\frac{E_{s}}{N_{0}}=\\frac{E_{b}}{N_{0}}log_{2}M", + "db1ca613a5f1654c.png": "(||f+g||_{p})", + "db1d207c4595178c.png": "Spec(A/p)", + "db23153c5bcd6b28.png": "U(x,y)=min\\{\\alpha x,\\beta y\\}", + "db2688ddba6b0983.png": "\\sqrt{1-\\omega^{2}r_{0}^{2}}", + "db293a391c6f8162.png": "S_{k}=\\frac{\\lambda}{k}(\\rho^{\\prime})^{k}sink\\theta^{\\prime}", + "db33c2ca90a6f66a.png": "\\langle X\\rangle_{0}", + "db33f364eb5e4096.png": "A_{1}x+B_{1}y=C_{1}", + "db348e0cf027e4a3.png": "id_{X}=\\eta_{X}", + "db4076adab80c83d.png": "f=T_{K}\\varphi+T_{K}^{*}\\varphi", + "db4734ea1c03e8d8.png": "1+2x+x^{2}", + "db4797da98d3ddd6.png": "(,)", + "db52d0bf42ec4d86.png": "e^{i\\mu t-\\sqrt{-2ict}}", + "db53676c2a8eccd8.png": "g=w/2-n+1", + "db61ac6189817ca0.png": "\\sum_{i=1}^{n}W_{i}\\times F_{i}=", + "db684248a959e337.png": "2^{2^{2^{2^{2^{2}}}}}-3", + "db6f2cd1b0446c80.png": "y_{b}+\\epsilon=y(b)", + "db731f2984f16415.png": "r=D_{K}[F(K,L)]", + "db765e69cdb091ff.png": "x_{n}\\in C^{*}(\\theta_{n})", + "db779e7f19e066d1.png": "K(P_{k}^{n})", + "db7d4b464b79bcc2.png": "F=eEexp(-i\\omega t)", + "db8729cad3cae29b.png": "\\sigma(X^{*},\\hat{X})", + "db8aa2cb644e5bd9.png": "f^{-1}(y)=\\pm\\sqrt{y}", + "db99477e6a3e6c2c.png": "W=\\int nRT/VdV", + "db9e3359f844091a.png": "\\partial_{+}\\partial_{-}X^{\\mu}=0", + "dba02617455cd2f0.png": "\\frac{\\omega_{1}}{\\omega_{2}}\\notin R", + "dbadf29592c2e213.png": "1/e^{z}=e^{-z}", + "dbaf67a06e4ae9aa.png": "\\delta(n)=n-(\\frac{D}{n})", + "dbb26c156ede464c.png": "\\sum_{i=1}^{20}i=210", + "dbc80616c6a4993f.png": "f(\\theta)=P(D|\\theta,M)", + "dbd6bd43af114862.png": "\\frac{ln(1+c)}{2c}", + "dbdf14da7327cd8d.png": "f^{*}(d\\omega)=d(f^{*}\\omega)", + "dbdfaea9241f73e0.png": "M=\\oplus_{\\lambda\\in h^{*}}M_{\\lambda}", + "dbe24dbf6c1138aa.png": "[q-1,k]", + "dbe4669811a897b6.png": "N(t)=N_{0}2^{-t/t_{1/2}}", + "dbe4a9d98ab7e04e.png": "I\\subset1,2...n", + "dbe7fde1907a2174.png": "det\\varphi_{w}^{\\prime}(0)=-1", + "dbec810e662bd5b1.png": "X[(p+m)\\Delta_{F}]", + "dc0030a7b5ff8380.png": "lim_{x\\rightarrow+\\infty}f(x)", + "dc0ffba6d5943ae8.png": "F=\\frac{1}{c}\\overline{E}e_{4}+\\overline{B}e_{123}", + "dc1f74be8ffe3ac6.png": "R_{ws}[m]", + "dc2fc553c8ac469e.png": "csc^{\\prime\\prime}(\\frac{1}{2}\\pi)=1>0", + "dc3bcf3e79a4a0ab.png": "u\\cdot\\nabla u=-\\frac{1}{\\rho}\\nabla p", + "dc5da9b47cb6f2f0.png": "(\\lambda_{i}^{+},\\lambda_{i}^{-})", + "dc7307d38f41e85f.png": "=\\sum_{i,j}a_{i}b_{j}|i\\rangle_{A}|j\\rangle_{B}", + "dc8c8a455753dd5d.png": "[\\begin{matrix}p_{1}&\\cdot\\cdot\\cdot&p_{i}\\end{matrix}]", + "dc8fe7e7df65cfa7.png": "\\partial\\{(I^{2},\\varphi_{\\lambda},S_{\\lambda})\\}_{\\lambda\\in\\Lambda}", + "dcb2e18f706c7665.png": "\\partial M=\\Sigma_{0}^{*}\\cup\\Sigma_{1}", + "dcb549561eda72fd.png": "r^{(m)}(k)\\rightarrow r(k)", + "dcb5d4e383681c7d.png": "I=|U(P_{1})|^{2}", + "dcc4d3f59e265684.png": "X=U_{2}U_{1}^{-1}", + "dcd7dfbca029ffd4.png": "D^{j}(G_{0})", + "dcdb8da18d1bfdd6.png": "\\frac{1}{n}E(f-Ef)^{2}", + "dce9cc5f566cb77d.png": "P=\\frac{I^{2}\\rho l}{A}", + "dcf5fac0037e7f26.png": "d=\\frac{\\pi}{4}\\times b^{2}\\times s\\times n", + "dd130989dad97f15.png": "\\dot{M}=\\dot{B}=0", + "dd134d0be9351795.png": "\\mu(X)=\\frac{a+4b+c}{6}", + "dd2af7fec28c80f2.png": "\\sqrt{a}\\cdot\\sqrt{b}=\\sqrt{a\\cdot b}", + "dd2b5067a09d75ad.png": "\\frac{3\\pi}{2}0", + "e1e8c0fad6f05b2c.png": "x=4^{k}(\\frac{-1+\\sqrt{5}}{2})", + "e1ecebba907f2f17.png": "\\Leftrightarrow V_{Ti}^{\\prime\\prime\\prime\\prime}+2V_{O}^{\\bullet\\bullet}", + "e208e7d406ce251e.png": "[0,1)", + "e21105cc9bb9ad0f.png": "(n+1)^{k_{n+1}}", + "e21392e73fbf3750.png": "\\frac{\\omega_{1}}{\\omega_{2}}\\notin R", + "e218a629764a3199.png": "a=(2x+3)y", + "e219431eae921be5.png": "lim_{x\\rightarrow0}\\frac{O(x)}{O(x)}", + "e2195d811aefdc78.png": "P^{\\prime}(t)=P(t)Q", + "e21f1540c46d5984.png": "\\partial_{v}f(x)=Df(x)v", + "e222197ef88ca140.png": "d^{n}y=f^{(n)}(x)(dx)^{n}", + "e24ed513ba72923c.png": "\\omega=\\frac{|r\\times v|}{|r|^{2}}", + "e24efc75f06b3468.png": "B=b-\\frac{a}{RT}", + "e255103cace52205.png": "(\\frac{3}{\\sqrt{10}},\\frac{-1}{\\sqrt{6}},\\frac{4}{\\sqrt{3}},0)", + "e2562e87d27274ea.png": "l(p)-KP(x)", + "e262959796a759c0.png": "R_{a}^{b}-1/2R\\delta_{a}^{b}=0", + "e26adbac652b0d00.png": "y^{2}(1-y)", + "e27b3c466f1fa4f3.png": "\\frac{1}{2}+i\\frac{2\\pi n}{logn}", + "e28b1129d60623d8.png": "P_{c}=(\\frac{k\\rho_{c}C}{\\mu H})^{\\gamma}", + "e291070651b4cd68.png": "[\\begin{matrix}1&0&-\\overline{c}_{D}^{T}&z_{B}\\\\ 0&I&D&b\\end{matrix}]", + "e298b11b9b7f5c3f.png": "a^{2}\\cdot(2\\sqrt{3}+\\frac{\\pi}{6}-3)", + "e2a531d39b931999.png": "R=\\frac{a+x}{b+y}", + "e2ad58e2c1c982e9.png": "d_{k-1}h/2", + "e3970db6392a6b59.png": "I=\\sum|\\varphi_{n}\\rangle\\langle\\varphi_{n}|", + "e398d4bd86b6e801.png": "H=\\frac{\\Phi^{2}}{2L}+\\frac{Q^{2}}{2C}", + "e3a1f508124a46b1.png": "[k]_{\\times}v=k\\times v", + "e3bd84842904191b.png": "A^{*}=-A", + "e3bda724027eb0e1.png": "L(G)=\\{a^{*}b^{*}c^{*}\\}", + "e3c8203aa9e9eb01.png": "f(0)=h(0,\\langle\\rangle)", + "e3dec563c01dc229.png": "O(\\lambda^{(d-1)/2}log\\lambda)", + "e4073f7e3f94c7f1.png": "GF=\\frac{\\Delta R/R_{G}}{\\epsilon}", + "e41097589cea57c5.png": "\\sqrt{x}=-1", + "e4181027628538c5.png": "\\alpha^{\\prime},\\alpha^{\\prime\\prime}\\in\\Phi^{+}(\\gamma)", + "e41c4d6d52544328.png": "T=\\dot{m}V_{w}", + "e41dd3bba0110690.png": "2^{10,000}", + "e41f07515d59fdbe.png": "(7)\\hat{B}_{ab}:=\\nabla_{b}k_{a}", + "e42a0616837bafe9.png": "R^{d_{x}}", + "e435ff1ae67a8b6d.png": "c(1-d)=d^{2}", + "e441d294a7056d85.png": "Q=P\\times_{m}L^{2}(R^{n})", + "e44661040ab3d9c2.png": "csc^{\\prime\\prime}(\\frac{1}{2}\\pi)=1>0", + "e45d43fdbec1b4d4.png": "x_{1}[n]*x_{2}[n]", + "e45df8a1dc4139fc.png": "V_{p}=0.5Sdln(\\frac{D}{d})", + "e4601742bc98f4d0.png": "(\\frac{\\sqrt{1}}{288})^{4}\\cdot9-9^{\\sqrt{10}}", + "e46bf898d15851a8.png": "\\sum_{j}M_{j-1}^{*}/M_{j}^{*}=\\infty", + "e46c49afa9741691.png": "(\\gamma=1.4)", + "e46d7c398327f9af.png": "[x:=x+1](x\\ge4)", + "e47f786f7473559d.png": "\\pi^{2}/(12ln2)", + "e48cf2266317cf32.png": "\\tilde{C}^{+}\\rightarrow\\tilde{l}^{+}\\nu", + "e49af0c8e77abba7.png": "\\lambda\\langle f,f\\rangle=\\langle f,T_{K}f\\rangle", + "e49b8fb85d9432c9.png": "D^{\\epsilon}(\\rho||\\sigma)", + "e4a277bb0246144c.png": "0.v_{1}v_{2}...v_{9}", + "e4b599bcb7ae1228.png": "\\tilde{E}^{a},B^{a}", + "e4c6476b49b3991f.png": "m_{+}", + "e4ccd95915cc81f0.png": "Z_{p^{r}}[X]", + "e4cdb860f443a85a.png": "V_{out}=A_{OL}\\cdot V_{in}^{\\prime}", + "e4dd0f06afd238ec.png": "\\{F_{i},F_{j}\\}=s_{ij}\\circ F", + "e4f3c8c3c8d0a2cc.png": "(|a|^{2},|b|^{2},...,|h|^{2})", + "e4f552886887e2f0.png": "\\Leftrightarrow|PA|^{2}=9|PB|^{2}", + "e4fb5d8144f1e2c8.png": "K^{+}\\hat{g}", + "e4fbc7dd4bc1903d.png": "f(x)0", + "e74b9507ca17ecdf.png": "C=\\frac{u\\Delta t}{\\Delta x}\\le C_{max}", + "e7570b1a8191c699.png": "O((Nmlogq)^{2})", + "e7735e2f566fa845.png": "I_{im+}", + "e77c1a1dbc364570.png": "\\frac{1}{n}E(f-Ef)^{2}", + "e78730d5b8e67c33.png": "\\frac{1}{1-\\delta}\\epsilon", + "e78eea7cd8e90a63.png": "P_{1}=(1:\\sqrt{2}:1)", + "e790066039f53e19.png": "L^{*}g=L(dg)", + "e7a296b1d41c0064.png": "CO=\\frac{VO_{2}}{C_{a}-C_{v}}", + "e7a6cd433073ed90.png": "D^{\\pm}(S)", + "e7ad973875a1e329.png": "(a,b):\\Sigma_{(x:A)}B(x)", + "e7be7b3165adf066.png": "\\frac{d^{2}y}{dx^{2}}=f(x,y)", + "e7bfdede71170586.png": "k_{a}f_{a}+k_{b}f_{b}+k_{c}f_{c}", + "e7c4ecbfbb641569.png": "a_{m}=\\frac{(-1)^{m/2}}{(m/2)!}", + "e7c92e69cb9a0dab.png": "L_{0}=\\Delta_{a}-\\sum_{\\alpha>0}A_{\\alpha}", + "e7c97d6fdb89dcb2.png": "(rk_{0},rk_{1},...,rk_{31})", + "e7ce63f23176c80a.png": "f^{-1}(y)=\\sqrt{y}", + "e7cfcd3d7126058a.png": "\\gamma^{\\mu}\\gamma^{\\nu}\\gamma^{\\rho}\\gamma_{\\mu}", + "e7d2d127c7b91777.png": "\\frac{hL(P-U)}{2PU}+\\frac{S}{L}", + "e7d32d206bd46c44.png": "v=\\frac{1}{\\hbar}\\nabla_{k}E(k)", + "e7da320483330eab.png": "\\pi^{+}\\rightarrow\\mu^{+}\\rightarrow e^{+}", + "e7fc9321929f5db2.png": "F(x|a,b)=e^{-bx^{-a}}", + "e803c7524a1af037.png": "x^{3}(x^{2}-x-1)+1", + "e80c9a83afe0740d.png": "(M,<,...)", + "e815752766dfae7b.png": "\\pi ln(3)\\sqrt{3}", + "e816db411c9e2e3f.png": "v_{i}\\in H_{0}^{3},i=1,2,3", + "e822d054ff9d7de4.png": "||D_{n}||_{L^{1}}=O(logn)", + "e82439eafaaf8e0e.png": "C|\\psi\\rangle", + "e827ed153516431d.png": "\\pi_{T}=a\\frac{n^{2}}{V^{2}}", + "e82f64fdf4cf9977.png": "-|I|>I_{0}", + "e83b5cdfa07f8863.png": "M_{n}=M(i\\alpha)^{n}", + "e8435f2b62785514.png": "T^{\\prime\\mu a}=\\frac{\\partial x^{\\prime\\mu}}{\\partial x^{\\nu}}T^{\\nu a}", + "e844ff2554cbcd85.png": "L_{0}^{\\prime}=x_{2}^{\\prime}-x_{1}^{\\prime}", + "e86a7424b86bca62.png": "x^{-1}\\in m_{R}", + "e870bfb3cf3a6fd5.png": "v_{i}=w_{i}/||w_{i}||_{2}", + "e872693d46db3c41.png": "p(n-1)\\le1/21", + "ec736d1b9b6fc9d9.png": "\\sqrt{1},\\sqrt{2},\\sqrt{3},\\sqrt{4},\\sqrt{5}", + "ec73d8cb74fd6b15.png": "\\overline{\\nu}+p\\rightarrow n+e^{+}", + "ec75cf7c701b3249.png": "lim_{k\\rightarrow\\infty}(1/k^{2})^{1/k}=1", + "ec778f1dfd493ee4.png": "r_{t}=ln(P_{t}/P_{t-1})", + "ec8ec5bfe1a81cf0.png": "\\sum(-1)^{n}(lnlnn)^{-1}", + "eca7042f89604859.png": "[v=\\frac{1}{2}\\sqrt{\\pi}erf(x)]", + "ecadfca990f39f83.png": "2\\Omega_{x}>\\Omega_{z}", + "ecba9e03838c272f.png": "d,d_{0}>d_{c}", + "ecbd81de269e1b88.png": "0,s(0),s(s(0)),...", + "ecbfc310ae765338.png": "(0,0,-1)", + "ecc6df77f8e0eb68.png": "e^{-iE_{n}t/\\hbar}", + "eccea302813f84d0.png": "f_{EW}(|\\vec{a}-\\vec{b}|)", + "ecd4a6b7293c2986.png": "\\frac{x_{1}-x}{x_{1}-x_{0}}", + "ece8c01bc36397b8.png": "x+2y-3=0", + "ece908396672ed0a.png": "P(Z\\ge k)\\le\\frac{1}{2k^{2}}", + "ecea62e2016c85dc.png": "\\Delta=S^{*}S=FS", + "ecf088212c8fb2a4.png": "E_{L}[u]=E_{M}[u]", + "ecf71b0cc66cdcec.png": "\\frac{\\pi}{L}\\cdot\\frac{L}{2\\pi T}=\\frac{0.5}{T}", + "ed0d477ffe5883fd.png": "1+\\frac{a}{ax+b}", + "ed1ce49e71eb3e07.png": "E_{k}(\\Lambda)=\\sum_{0\\ne\\lambda\\in\\Lambda}\\lambda^{-k}", + "ed30eea260ce2df8.png": "\\hat{x}_{0|0}=[\\begin{matrix}0\\\\ 0\\end{matrix}]", + "ed345bc855c13b86.png": "\\underline{n}=n+i\\kappa", + "ed3b73212aed280f.png": "\\omega_{\\overline{x}}^{A}=\\neg\\omega_{x}^{A}", + "ed3ccd67aba071e2.png": "H=\\sigma(W^{T}X)", + "ed3dbe0eea187083.png": "N=[N_{x},N_{z}]", + "ed4de0882748f7b9.png": "Z_{F+G}=Z_{F}+Z_{G}", + "ed4e69d3a182f329.png": "p_{o}=p_{o+}", + "ed513edd5eb8b9e6.png": "(\\Theta\\subset R^{r},S)", + "ed522b3fef26f8b6.png": "B=\\frac{\\mu_{0}I_{enc}}{2L}", + "ed612e5e4173f7df.png": "\\frac{hL(P-U)}{2PU}+\\frac{S}{L}", + "ed6c16ddf60e1af5.png": "\\Omega=\\sqrt{|\\chi_{g,e}|^{2}+\\delta^{2}}", + "ed75f6c7a7d45d14.png": "\\partial_{v}f(x)=Df(x)v", + "ed8854187ecebdde.png": "\\theta=(\\mu,\\sigma^{2})", + "ed8953b048427ded.png": "\\frac{mX}{n(1-X)}\\sim F(n,m)", + "ed8debb205998a92.png": "(be)e=be", + "edacec215584ef9c.png": "V_{0}\\oplus W_{0}=V_{-1}", + "edb83bf8ea8c3589.png": "G=\\xi\\partial^{\\mu}A_{\\mu}", + "edb877dc72153ac0.png": "P(f", + "edb924781e93bec5.png": "\\frac{f(x-)+f(x+)}{2}", + "edda26390bad1b00.png": "s-t=s^{\\prime}-t^{\\prime}", + "edea78f4d7b713be.png": "w[N/2-1]=w[N/2]<1", + "ee0d2b3fed4df6af.png": "2c>\\frac{q}{2}", + "ee24ee66f7f3aec4.png": "[1]p\\equiv p", + "ee2fda8bc0ff83db.png": "a=-\\omega^{2}r", + "ee38c41feee29160.png": "tan\\varphi^{\\prime}=(\\frac{c_{1}}{c_{2}})", + "ee3bf7eab793e511.png": "De=B.Da", + "ee3c12010bd82186.png": "a=(1-\\alpha)^{\\frac{1}{n}}", + "ee42c4c44adbfad0.png": "\\sqrt{k}(l+\\frac{5}{2})=E_{l}", + "ee565e7ab59d6195.png": "(X\\perp\\perp Y)|W", + "ee584784f1f798bf.png": "z_{i}\\in R^{k}(1\\le i\\le n)", + "ee65de3f9f832738.png": "n_{1AU}\\approx\\sqrt{G}", + "ee6cb66913896665.png": "\\partial_{t}\\phi^{t}(x)=F(\\phi^{t}(x))", + "ee6e3747956897b8.png": "C_{\\frac{1}{2}}", + "ee6f2a6881d6270b.png": "17.836=\\frac{1}{2}k\\cdot0.15^{2}", + "ee78d704aceaa65b.png": "\\frac{3}{14}=0.2\\overline{142857}", + "ee828ef2cf500fd1.png": "\\sum_{i=1}^{n}i^{2}", + "ee89b1e99ce0edad.png": "(x-b)^{2}-c", + "ee930241d95d2bc2.png": "O(nlog^{d-1}n)", + "ee987c6350928d1a.png": "U_{a}(z)=", + "eeaba3f4cbf30e4f.png": "|\\begin{matrix}A&B/2\\\\ B/2&C\\end{matrix}|", + "eeaf8163f8999258.png": "f(x)>f(y)", + "eeb4e7dc078f38da.png": "I_{c}=\\frac{\\Sigma x^{2}}{(\\Sigma x)^{2}}", + "eeb605abb30e8e65.png": "Im2\\overline{A}B", + "eebfe9ac0d70855d.png": "y^{\\prime},y\\in S(a,b)", + "eec3f59d6f28a37f.png": "P(x)=|\\langle x_{0},x\\rangle|^{2}", + "eec4a3befc399ff3.png": "(RU^{2}D^{-1}BD^{-1})", + "eec4dbb0a3b61fcb.png": "x_{1}^{2}+x_{2}^{2}+x_{3}^{3}\\le81", + "eec82994ef4119a5.png": "0,1,...r-1", + "eed986ba1360ead0.png": "lim_{\\Delta x\\rightarrow0}g(\\Delta x)=0", + "eededf2bfbda03e5.png": "\\frac{1}{n_{0}}=\\frac{16}{3}\\frac{\\pi ld^{2}}{4}", + "eee0a0eea75f3ea0.png": "t=\\pm\\frac{1}{1,3}", + "eee809cfa9afb2e1.png": "\\frac{q}{2}\\int_{-\\infty}^{\\infty}\\frac{z^{q-1}}{1+z^{p}}dz", + "eef601435b25092f.png": "\\frac{1}{2}(2-\\frac{6}{4})=\\frac{1}{4}", + "eefc3237fe3cdb20.png": "\\frac{}{*:-\\alpha\\vdash\\top}", + "ef1d69b9d28d992c.png": "t_{2}/t_{1}=(n_{2}/n_{1})^{a}", + "ef1de3ad0dd8137b.png": "2^{-1/2}", + "ef34448bb13b7fd5.png": "x=\\sum_{k\\in B}\\langle x,e_{k}\\rangle e_{k}", + "ef3ce668e8b20efa.png": "y^{2}=x^{3}-n^{2}x", + "ef4781b9df3c2643.png": "C=(\\begin{matrix}0&1\\\\ -1&0\\end{matrix})", + "ef4a86c082019fab.png": "-nr^{-n-1}cos(n\\theta)", + "ef55b72badf82913.png": "z_{n+1}=z_{n}^{2}", + "ef6cf66db0dedc69.png": "040.74", + "efbcb22b3ef681c3.png": "s=\\frac{a+b+c+d}{2}", + "efbe185de0fc4ad9.png": "=n(c_{V}+R)\\Delta T", + "efd3dd257200f9d0.png": "E_{1}\\cup E_{2}\\cup...=B", + "efedcd1a6f476059.png": "\\sqrt[n]{\\frac{a}{b}}=\\frac{\\sqrt[n]{a}}{\\sqrt[n]{b}}", + "efefd35c6039a985.png": "\\underline{T}(t)=\\frac{d\\gamma}{dt}", + "eff30d77f4055918.png": "A_{0}\\equiv e^{-\\pi y^{2}}", + "eff31a069a6864a7.png": "B(x)>B_{x}(x)", + "f00929e69df924d0.png": "-0.3>\\alpha>-1.6", + "f00f090e3da4f59b.png": "(Div)P^{(0)}=0", + "f02aac40a2ea5aab.png": "\\Psi=\\Psi(r,s_{z},t)", + "f02cd95190710ad5.png": "a=(\\alpha p_{0i})_{i=1}^{J}", + "f03cc6d952dec13f.png": "W=W(\\overline{I}_{1},\\overline{I}_{2})", + "f048679d04746594.png": "\\frac{1}{7}+\\frac{1}{14}+\\frac{1}{28}=\\frac{1}{4}", + "f048b5956802c454.png": "\\vec{n}_{i}\\cdot\\vec{x}\\le b_{i}", + "f04cbd966338120d.png": "y=-\\frac{221}{423}", + "f06cfa7ccfa8fc36.png": "\\omega_{d,m}t", + "f07412f65a7e1c8f.png": "\\delta[k]=\\delta_{k,0}", + "f074815d51c3bf46.png": "\\frac{d^{2}\\psi_{2}}{dx^{2}}=-k^{2}\\psi_{2}", + "f0795614063dcb89.png": "R/Q\\cap Q/P=\\{0\\}", + "f080abc77a436cd2.png": "\\Gamma=C([0,1],X)", + "f0aecee961a291eb.png": "0\\le F(X,Y)\\le1", + "f0b39ca869cbc7fd.png": "\\beta(\\frac{f_{T}}{10})\\approx-j10", + "f0c0cd2f8cae845c.png": "1000\\times9.5=9,500", + "f0c4ba14f38bb979.png": "\\Theta(n^{3}\\cdot|G|)", + "f0cfceae2a4c2f32.png": "\\vec{F}=q\\vec{v}\\times\\vec{B}", + "f0d6842cdcd310c9.png": "T([x])", + "f0d6fe0107bd030b.png": "(t^{2},t^{3})A", + "f0e8398eee65441c.png": "J_{9-p}", + "f0e9f7761e27c646.png": "r_{Y,i}=y_{i}-\\langle w_{Y}^{*},z_{i}\\rangle", + "f0eecb885db56fe0.png": "(\\phi^{\\Rightarrow x})^{\\Rightarrow y}=\\phi^{\\Rightarrow x\\wedge y}", + "f0f2a08caec07186.png": "K_{z}*K_{z^{\\prime}}=K_{z+z^{\\prime}}", + "f0f847d75919c80a.png": "S_{ijk}\\rightarrow S_{ij}(\\omega_{k})", + "f10658d2eeb00d2e.png": "\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{a^{2}}-\\frac{z^{2}}{b^{2}}=0", + "f10f4047c8fd4ec7.png": "\\delta(q_{s},q_{c})\\rightarrow q_{t}", + "f110f5868cc73806.png": "W=\\int_{t_{1}}^{t_{2}}\\frac{dW}{dt}dt", + "f115232bce7fc917.png": "\\overline{\\nabla}_{X}Y=\\nabla_{X}Y", + "f11b71e04e9e3d2d.png": "E_{L}[u]=E_{M}[u]", + "f11facb1c5f83265.png": "[p^{2}(1-f)+pf]", + "f124d8fc4a59f7a3.png": "\\theta=(m_{0},\\mu,\\overline{\\sigma},b,\\gamma_{1})", + "f1339b1e0d74b240.png": "(j-(-j))", + "f136a698bd4fca62.png": "D_{a}=E_{a}-I_{a}", + "f13e10ae0de8d0be.png": "\\sqrt{R}=\\frac{k_{1}-k_{2}}{k_{1}+k_{2}}", + "f14d4721278e5c2c.png": "R_{S}\\approx R_{H}sec(\\alpha)", + "f169eac6048fe627.png": "\\nabla_{e_{i}}e_{j}=\\Gamma_{ji}^{k}e_{k}", + "f16e20f91f6fc1c8.png": "\\alpha>0,\\beta,\\delta>0", + "f17239cd5f183612.png": "J(f)\\le+\\infty", + "f175f863c39e57e4.png": "f(x)\\equiv\\frac{1}{1+e^{x}}", + "f1873bf69d8d4f9e.png": "f_{+},\\varphi", + "f1883c62677bcf25.png": "2Rsin(\\frac{a}{2})", + "f18d4a28e26b6617.png": "Be=\\frac{\\Delta PL^{2}}{\\rho\\delta^{2}}", + "f18ee8ec4fe7c2f5.png": "0\\le\\delta<1-\\frac{1}{q}", + "f197abe811480e10.png": "V_{0}\\oplus W_{0}=V_{-1}", + "f1a29e33beef4d01.png": "\\phi_{SP}=\\phi_{1},\\phi=\\phi_{2}", + "f1a3857e2c6ac83a.png": "10\\times(\\frac{1}{2})^{6}=\\frac{5}{32}", + "f1aae748c7994c18.png": "lim_{\\Delta x\\rightarrow0}g(\\Delta x)=0", + "f1acffc7d7fd27a0.png": "Q_{V}(\\vec{R}_{N},N|\\vec{R}_{0}.0)", + "f1ad006fca435c29.png": "\\overline{F}(x)\\equiv Pr[X>x]", + "f1bb472de7cc860a.png": "\\prod_{i=1}^{N^{2}}\\int_{R_{i}}\\Psi dA", + "f1c9da706241ec35.png": "I(S;\\Omega-S)", + "f1df37422f6693a6.png": "DM(x1^{2^{|x|^{c}}})", + "f1e67d1ca6b13cfa.png": "\\Gamma=C([0,1],X)", + "f1f4d83b8892c87b.png": "\\sum|a_{k}|", + "f1f7f582e4f02419.png": "y=\\frac{ke^{ax}-b}{a}", + "f207ff6aa019439d.png": "(0\\le m<2\\pi)", + "f20d0dc3ac75fe14.png": "p_{j}(x)=j\\sum_{i=1}^{j}|x_{i}|", + "f20eebdede453861.png": "32x+4(1-x)=1", + "f219b2a49d7a6bae.png": "I(c_{v})=log_{2}|C_{v}|", + "f23084d6f3f7975d.png": "\\phi(ln(x))=y(x)", + "f235064e9c258727.png": "M_{x}=\\frac{u_{x}}{a_{x}}=\\frac{W}{a_{1}}", + "f23587b33011f73f.png": "Pr(B|A^{\\prime})=0", + "f236b295c70a800e.png": "H=\\frac{\\Phi^{2}}{2L}+\\frac{Q^{2}}{2C}", + "f23c9a0211371a80.png": "C=\\frac{8L^{3}}{E^{*}wt^{3}}", + "f244e821a9bf6d4a.png": "\\frac{\\rho^{4}}{\\lambda^{4}}\\ll8\\frac{z^{3}}{\\lambda^{3}}", + "f247b920960f3496.png": "[\\hat{a}(t),\\hat{a}^{\\dagger}(t)]=1", + "f249f23f4055bcbb.png": "\\hat{\\Pi}\\equiv I-\\Pi", + "f24a58df5caca311.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=\\frac{n^{\\underline{k}}}{k!}", + "f250d00a447f80f8.png": "F:Z[x]\\rightarrow Z[x]", + "f252be0fb259dd1b.png": "(\\frac{i}{2\\pi})^{n}\\delta^{(n)}(\\xi)", + "f253686e1abbd522.png": "\\Rightarrow|\\overline{AF}|=|\\overline{FD}|", + "f25686c5aec70837.png": "p_{i}\\#=\\prod_{j=1}^{i}p_{j}", + "f256d269861c56df.png": "Z_{bus}={Y_{bus}}^{-1}", + "f2710d28bbade5f2.png": "g:=g^{+}-g^{-}", + "f278e6a6d05b8992.png": "\\dot{\\tilde{\\chi}}=-i[\\tilde{H}_{BS},\\tilde{\\chi}]", + "f2814372e2f223c0.png": "T_{pq}(e_{p}\\otimes e_{q})", + "f283d6b70d155a50.png": "\\dot{V}=r\\dot{r}", + "f28e1bc38b8673ee.png": "D(a_{k,k},r_{k})", + "f2935c1a21106aff.png": "2^{2^{\\cdot^{\\cdot^{\\cdot^{n}}}}}", + "f296837b1d600c07.png": "Q_{min}=18\\lambda_{1}/h^{2}", + "f29714aa65bfdefa.png": "\\frac{B(rc)^{2}}{2\\mu_{0}}=nmv^{2}\\Rightarrow", + "f29a168a9973b70a.png": "\\partial_{+}\\partial_{-}X^{\\mu}=0", + "f2a07ee5c6a01138.png": "\\begin{matrix}a&=&b+c&(1)\\\\ d&=&e-f&(2)\\end{matrix}", + "f2a880edc0efc236.png": "|g,n\\rangle\\rightarrow|e,n-1\\rangle", + "f2ad68ebe4f44428.png": "1\\notin pR", + "f2b1d2129eace817.png": "f(z)=\\frac{e^{iz}}{z}", + "f2b1ea4c21c0d296.png": "\\tilde{v}_{i}=\\tilde{u}_{i}", + "f2c7e3aae5b12f2c.png": "\\omega^{*}=\\Sigma_{i=1}^{M}|S_{i}|-n", + "f2d2a497d1213467.png": "\\frac{1}{n+1}x^{n+1}+C", + "f2d976306821930f.png": "2\\pi^{2}k\\delta(x)\\delta(y)\\hat{z}", + "f2df9ed763ae650d.png": "\\Sigma\\int h(x)k(u)du", + "f2e6873a235aa4a7.png": "EV=g\\wedge\\bigcirc S_{0}^{2}V", + "f2ebdb457375882d.png": "\\{\\eta_{t}(.)", + "f2ec5457fa9657d5.png": "k_{Ds}r_{12}<<1", + "f2f0011be8c5df1b.png": "16pi/3=H^{2}", + "f2f895f8da1f5ab4.png": "Q_{y}(q|X_{t})=X_{t}\\beta_{q}", + "f30974dc8b6b2f8c.png": "a_{i}=\\langle\\tilde{\\Psi}|T^{\\dagger}\\hat{A}T|\\tilde{\\Psi}\\rangle", + "f3111240b855b9aa.png": "[\\hat{a}_{1}(t),\\hat{a}_{2}(t)]=j/2", + "f312a082153b0bf3.png": "\\int_{x_{1}}^{x_{s}(t)-\\epsilon}w_{t}dx\\rightarrow0", + "f313cf68a1e6e521.png": "g^{\\prime}(\\alpha)-\\frac{k}{\\alpha}g(\\alpha)=0", + "f3199e72256b704a.png": "D(M[v])[h]", + "f3312ffb45fd8d9c.png": "\\psi^{[-1]}", + "f33a64a66da4fcfa.png": "\\bigcup_{n\\in F}(S-n)=N", + "f33a7320b3232c7b.png": "\\int e^{cx}dx=\\frac{1}{c}e^{cx}", + "f34b88baba644f8e.png": "[S_{x}]=\\frac{\\hbar}{2}\\cdot[\\begin{matrix}0&1\\\\ 1&0\\end{matrix}]", + "f353b93a4ab9bfa9.png": "\\Omega=arg(-z_{2},z_{1})", + "f358027d08cb91d1.png": "P_{f}-U=0", + "f35f8ba4f0bda82a.png": "2^{\\pi}=8.8249778...", + "f365b2da8757d113.png": "F^{2}(f)=f(-t)", + "f3660759fc799ac5.png": "lim_{n\\rightarrow\\infty}Pr(X_{n}=0)", + "f39872ee84f7864f.png": "cos3\\theta=\\frac{3\\sqrt{3}}{2}\\frac{I_{3}^{\\prime}}{I_{2}^{\\prime\\frac{3}{2}}}", + "f39d56d87f075a0a.png": "1-z=r^{2}", + "f39e940bdd51af44.png": "D^{\\epsilon}(\\rho||\\sigma)", + "f39edcef66d18e50.png": "\\int_{a}^{b}f(x)d_{h}x", + "f3a0a6fe4f0403ef.png": "j_{0}=f^{2}\\partial_{0}\\theta(t)", + "f3a209847b646b46.png": "\\sum_{i\\in N}XY^{i}", + "f3a9b5513eaae59a.png": "\\neg(xb", + "f6e5f8d0518642f7.png": "\\int_{E}f_{n}d\\mu\\rightarrow\\int_{E}fd\\mu", + "f6f26811e1014fbb.png": "\\int_{E}f_{n}d\\mu\\rightarrow\\int_{E}fd\\mu", + "f6f27c4478bc3fd8.png": ")", + "f6fec9906e39d215.png": "|A|=1", + "f703e5e22dc068bf.png": "(p_{i},|\\phi_{i}\\rangle)", + "f72104ceb776e6d0.png": "F(\\{a_{i}\\},\\{A_{j}\\})", + "f73b20fcca666ca5.png": "g^{-1}\\mu(A)=\\mu(gA)", + "f73ca1a35fd2b972.png": "V=f(t)=V_{0}e^{-\\frac{t}{\\tau}}", + "f7461c5321493900.png": "\\frac{n!}{(n-k)!\\cdot k^{n}}=m", + "f76866fa55d94c2c.png": "[\\begin{matrix}0&1\\\\ 0&0\\end{matrix}]", + "f76ce74da4570214.png": "H^{\\prime}=1/M\\Delta\\tau", + "f77b88d54efc8e2b.png": "A=1+2(\\frac{M}{C})", + "f77c8c6f7facb4e5.png": "H_{1}=-\\vec{d}\\cdot\\vec{E}", + "f7869720b04a37ee.png": "f(\\vec{a},\\vec{b})=f(\\vec{b},\\vec{a})", + "f78c88c971b6e82b.png": "Y_{11},Y_{22},...,Y_{nn}", + "f79159312e3a4629.png": "\\int_{A}(g-f)d\\mu=0", + "f799a4ce68495d65.png": "\\frac{d^{2}y}{dx^{2}}=f(x,y)", + "f7a2fb9aed0a42a1.png": "\\sigma=|c|\\frac{\\Delta t}{\\Delta x}\\in N", + "f7ae2fdab778d35f.png": "k_{a}f_{a}+k_{b}f_{b}+k_{c}f_{c}", + "f7b3557ac8e3ed74.png": "F_{q^{k}}^{*}", + "f7b414118abca859.png": "\\Delta\\tau=Gb\\sqrt{c}\\epsilon^{3/2}", + "f7b7e7248cbbe2e1.png": "1^{1/2}=-1", + "f7baa06779e2dd17.png": "(\\begin{matrix}1\\\\ 1\\end{matrix})(\\begin{matrix}11\\\\ 1\\end{matrix})(\\begin{matrix}4\\\\ 2\\end{matrix})(\\begin{matrix}10\\\\ 2\\end{matrix}){(\\begin{matrix}4\\\\ 1\\end{matrix})}^{2}", + "f7bb0b89ff8bc16b.png": "f(3\\cdot4^{4^{4}}+4,4)", + "f7c12e86fd353fd5.png": "J_{9-p}", + "f7ce2fccdd66c8f7.png": "f_{N}-g\\in a\\backslash b_{N}", + "f7f9b394e77cf5eb.png": "=(t+1)^{(p-1)}", + "f7fd789a986fe536.png": "F=\\frac{\\alpha}{r^{2}}", + "f801a91a63145d4d.png": "\\sum_{n=1}^{\\infty}\\frac{1}{n}z^{n}", + "f809f5623f425e78.png": "T_{j_{1}...j_{q}}^{i_{1}...i_{p}}[f]", + "f80ec0f6a05ad84e.png": "(\\frac{\\partial F}{\\partial V})_{T,\\{N_{i}\\}}=-p", + "f81ca4c27412ac92.png": "(x-\\lambda_{i})^{\\nu_{i}}", + "f8208dfb37ec88f0.png": "\\overline{X}+X_{\\xi}", + "f822f4dc7e2980f7.png": "\\alpha_{j}=-E[S_{j}-T_{j}]", + "f82615dc083ff6e2.png": "I(V+ksin(\\omega t))", + "f82b9ca9d2ee1e2c.png": "L(G)=\\{a^{*}b^{*}c^{*}\\}", + "f83435e8c9003b3c.png": "v_{i}\\in H_{0}^{3},i=1,2,3", + "f8489fbf97de2f3a.png": "(By+\\beta)^{n}-B^{n}y^{n}", + "f857289eeb2a8964.png": "(\\frac{m}{s^{2}})", + "f858dde7b47ff3d0.png": "\\frac{j^{2}\\pi^{2}}{L^{2}}", + "f85d591feca20215.png": "E=mc^{2}=pc", + "f86e6383891c5612.png": "\\frac{3^{h+1}-1}{2}", + "f8805b9308fc9cb3.png": "R=\\frac{a}{\\sqrt{3}}", + "f884388796f654a4.png": "V_{n}=a^{n}+b^{n}", + "f887c1c1d38b46be.png": "A=\\overline{B_{R}}", + "f88bf6086f892ff7.png": "E_{l}=\\frac{\\hbar^{2}}{2I}l(l+1)", + "f88f613cfd87ad9f.png": "j_{z}=-\\frac{1}{\\mu_{0}}\\nabla^{2}A", + "f89f4daa867e005a.png": "Z(R_{R})\\ne Z(_{R}R)", + "f8af33c5237e862d.png": "(1)G(x,u,p)=0", + "f8b3a9d3a2dc9bf9.png": "A=0,B=1", + "f8c2dc2b3524c534.png": "*3=", + "f8d36f25a996da09.png": "F(X_{j+m})-F(X_{j})", + "f8d7868ad41e729e.png": "J_{n+1}=2^{n}-J_{n}", + "f8d9c87d1ca01357.png": "(u^{+i})^{*}=u_{i}^{-}", + "f8ec2100e97ff37d.png": "l_{e}=m_{0}\\omega_{e}r_{e}^{2}=\\hbar/2", + "f901fa248194ed56.png": "h(k)+x^{2}(modb)", + "f91ab1be28a9b813.png": "q=||u||", + "f92d494a227b8ceb.png": "(s,t,f(s,t))", + "f9370dd2f6cb8d21.png": "0,1,3,7,15,...", + "f93c21df764d6d75.png": "V_{BE}=V_{BE}(I_{B})", + "f9563c7c140d56f9.png": "\\frac{1}{2}sin^{2}0=0", + "f9634df6962dd806.png": "f=T_{K}\\varphi+T_{K}^{*}\\varphi", + "f9644b890cc3c59b.png": "(a,b):\\Sigma_{(x:A)}B(x)", + "f964b31991a8cacf.png": "2cos\\frac{\\pi}{3}=1", + "f9658c159d6d0936.png": "2x_{1}=D+\\frac{r_{1}^{2}-r_{2}^{2}}{D}", + "f96ed1a362df8481.png": "BG_{m}(F_{q})", + "f9876b87ca010c2c.png": "(X,Y)=TrXY^{T}", + "f98c8b4c17f401d5.png": "2^{S}", + "f9a7f439f6914fbf.png": "p=\\frac{n^{2}+n+2}{2}", + "f9a8a15f5fc14eea.png": "F=\\frac{1}{4\\pi\\epsilon_{r}\\epsilon_{0}}\\frac{q_{1}q_{2}}{r^{2}}", + "f9bda893e06a7471.png": "S_{Z}=B^{\\frac{1}{2}}\\cdot T_{Z}.", + "f9c9d4137db06099.png": "R=Q\\frac{|V_{||}|^{2}}{\\omega W}", + "f9de8fb22a5352cc.png": "\\sigma=|c|\\frac{\\Delta t}{\\Delta x}\\in N", + "f9e887b1224a4019.png": "A^{+}=0", + "f9fb4ce5ce59e617.png": "|\\nu_{\\alpha}\\rangle=\\sum_{i}U_{\\alpha i}^{*}|\\nu_{i}\\rangle", + "fa08e56c1003fcde.png": "\\psi^{u}(x):=\\pi_{x}u", + "fa093154c8ae7279.png": "\\frac{f(x_{1})+f(x_{2})}{2}", + "fa1b2f9760b04612.png": "\\sigma^{2}*(X^{\\prime}X)^{-1}", + "fa2a8160feaed94e.png": "K=\\sigma Y\\sqrt{\\pi a}", + "fa33ed20b52ca8a1.png": "(modk)", + "fa4fd6dd3d08605d.png": "1+2+3+4=10", + "fa58f6ed528daeea.png": "\\hat{g}=\\frac{k}{T^{2}}", + "fa621be0bae40343.png": "(x-a)^{2}H(x-a)", + "fa6b5af76d7e3d49.png": "\\partial_{\\mu}E_{n}=\\langle n|\\partial_{\\mu}H|n\\rangle", + "fa74b61b3e6e21f7.png": "\\sigma[N(R^{n}\\backslash B_{\\delta}(x))]", + "fa74c45316f84a73.png": "P_{V}f(u,\\xi)", + "fa8151056ba1a5f5.png": "0.082H_{s}^{2}", + "fa8690d121ebed4a.png": "\\lambda x.yz=\\lambda x.(yz)", + "fa8963a398f13674.png": "j:=1:(i-1)", + "fa9d51a9bde9e558.png": "(c,\\vec{v})", + "faa1f2da57149ee3.png": "D\\rightarrow D/m_{D}", + "faa489cc86a03a8b.png": "\\langle\\Psi,s\\rangle=\\langle\\Psi,s^{\\prime}\\rangle", + "faab4d27d144e637.png": "g(x)F(x)+C", + "fab3e39a5b046367.png": "0=f_{N}(s)", + "fab4538f41ba637c.png": "N=N_{\\hat{B}}+N_{\\hat{a}}", + "fab6e24ab3527ab3.png": "J_{\\hat{n}}", + "fabb7bd195c7ca54.png": "V=1096.7\\sqrt{H/d}", + "fabb9fc34244dda2.png": "c^{2}-", + "fabc377b37bfff9f.png": "\\prod_{k=1}^{\\infty}\\frac{1}{1-x^{k}}", + "fac2fc1fc91cadd2.png": "Q=\\frac{N}{D}\\frac{F_{1}}{F_{1}}\\frac{F_{2}}{F_{2}}\\frac{F_{...}}{F_{...}}", + "fac97c0b876e3231.png": "\\alpha_{i}|\\alpha_{i+1}\\forall1\\le ih/2", + "fc05b5b75b64c47a.png": "\\sum_{k=0}^{n}(q+1)^{k}", + "fc075f8ba42dc99b.png": "(-2\\sqrt{\\frac{2}{5}},0,0,0)", + "fc11e75d3b63c829.png": "y_{2}=\\frac{2}{x}+\\frac{3}{x^{2}}e^{-2x}", + "fc1f83edf022059e.png": "R_{H}=a(\\frac{m}{3M})^{\\frac{1}{3}}", + "fc2c5aa25fb696a9.png": "K_{L}=\\frac{sin(\\alpha)}{sin(\\beta)}", + "fc3af9b6d73dd6d5.png": "y_{i}E_{2}(\\alpha_{i})=Q_{2}(\\alpha_{i}", + "fc407568d5ab1f23.png": "P^{\\prime}(\\vec{a})", + "fc44ad9691d6321d.png": "F_{x}v=m\\dot{v}v", + "fc464983a71ece28.png": "P_{0|0}=[\\begin{matrix}0&0\\\\ 0&0\\end{matrix}]", + "fc47d6c240a5c48f.png": "\\exists\\overline{x}.P", + "fc48941514fd902e.png": "2|E", + "fc497c055502604a.png": "\\{u_{j}\\}_{j=1}^{p}\\in C^{p}", + "fc612d2cfc54a85a.png": "U=e^{i\\hat{p}\\sigma_{z}}H", + "fc764d82cedec627.png": "VdV+\\frac{k.p}{\\rho^{2}}.d\\rho=0", + "fc8ee800105cd21f.png": "V_{0}\\oplus W_{0}=V_{-1}", + "fc94f34df33af5cb.png": "K(t)=logE[e^{tX}]", + "fc99fadfcab2a1a9.png": "\\frac{d^{2}w}{dx^{2}}=-\\frac{M}{EI}", + "fc9aad2921e4c411.png": "E_{n_{1},n_{2}}^{(0)}", + "fc9b579deaafe479.png": "a=p_{1}p_{2}^{k_{2}}...p_{l}^{k_{l}}", + "fca722a6645bb7eb.png": "u_{1}=[\\begin{matrix}1\\\\ -i\\end{matrix}]", + "fcb29830123cff23.png": "(dy,-dx)=\\hat{n}ds", + "fcc22e1317a683b2.png": "f^{-1}(y)=\\pm\\sqrt{y}", + "fccde4056a64f303.png": "\\pi:\\Sigma^{*}\\rightarrow P(A)", + "fce3667ecaa749e2.png": "(0,e^{-x^{2}/2}/\\sqrt{2\\pi}]", + "fce6d7a3f4fcea9c.png": "f^{-1}(y)=\\sqrt{y}", + "fcf12d31b36f3fc3.png": "J:V\\rightarrow\\overline{R}", + "fd0d8455db609c3d.png": "\\hat{\\Pi}\\equiv I-\\Pi", + "fd0f84fac9292fdd.png": "\\frac{\\partial^{2}f}{\\partial x\\partial y}=\\frac{\\partial^{2}f}{\\partial y\\partial x}", + "fd1c430d6412d880.png": "\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{a^{2}}-\\frac{z^{2}}{b^{2}}=0", + "fd23431d0a74cb3c.png": "\\hat{T}(0)=\\hat{I}", + "fd2a24576e682eaf.png": "(\\begin{matrix}101\\end{matrix})(\\begin{matrix}42\\end{matrix})(\\begin{matrix}361\\end{matrix})", + "fd333c083e8bc473.png": "2^{<\\omega}", + "fd34daabac4742a6.png": "(\\frac{x}{a})^{2}-(\\frac{y}{b})^{2}=1", + "fd4fcad2c82c1a06.png": "A_{0}=\\frac{\\sqrt{3}}{4}a^{2}", + "fd567507f026b490.png": "c_{1}|\\psi_{1}\\rangle+c_{2}|\\psi_{2}\\rangle", + "fd5a2b8ead1ef9bc.png": "de-let[f(qq)]", + "fd5da762ce1ef8a2.png": "\\{P_{k}:k>1\\}", + "fd6619e0f562c2ca.png": "U(\\hat{\\alpha}(q,r_{c}),\\tilde{u})", + "fd72e75aa2440cc4.png": "F(x,y^{*})=0", + "fd7d7cdbfcebee9d.png": "v_{p}=\\omega/k,v_{g}=\\frac{\\partial\\omega}{\\partial k}", + "fd840db1339f09a8.png": "F_{q^{k}}^{*}", + "fd975692a0a19142.png": "sup_{t}|G_{n}(t)|", + "fd9958c355952a43.png": "\\pi_{n}(X,p)\\cong\\langle S^{n},X\\rangle", + "fd9a7e06d5a5fe64.png": "x_{0}^{2}+(y_{0}-r)^{2}=r^{2}", + "fd9c003f2466935a.png": "p_{1}/\\pi_{1}\\varphi(m)", + "ff40b8732b1b5f36.png": "N(t)=N_{0}2^{-t/t_{1/2}}", + "ff4170435f042389.png": "\\pi_{X_{4}}-1", + "ff4636ede91fa3e0.png": "\\frac{\\gamma^{\\mu}\\gamma^{\\mu}}{\\eta^{\\mu\\mu}}=I", + "ff48160fe9ef2712.png": "t^{\\prime}=\\gamma(1-av)t", + "ff48c4076d26c9c2.png": "\\{(x,y)|\\phi(x,y)\\}", + "ff4e1970d4e903df.png": "||\\cdot||_{l^{2}}", + "ff4ed0e041567e7b.png": "\\frac{9}{4\\sqrt[3]{2}}", + "ff5b35f0dd39d22b.png": "n=t|m-T|^{-2}pq", + "ff5d77299aadc081.png": "T_{f}=\\frac{T_{w}+T_{\\infty}}{2}", + "ff6365dc2925f98a.png": "E=\\frac{\\lambda sin\\phi_{1}sin\\rho}{\\rho}", + "ff6a7cc36ec39885.png": "K:X\\times X\\rightarrow R", + "ff8a5f32244d4822.png": "J(f)\\le+\\infty", + "ff9d8d82a54aa330.png": "\\overline{\\psi}(\\gamma^{\\mu}\\gamma^{\\nu}-\\gamma^{\\nu}\\gamma^{\\mu})\\psi", + "ff9e6abec8571b91.png": "T+?T", + "ffa33de76380a0b9.png": "|\\frac{q}{p}|=1", + "ffa48319a372ef94.png": "\\sum_{n=0}^{\\infty}f_{\\tau(n)}(x)", + "ffa7f5c556d25c02.png": "exp(2ik\\Omega d^{2}/v)", + "ffaee3cba138d53b.png": "P\\equiv log_{10}\\frac{p_{i}}{f_{B}T}", + "ffb0a9296d68c94a.png": "\\dot{p_{i}}=\\dot{m}_{i}v_{i}+m_{i}\\dot{v}_{i}", + "ffb29a09d60934f6.png": "(k+1)^{2}=k^{3}", + "ffc81d312b889366.png": "U_{a}^{\\prime}:=\\bigcap_{b\\in B_{0}(a)}U_{a,b}", + "ffca40bd1fc5247d.png": "x(t)=vt,y(t)=0", + "ffcd474886e27cfd.png": "D(D):=D", + "ffd3a74c1f14e94f.png": "u_{t}-u_{xx}=0", + "ffe04fc2c139a33e.png": "(coshx+sinhx)^{n}", + "fff5327f2c0ce528.png": "\\theta^{1},\\theta^{2},\\overline{\\theta}^{1},\\overline{\\theta}^{2}", + "fff55fb16db1ec68.png": "\\eta_{+-}\\ne\\eta_{00}" +} \ No newline at end of file diff --git a/train/labels.json b/train/labels.json new file mode 100644 index 0000000000000000000000000000000000000000..f77e3447fdfa23adbcc088950ed2815bc23a4d8d --- /dev/null +++ b/train/labels.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:008f883eb779e87c13b045fc4695010e24be4467844d6d60ed5bcc51adbc51d8 +size 14501271 diff --git a/train/output_images/00001d1472a8709f.png 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"A_{\\mu}\\rightarrow A_{\\mu}+\\partial_{\\mu}\\phi(x)", + "017c4e5970880570.png": "2,\\sqrt{5},\\sqrt{6},3", + "01844e9baa82698c.png": "\\rho(r)\\sim e^{-2Z_{\\alpha}r}", + "018b8fb309ce7af2.png": "d\\overline{v}=-\\frac{e\\cdot\\overline{E}}{m}dt", + "018f456e217f1301.png": "log\\hat{\\lambda}\\approx Z\\sqrt{4/D}", + "018f48ac8fe4bd53.png": "|0|<|1|+|-2|", + "018f8eb18419d5bb.png": "\\tilde{v}", + "018fb881d2eef21d.png": "F_{r}=\\frac{v}{\\sqrt{g\\frac{A}{B}}}", + "01927fe0f1d3c23d.png": "(\\begin{matrix}0&1\\\\ -1&0\\\\ \\end{matrix})", + "0198a68035125b5a.png": "G", + "01992bb808919d17.png": "1^{\\prime}s", + "01998b624db95830.png": "\\hat{\\beta}=(\\overline{y/x})", + "019d0ab8b91ae217.png": "L_{X}dz=f(z)dz", + "01a0415f932322d3.png": "\\rho(\\nu)d\\nu=\\frac{u(\\nu)d\\nu}{V}", + "01a0b54b759ab60d.png": "3k+1=2^{a}k^{\\prime}", + "01a33dcbdaf5d858.png": "\\hat{\\theta}=\\hat{z}", + "01a595d8d764a7b7.png": "f_{c}=\\frac{1}{2\\pi C(R+S)}", + "01ab63ab784befeb.png": "C[x,y]/(x,y)\\cong C", + "01afdb3e5885a92e.png": "Z\\notin A", + "01ba83643730c5de.png": "D=\\pi\\overline{\\pi}", + "01c6fa23cc55f9b5.png": "\\hat{n}\\cdot\\hat{m}=0", + "01c763d4dc2c0f7b.png": "0<4-2\\alpha-\\beta", + "01c8b6bf03461430.png": "a,b\\in\\hat{R}", + "01c9c8eabc606030.png": "d=(1/2)b_{2}", + "01caf09d3c268a62.png": "D\\{J\\}\\subseteq\\tilde{D}", + "01d23354b74a314b.png": "Q>\\sqrt{\\frac{1-k^{2}}{2}}", + "01d7e75800e155ff.png": "(\\overline{y}^{i})", + "01d914f73dac0056.png": "log^{-1}(\\delta^{-1})", + "01dad228bc703cd9.png": "|\\overline{VT}|", + "01dae525096a98d8.png": "r^{\\prime}(d)=\\frac{1}{cos^{2}(d/R)}", + "01e2141af4688612.png": "\\hat{t}_{g}(t,\\omega)", + "01e91c0fe3870264.png": "\\int_{S}H^{2}dA", + "01f0c52a1d63c65c.png": "\\overline{K}(C)", + "01f1c306074573c4.png": "\\tilde{P_{n}}(x)", + "01f34cb89e7569cc.png": "S=\\int wdx", + "01f4535d0510517a.png": "x^{\\prime}=\\gamma(x-vt)", + "01f550ac46e27ad8.png": "[\\begin{matrix}A&B\\\\ C&D\\end{matrix}]", + "01f60638b521fcfa.png": "1-e^{-n^{2}/(2\\times365)}", + "01f610152b8ee452.png": "(xy)^{n}=x^{n}y^{n}[y,x]^{(\\begin{matrix}n\\\\ 2\\end{matrix})}", + "01f629c06e785801.png": "(\\begin{matrix}6\\\\ 4\\end{matrix})", + "01f63cd74f51acbd.png": "t\\notin\\gamma", + "01f76dc2902158d1.png": "A=\\frac{\\sqrt{3}}{4}a^{2}", + "01f7d578f71e9296.png": "\\forall j\\notin S", + "01fe4387cf57cadb.png": "\\tilde{K}^{n+2}(X)=\\tilde{K}^{n}(X)", + "01ff5719c87fee7b.png": "\\int dx=x+C", + "02007a14be74702d.png": "\\chi(x,y,z)=(x,y)", + "0207674815339c52.png": "(\\begin{matrix}n\\\\ i\\end{matrix})2^{-n}", + "020f181eb5a8dade.png": "\\partial_{t}v=-\\delta_{u}H(u,v)", + "02111fb4fcdeaa11.png": "|\\Psi_{A_{1}...A_{m}}\\rangle", + "0219326a0f03aaad.png": "\\langle\\Psi_{1}|\\Psi_{0}\\rangle=0", + "02196236beee9488.png": "x_{1},x_{2}\\in\\Omega\\\\ X", + "0229adad31bd6ce6.png": "L=-\\tilde{F}\\dot{v}^{2}+2\\dot{v}\\dot{r}", + "022c63bd11dd057a.png": "\\sqrt{-1}", + "0238a713657f3f98.png": "V(\\tilde{\\beta})", + "023e8d97ca009298.png": "\\int_{\\Omega}|f\\varphi|dx<+\\infty", + "023fce90b50ec425.png": "S=\\sum_{i=1}^{g}n_{i}(\\overline{r_{i}}-\\overline{r})^{2}", + "0249fcae2a892125.png": "I^{i+j+1}", + "025389753384ca9a.png": "C", + "0258eeb102cc8ec9.png": "\\xi=\\prod_{j=2}^{\\infty}(1-\\frac{1}{d_{j}})", + "026800ccaf27ca23.png": "w_{i}=\\frac{\\partial R}{\\partial a_{i}}", + "0270a5a5c92c6df0.png": "\\Delta\\vec{F}=A\\Delta\\vec{p}", + "0277b3b795607a4c.png": "\\overline{X}_{n}=\\frac{1}{n}(X_{1}+\\cdot\\cdot\\cdot+X_{n})", + "0278c238e066d7d2.png": "U\\subset2^{(\\Gamma^{*}\\times\\Sigma^{*})}", + "027ea2b9430ed7b2.png": "\\int d^{3}xJ^{0}", + "02857e5be2f6c73f.png": "\\int dy", + "028679cd23bcdcd3.png": "T=a\\dot{\\gamma}(t)+bt\\dot{\\gamma}(t)", + "0287f57cb05d52e3.png": "-\\overline{u^{\\prime}v^{\\prime}}", + "0287f6b826c8e21c.png": "\\overline{X}_{n}=(X_{n1},...,X_{nk})", + "028b0cf7c7b136a6.png": "\\hat{z}=\\pm\\hat{p}", + "028bfc3df3c1ead8.png": "p_{k}=\\frac{\\partial S}{\\partial q_{k}}", + "029091ef7cb77942.png": "\\frac{\\sqrt{2}}{12}", + "02a18c6b93ef8f5a.png": "\\psi_{\\alpha}(z)=|f(z)|^{\\alpha}", + "02a215a34f76299d.png": "-(2\\alpha+1)x", + "02a3724ad26f3fa9.png": "R=\\mu_{1}+\\sqrt{S_{1}}X", + "02a96f889596646c.png": "1=\\sqrt{(N_{x}^{2}+N_{z}^{2})}", + "02b5fbdfb817a1d0.png": "\\int f^{2}dP<\\infty", + "02b84ec09813f4d8.png": "\\tilde{H}_{d}", + "02b8d436b5ff27df.png": "m\\ge(\\begin{matrix}k\\\\ 2\\end{matrix})", + "02b9fe007833159f.png": "v(t)=I\\frac{dl(t)}{dt}", + "02c4a6d862511830.png": "\\underline{\\lambda}", + "02c4b7e3fd9b722e.png": "A.A_{2}=O", + "02cdc41b22ef974a.png": "Tx=\\sum_{k=1}^{s}a_{k}(a_{k}\\cdot x)", + "02d0defd926a5a97.png": "FV(xy)=\\{x,y\\}", + "02d5c5a7f740c471.png": "P=[\\begin{matrix}1&0\\\\ 0&0\\end{matrix}]", + "02dc214fe1b13bfc.png": "(\\begin{matrix}p&q\\\\ nq&p\\end{matrix})", + "02dcc79cdc7ee3f0.png": "F_{0}=XZ-Y^{2}", + "02e122b1af92f3fe.png": "f(k;\\lambda)=\\frac{\\lambda^{k}e^{-\\lambda}}{k!}", + "02e60cafcdda43ff.png": "x=1+(-1)", + "02e71c2f96463460.png": "\\forall j\\notin S", + "02e7f6eab554ea46.png": "(\\begin{matrix}n\\\\ k\\end{matrix})k!2^{(\\begin{matrix}n\\\\ 2\\end{matrix})-(\\begin{matrix}k\\\\ 2\\end{matrix})}", + "02f5ace6fe0e5182.png": "L,\\overline{k}", + "02f5be48b07a6ec4.png": "\\psi_{1}({\\Omega_{2}}^{\\Omega_{2}})", + "02f88d6ee41d4ee1.png": "T=\\frac{\\overline{X}-\\mu}{S/\\sqrt{n}}", + "02fb048bf32b830e.png": "x\\sqrt{3}", + "02ffceec7744d550.png": "\\mu_{3}^{4}n(logn)^{2}", + "03027246b586dac1.png": "x_{i}|x_{1}\\cdot\\cdot\\cdot x_{i-1}x_{i+1}\\cdot\\cdot\\cdot x_{n}+1", + "030b08403a465942.png": "\\frac{1}{T}\\frac{d^{2}T}{dt^{2}}=-k^{2}", + "030d4730ba6cce59.png": "\\hat{a}_{j}", + "030e6dbc833522a5.png": "U_{\\rho}=v_{r}-v_{r}^{\\prime}+\\frac{ra_{r}^{\\prime}}{c}", + "0313a2e6a88ddd22.png": "(\\begin{matrix}p+q\\\\ q\\end{matrix})", + "0316d93a3d5b750c.png": "H_{\\omega^{\\omega^{\\omega}}+\\omega^{\\omega}}(1)-1", + "031c8126a9ace4a6.png": "[\\begin{matrix}4&6\\\\ 3&5\\end{matrix}]", + "0320b540fd696afb.png": "b_{k}|k>0", + "03288283f74572f9.png": "2((\\begin{matrix}n\\\\ 1\\end{matrix})+(\\begin{matrix}n\\\\ 2\\end{matrix})+(\\begin{matrix}n\\\\ 3\\end{matrix}))", + "032a9d28747f9bc6.png": "Q(\\sqrt{13})", + "032e4fa85ea80213.png": "\\frac{q}{A}=-k\\frac{dT}{dx}", + "0332e23a538306d4.png": "x^{p^{2}},y^{p}\\in G^{\\prime}", + "033488d7a4d2eb75.png": "\\{f_{n}:S_{n}\\rightarrow T_{n}\\}_{n=0}^{\\infty}", + "0335951405c01a09.png": "p_{1}=p(x_{0}+\\Delta x)", + "033a1099450aa893.png": "\\int d^{D}x\\sqrt{-g}G", + "033fecd9b9bf5df2.png": "\\hat{S_{z}}", + "0348098b3d25778a.png": "\\frac{\\partial u_{i}}{\\partial x_{i}}=0", + "0350ccecbad0ccbb.png": "(\\begin{matrix}n\\\\ q\\end{matrix})", + "0355170d1d9c8fb1.png": "\\int_{E}w(x)dx", + "03571691a35553bc.png": "\\int_{0}^{t}f(u)du", + "03600c84bd03c11a.png": "s_{n}=\\prod_{i=1}^{n}\\pi_{i}", + "03629edeb52f488e.png": "\\pi(p^{k})=p^{k-1}\\pi(p)", + "0367a57bbda63fa2.png": "\\mathbb{E}", + "0368d1073da40a57.png": "V=R(\\frac{Tn}{P})", + "0371985450e0152f.png": "\\{v_{1},v_{2}\\},\\{v_{2},v_{3}\\}", + "0372fa83e05129d6.png": "\\int fg=f(x)\\int g", + "037adeb96ad22cab.png": "\\hat{se}_{\\theta}", + "037b527312c66917.png": "\\frac{d^{2}x}{dt^{2}}", + "0380640569d40b5b.png": "\\int_{0}^{1}\\cdot\\cdot\\cdot dx", + "0383de7a3e22c339.png": "\\vec{v}_{B|A}=\\vec{v}_{B}-\\vec{v}_{A}", + "038640fabb567de8.png": "\\overline{Y_{v}}=P_{\\overline{x}}\\overline{X_{v}}", + "0387b745a9818f3c.png": "z=a_{x}x+a_{y}y+d", + "038ae84c98527c1a.png": "[\\begin{matrix}U_{1}\\\\ U_{2}\\end{matrix}]", + "038d31c83e1f2a14.png": "\\frac{P_{t+1}}{P_{t}}=1-\\frac{1}{2N}", + "038d81cbc3fee8a4.png": "I=\\int xcos(x)dx", + "038e354e5c479630.png": "Pr(R_{i}<\\underline{R})", + "0392bc8541fd16c6.png": "L(\\phi,\\partial_{\\mu}\\phi)", + "0392f8a3ba83db99.png": "\\int pdq", + "039a3595e4f5a9be.png": "V^{*}(a\\otimes h)=\\Phi(a)h", + "03a41599f17633fa.png": "1+k_{i}4^{k_{i}}", + "03afcb804041bd02.png": "u(0)=f(x_{0})", + "03b504a915a073ee.png": "-I=I_{0}sin\\delta", + "03b51b2c81f6a509.png": "F_{x}[f(x)]", + "03c3da1a7fdbabf1.png": "A=(a_{ij})", + "03cb498f31bf335f.png": "E^{2}=p\\cdot p+{m_{0}}^{2}", + "03cb8f488c22c843.png": "tan2\\theta\\equiv|p|/m", + "03d03ea46c28a257.png": "\\int p(x)f(x)dx=-H", + "03d48a19c52751e6.png": "x^{3}-2x^{2}-5x+6", + "03d57e6f4ff2af26.png": "\\tilde{Y_{k}}", + "03d8b0dbcfc65b11.png": "d\\in D^{n},r\\in R", + "03e180727a5a53cb.png": "\\Omega=\\rho+i\\tilde{\\rho}(\\rho)", + "03ede575c929120f.png": "\\int_{0}^{1}f(x)v(x)dx", + "03efc14f58317aa5.png": "\\hat{e}_{3}", + "03f20fd9f00d4d76.png": "b_{\\mu^{7}}", + "03faa80dacddebb4.png": "\\frac{dv}{dr}", + "0400b6822431b3b3.png": "\\hat{R}", + "0404ffd10433f331.png": "\\psi_{1}({\\Omega_{2}}^{\\Omega_{2}})", + "0408e58bea1050d6.png": "\\tilde{S}(q,\\omega)", + "04091d689e72099f.png": "L(s,\\pi,r),L(s,\\tilde{\\pi},r)", + "040ca87dce4ed6fe.png": "\\frac{\\partial u_{i}}{\\partial p_{j}}<0", + "040d05ba2734ba84.png": "q(1)^{2}+q(1)-1", + "040dc3fb3e7b1fe0.png": "\\frac{C}{MR_{e}^{2}}\\approx0.3313", + "041047bad039bcce.png": "x_{1}+y_{1}\\sqrt{n}=u^{2329}", + "04127c114679458c.png": "{(\\begin{matrix}41\\end{matrix})}^{3}", + "041280bf5f9c0ac2.png": "\\int cos^{2}xdx", + "041506e78a61a899.png": "V(P,e(P,u))=u", + "0415482481846d81.png": "\\int_{S}1dS", + "0418d37054f32efd.png": "u=+\\frac{\\partial\\psi}{\\partial y}", + "041a70c640f4b16e.png": "T=37^{\\circ}C=310K", + "041cf00628ce3e7b.png": "(\\frac{K}{N})\\ge2r_{o}-1", + "041e2c67db70a2ec.png": "f_{0}(x)+u(4x)/4", + "041e839944f8ea98.png": "0()", + "042414f532c2d22c.png": "\\frac{d^{2}y}{du^{2}}+y=g(u)", + "042be0721558671b.png": "g_{kl}=2\\chi\\Delta n\\overline{n}", + "042d6a89524751b6.png": "\\tilde{\\beta}", + "043270c362331308.png": "(B_{E}u)(v)", + "04335a39a4fde0b0.png": "(\\begin{matrix}ix&w\\\\ \\overline{w}&-ix\\end{matrix})", + "04365365f3f36017.png": "A\\le\\tilde{A}", + "04386b78684c53be.png": "W=\\int PdV", + "04394a4a3825d1fc.png": "\\hat{\\alpha}", + "043e198f42a3dbd1.png": "\\frac{d\\beta}{dt}", + "0441649263607278.png": "[f]=::[\\begin{matrix}a&b\\\\ c&d\\end{matrix}]", + "0447b1f41e39c5b3.png": "\\hat{H}^{\\prime}=-\\frac{e}{mc}\\hat{A}\\cdot\\hat{p}", + "044d42fb33dd88a4.png": "S=\\int wdx", + "045345ba0acc7fc5.png": "(2e^{0i})^{0.5}=\\sqrt{2}", + "04570f0942863a2f.png": "M<_{DM}N", + "04571e987352083a.png": "x_{0}\\in M(t_{0})", + "0461731c99bc1e3c.png": "s_{n}=\\prod_{i=1}^{n}\\pi_{i}", + "0461ec2eaa2404cc.png": "NE(X)", + "0466e827b1be80bd.png": "y=(\\begin{matrix}v\\\\ u\\\\ p\\end{matrix})", + "046ce410835a0748.png": "\\tilde{O}(log(n)^{7.5})", + "0472236490de12d1.png": "F(X)=\\prod_{i=1}^{s}f_{i}(x)", + "0473355c2916778e.png": "L^{2}(R^{n}),l^{2}(Z)", + "04745cc58f2939a7.png": "(\\begin{matrix}bi&z\\\\ -z&di\\end{matrix})", + "047850542e97ced3.png": "(\\begin{matrix}n-1\\\\ r-1\\end{matrix})", + "04815167aa93b7c3.png": "X_{1}\\approx\\sqrt{R_{1}R_{2}}", + "04853826ad8eab8b.png": "\\frac{dx}{ds}=e^{x}", + "0488bcee0d319019.png": "\\frac{dE}{dx}=0", + "048a3bec5d340abc.png": "\\overline{w}_{g}\\in R^{d}", + "048c7aee467893a8.png": "n^{*}=\\sqrt{2E_{i}}/Z^{2}", + "049527cd2bac6190.png": "|\\alpha|=\\Sigma_{i=1}^{N}\\alpha_{i}", + "0496e1256fa8df3d.png": "(0.999)x-y=2", + "049768daf9ed69af.png": "Q=\\omega\\cdot\\epsilon_{r}^{\\prime\\prime}\\cdot\\epsilon_{0}\\cdot E^{2}", + "04a765d2780b6a79.png": "cf(\\prod A/D)<\\lambda", + "04a84573cb51a1f0.png": "cf(\\aleph_{\\delta})=cf(\\delta)", + "04ab1bd76738b805.png": "\\pi_{n}=p_{1}(\\pi_{n-1})", + "04b0460787469bef.png": "\\sigma=\\int\\sqrt{k(s)}ds", + "04b3114f218b305f.png": "\\overline{P}(A)", + "04b5600de3bbaa34.png": "Ag^{+}+e^{-}\\rightleftharpoons Ag(s)", + "04bc6ca68b2d1c89.png": "y=a\\frac{d-c}{a-b}+c", + "04bcab8ded274ebb.png": "\\frac{1}{Z_{n}}e^{-ntrV(H)}", + "04c608f3e63de162.png": "\\hat{d}(n)", + "04c6e497b6833f48.png": "C_{1}C_{2}R_{1}R_{2}=1", + "04cba84c1cba4c5f.png": "n->\\infty", + "04cc13393c629cc0.png": "NPV_{0}<0", + "04ce366a6528989e.png": "L(\\phi,\\partial_{\\mu}\\phi,x^{\\mu})", + "04d0ea3c16359188.png": "\\frac{1}{2}v^{2}=U(x)", + "04d3798c9e2f78a1.png": "e^{-}e^{-}\\longrightarrow e^{-}e^{-}", + "04d630767e6d9779.png": "f=\\frac{n_{1}}{n_{0}}=\\frac{2(1-a)}{a}", + "04dcbde3ebfeaba5.png": "S", + "04e0c52aa8da96ae.png": "s_{k}=\\prod_{i=1}^{m}x_{i}", + "04ea506b5a75ca41.png": "\\sqrt{(}t)", + "04ef5dec00edcc6d.png": "\\frac{d^{2}y}{d^{2}t}", + "04f92a2e3e4c714f.png": "y=(\\begin{matrix}v\\\\ u\\\\ s\\end{matrix})", + "04fa8bca5ac3efe2.png": "x^{d}-1=\\prod_{m|d}\\Phi_{m}(x)", + "0504db2b6a091e11.png": "V_{in}\\approx\\frac{I}{j\\omega C}=V_{C}", + "050d4f4c5744ba1b.png": "\\tilde{\\epsilon}_{ij}", + "0512a89b597211cd.png": "\\int_{A}(g-f)d\\mu=0", + "05147eaf65958897.png": "\\tilde{D}_{6}", + "052016cb531ddeac.png": "X_{j}\\sim lnN(\\mu_{j},\\sigma_{j}^{2})", + "052654aa26e4cf36.png": "p=\\gamma_{(u)}m_{0}u", + "0526ea0829aa91d0.png": "\\tilde{e}_{i}B\\subset B\\cup\\{0\\}", + "0527c36f37ca217b.png": "Fe(x)=\\frac{\\varphi^{x}-\\varphi^{-x}}{\\sqrt{5}}", + "0535061b25d0975b.png": "\\frac{2.5^{0}e^{-2.5}}{0!}", + "053b531c509f6245.png": "\\tilde{t}", + "053eaa1f2fed7d13.png": "\\int_{a}^{b}f(x)dx", + "053f53f7aad8c875.png": "\\langle f,\\varphi\\rangle=\\langle T_{f},\\varphi\\rangle", + "054cee547dd1a234.png": "E_{i}=\\int E(t)dt", + "054e0fc66c888dfe.png": "m=(n^{\\prime}-n)", + "0558c0dd42e7771c.png": "C_{L}=C_{o}(f_{L})^{k-1}", + "055e316bc6e80440.png": "\\prod_{t\\in T}(1-x^{t})^{-1}", + "056bb92e362c0350.png": "\\frac{d^{2}u}{dy^{2}}=\\frac{1}{\\mu}\\frac{dp}{dx}", + "0572af993eeabc05.png": "i\\notin F", + "057680cb74a93e7e.png": "x\\notin x", + "0577006f9c97bbee.png": "\\frac{du}{dx}", + "057bb7dbcc740228.png": "(\\begin{matrix}n\\\\ 3\\end{matrix})", + "057d8aab9d8095e9.png": "y_{i}=Y_{i}-\\hat{\\mu}", + "0580a1e9d29b7817.png": "\\tilde{E}_{6}(q)", + "058efe6ebaaa6f3f.png": "\\sum_{j=1}^{20}n(j)M^{n}(j,j)", + "0591136fd2a62d5e.png": "(\\begin{matrix}n\\\\ b\\end{matrix})", + "0591f120952ebdec.png": "c(k)=(\\begin{matrix}2k\\\\ k\\end{matrix})", + "059f2a10c6ca7237.png": "e^{-0.0004286t}=y", + "05a318cb2953d7ba.png": "\\sqrt{2}", + "05a43128ce8dc0f5.png": "(\\begin{matrix}n\\\\ 2k\\end{matrix})", + "05a5411714ff7776.png": "\\overline{Y}=X", + "05ac988412532176.png": "y=-21x-32", + "05aed2450e688cdd.png": "k_{\\tau}^{\\psi}", + "05b77a23037b75ee.png": "\\tilde{\\rho}", + "05b8045eece3183a.png": "f(t)G(t)+g(t)F(t)", + "05baf6b90b332f1b.png": "trH=a+d", + "05bc33679b567317.png": "R_{e}\\propto\\langle I\\rangle_{e}^{-0.83\\pm0.08}", + "05c96a4592bfe5b3.png": "\\sqrt[5]{100}\\approx2.512", + "05d3552353ca5643.png": "E_{W}=\\frac{1}{2}w^{T}w", + "05ddee0f9b5d468a.png": "a_{i}-a_{j}=a_{k}-a_{l}", + "05e85c46c7035d5c.png": "=60\\int_{0}^{2\\pi}d\\theta", + "05ec254d78fc781e.png": "Z\\overline{Z}", + "05effec2064c4dc5.png": "\\hat{y}_{i}", + "05f1a93714e00be9.png": "g=\\int Gdz", + "05f3ae884cf70f31.png": "\\int_{0}^{L}F(x)dx", + "05f4926beaeb7afb.png": "s\\{\\begin{matrix}4\\\\ 3\\end{matrix}\\}", + "05fa4a49915db374.png": "M=[\\begin{matrix}a&b-a\\\\ 0&b\\end{matrix}]", + "06003e6339b68d64.png": "1-e^{-ln(q/p)}", + "06015de309c1971b.png": "a", + "0604d303da66a5d4.png": "[\\begin{matrix}1&0&0\\\\ 0&1&0\\\\ 0&a&1\\end{matrix}]", + "0608e75e097984ba.png": "\\hat{A}_{n,\\alpha}^{\\dagger}", + "06117534c28b856b.png": "\\frac{t+1}{2}\\approx1.42", + "06229d7353da00aa.png": "\\alpha\\le\\zeta_{1}=\\phi_{2}(1)", + "062509f1b698af1c.png": "\\tilde{\\delta}", + "0625e47fae0a2ef2.png": "F_{21}RF^{-1}", + "0629081da7b3452f.png": "z(n;t)=O(n^{2-1/t})", + "063b4878e6608c8d.png": "v\\notin N(T\\backslash S)", + "063cc3f9e0210583.png": "[\\Lambda]=[\\begin{matrix}I_{1}&0&0\\\\ 0&I_{2}&0\\\\ 0&0&I_{3}\\end{matrix}]", + "063dcdb61ac68648.png": 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PSL(2,5)", + "07f2fabdaca7fd91.png": "C=\\frac{6000}{200-2x}", + "07f7f19738a14b9b.png": "\\omega:R_{\\ge1}\\rightarrow R_{>0}", + "07f87d5b7a2bbe81.png": "=\\lambda_{n}x^{T}x", + "07fbe064c53fc45f.png": "\\gamma\\vec{u}=d\\vec{x}/d\\tau", + "080442f4322e38ed.png": "A_{eff}=\\frac{P_{o}}{PFD}", + "08048f527c9625ec.png": "-\\sqrt{x}", + "080731142989f0ff.png": "\\hat{\\eta}", + "08085114bd12a57a.png": "01(01)^{*}\\cup100^{*}", + "080987bc0b6f2e80.png": "f:\\{0,1\\}^{*}\\rightarrow Z_{n}", + "081295f5a4ddb819.png": "m\\frac{d^{2}x}{dt^{2}}+kx=0", + "08155f5d1475a284.png": "T(\\theta)=\\frac{M(\\theta)-C_{1}}{C_{2}}", + "08169567cddc445c.png": "\\sigma^{-1}(m-m^{\\prime})", + "0818a8ee08a65d71.png": "K_{G}(X)^{\\wedge}\\cong K(X_{G})", + "081a982e7759ac5d.png": "I(\\tilde{\\nu})", + "081df7b57e4ff735.png": "K^{\\prime}(\\hat{s})=x", + "081e88cc78d0fedd.png": "(\\begin{matrix}5\\\\ 5\\end{matrix})", + "0825d96ed680809c.png": "\\hat{J}_{a}", + "08262ef20aba3d15.png": "\\int_{a}^{b}dx", + "08275ddc845c9cc8.png": "(\\begin{matrix}131\\end{matrix})(\\begin{matrix}122\\end{matrix})(\\begin{matrix}21\\end{matrix})", + "08296539e005251c.png": "E_{e}^{-}=X", + "0830b47e77b27103.png": "\\frac{d}{dx}\\delta(x-a)", + "08337ccb5fc60b07.png": "(\\begin{matrix}d+n-1\\\\ d\\end{matrix})", + "083a18abce07a058.png": "-I_{+}=I_{-}=I_{i}^{max}", + "0848bac507dc32e8.png": "\\frac{1}{\\frac{1}{88}-\\frac{1}{365.24}}\\approx116", + "084f2b32251450f3.png": "e\\overline{\\psi}\\gamma^{\\mu}\\psi A_{\\mu}", + "0853480158e83779.png": "1/\\sqrt{2}(\\pm1,\\pm1,0)", + "085780229f478909.png": "[g,g]", + "085836b8672e62d4.png": "(\\theta_{i})^{2}=0", + "085eca0811332239.png": "\\{k\\}_{k=1}^{M}", + "08635c60bbecc7ec.png": "M_{s_{\\alpha}\\cdot\\lambda}\\subset M_{\\lambda}", + "0869ce12f50d48c4.png": "\\sqrt{2t}", + "086d1ae4e44d0947.png": "(\\begin{matrix}n\\\\ 3\\end{matrix})", + "0872228373a79361.png": "(P_{j}(G))_{j\\ge0}", + "0874756600d14a00.png": "M<_{DM}N", + "088781bb7a9891d3.png": 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"[\\frac{\\alpha}{\\pi}]=[\\frac{\\alpha}{\\theta}]", + "08c2a75cc7bea9ac.png": "W", + "08c7a9b315a96e7b.png": "\\sqrt{\\frac{5}{126}}", + "08c960fe9e27ec93.png": "\\int_{a}^{b}\\cdot\\cdot\\cdot dx", + "08cee39f2ce5b95a.png": "(R^{3})^{*}", + "08d17d94e8c897bb.png": "F=-\\frac{m_{1}m_{2}}{r^{2}}", + "08d832f4f8a906cf.png": "M(\\hat{G})", + "08d9d9ecb51b217c.png": "\\Pi=(\\pi^{ij})_{1\\le i,j\\le d}", + "08db9c2fb885e974.png": "\\overline{x}\\in X", + "08db9eea13e60486.png": "A=B=P(N)", + "08e3fe5851be32a1.png": "\\overline{op_{1}}^{\\prime}=\\overline{op_{1}^{\\prime}}", + "08e54c0a83b74f54.png": "\\frac{s(n)nat}{nnat}", + "08e5923bc494a18b.png": "\\{(x_{n},f(x_{n}))\\}", + "08ee033db2a4420e.png": "n^{\\overline{m}}", + "08f43bda1d43ec39.png": "[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "08f531ab2246fb72.png": "D=\\frac{3(\\mu-\\delta)}{\\mu}", + "08f5f90b491e031a.png": "c_{2}=t_{2}-at_{2}^{-1}", + "08f72db54386b3e4.png": "[q^{2},klogq]", + "08fdfd2492938277.png": "1/|G|", + 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"0c6baa8409dee47c.png": "s\\notin T", + "0c717f71f6333a4d.png": "e_{1}=(\\begin{matrix}0&1\\\\ 1&0\\end{matrix})", + "0c72e0e1b3fb7f3b.png": "(ab)=a_{1}b_{2}-a_{2}b_{1}", + "0c746d701e7ad6b3.png": "r=r(r,\\theta,t)=r\\hat{e}_{r}", + "0c7705b2c486fbd8.png": "R_{n}^{(\\alpha_{n},\\beta_{n})}(x)", + "0c7b2fa25b76ec07.png": "1/2\\pi\\tau_{M}", + "0c80e2910a542b2a.png": "O(n(n+m))", + "0c8897e5ff44df0b.png": "\\tilde{t}_{j}", + "0c8eeef8ccd1454f.png": "\\partial_{t}v=-\\delta_{u}H(u,v)", + "0c8ff5276dbbb009.png": "(N-x-1,0)", + "0c903effa4933268.png": "G\\overline{t}", + "0ca01cfc086a1b9f.png": "\\tilde{g}_{33}", + "0ca8a7286a64e8be.png": "\\Theta_{n}[_{0}^{0}](i,A)", + "0cacc202189f5096.png": "{\\Xi^{\\sigma}}^{m}", + "0cae5d51adf5d260.png": "\\frac{1}{X}\\sim lnN(-\\mu,\\sigma^{2})", + "0caeb7dd4c6a4070.png": "\\int_{D}f\\Delta g=0", + "0cb2bd6a501788c9.png": "M(x)=\\int V(x)dx", + "0cb6ded5e97ea4bd.png": "\\vec{x}_{1},\\vec{x}_{2}\\in R^{2}", + "0cb8e9c2a8cc7522.png": "=\\partial_{\\mu}A_{\\nu}-\\partial_{\\nu}A_{\\nu}", + "0cba969ebbd99e2e.png": "\\hat{a}_{2},\\hat{a}_{3}", + "0cbbdac188a2fece.png": "\\sqrt{n}\\in Z", + "0cc0d0cbc74a7fdd.png": "\\hat{H}=\\hat{H}(\\hat{P})", + "0cc536a471f73820.png": "-\\sqrt{x}", + "0cc60b529c1e577a.png": "2(\\sqrt{xy}-\\frac{x+y}{2})", + "0ccb9139bc3ca327.png": "[\\begin{matrix}a\\\\ b\\\\ c\\end{matrix}]", + "0cce956fa9fc042e.png": "1/b>10^{-b}", + "0cd35d3940d7a5e0.png": "f(u)=\\beta_{1}+\\beta_{2}e^{-u}", + "0cdab29d8a05cb1c.png": "\\int d\\Omega", + "0cdf6af49e49c59e.png": "P_{1}=", + "0ce3f78066f99541.png": "\\nabla_{i}\\nabla_{j}\\varphi=\\nabla_{j}\\nabla_{i}\\varphi", + "0cec57ec64ce8173.png": "\\hat{H}=\\hat{H}(\\hat{P})", + "0ced18caedb4fb88.png": "\\Delta(n)=O(\\frac{1}{n^{2}})", + "0cef5a2d57157be5.png": "BC", + "0cf2ac2bc83acfbd.png": "E_{f}=p_{f}^{2}/2m_{f}", + "0cf675f280d390de.png": "C(\\vec{N})", + "0cffb730d6a69720.png": "\\sqrt{(}t)", + "0d0171988e203678.png": "\\Omega^{(d+2)}=d\\Omega^{(d+1)}", + "0d063849016a4831.png": "\\frac{\\partial\\sigma}{\\partial x}+f=0", + "0d0712a57c95e09a.png": "a_{n}\\rightarrow\\sqrt{S}", + "0d1175d46fa1ecda.png": "u^{n_{w}}", + "0d15bb00c38ec1b8.png": "T^{t}:=S^{1}\\times\\cdot\\cdot\\cdot\\times S^{1}", + "0d1864a6b2aa635c.png": "\\sum_{k=1}^{n}\\frac{1}{p_{k}}\\sim loglogp_{n}", + "0d188056281baaf7.png": "\\tilde{E}_{i}^{3}", + "0d1bee66911d5b6e.png": "(1/R^{3})(dR^{4}\\Omega^{2}/dR)", + "0d1f1fd12a1166cf.png": "3\\sqrt{2}", + "0d21630ea7ccb889.png": "\\int_{a}^{b}|f(x)|dx=0", + "0d29490bb22d264d.png": "\\frac{\\partial C}{\\partial\\sigma}", + "0d2b09d07654265d.png": "(a_{n_{k}})_{k\\in N}", + "0d2ef85b3b1d074a.png": "-logp(s|m)", + "0d3344e0f5f508a6.png": "c=\\sqrt{n}", + "0d3a4081259df366.png": "|S|\\le(\\begin{matrix}n\\\\ \\lfloor n/2\\rfloor\\end{matrix})", + "0d3d1165421de47d.png": "(I=\\Sigma mr^{2})", + "0d3e82782292a458.png": "dn-(\\begin{matrix}d+1\\\\ 2\\end{matrix})", + "0d4ed162844d4294.png": "\\int K=1/6", + "0d56759c3441b7a9.png": "s(P,E_{i})=\\prod_{k}s(P,E_{ik})", + "0d57ce1d5423a0a2.png": "\\hat{p}_{o}", + "0d5d5bf4f0c4d7b5.png": "u^{\\prime}(t)=\\Delta_{D}u(t)", + "0d5d692ff56ef397.png": "\\beta^{2}\\equiv1-J^{\\prime}(u_{0})", + "0d689f27b22c49ed.png": "S(h_{k})=(-1)^{k}e_{k}", + "0d68d9c221eab07a.png": "A_{5}/\\{e\\}", + "0d6b7a3ef4aa3be7.png": "\\int_{0}^{t}Z_{s}ds", + "0d7426e006bd5ecd.png": "\\frac{v_{m}}{v_{r}}=\\frac{p_{b}}{p_{b}-p_{r}}", + "0d797984827576b1.png": "\\lambda(s)=f_{s}^{\\prime}(0)", + "0d7a071742022d22.png": "(k^{\\prime}+p^{\\prime})^{2}\\approx", + "0d7bba4a4967e339.png": "H_{1}(G;Z)=0", + "0d7d2193593517b9.png": "f(x)=g(x\\cdot\\hat{n})", + "0d7e9180e5c02e0e.png": "W=\\int_{1}^{2}Fds", + "0d87f0fceadd7f52.png": "U=[\\begin{matrix}M\\\\ N\\end{matrix}]", + "0d8856e42d643bda.png": "A=\\sum_{k=0}^{r}a_{k}D_{x}^{k}", + "0d88b779efdf5bc8.png": "[\\begin{matrix}1&0\\\\ -sC&1\\end{matrix}]", + "0d97b1d21e93dee0.png": "Q", + "0d9b6828fff81f75.png": "2^{\\frac{1}{2}}=\\sqrt{2}", + "0d9db98dbcee20a5.png": "\\hat{f}(a)", + "0d9e5bc60e4e4878.png": "\\int dy\\int f(x,y)dx", + "0d9f64a106ff03c5.png": "\\frac{F_{2n}+F_{n}}{2}", + "0da14d9e09a88aa1.png": "Z_{L}=R_{L}(\\omega)+jX_{L}(\\omega)", + "0da8a66b596bcfd9.png": "\\sum_{i=0}^{2}(\\begin{matrix}4\\\\ 2i\\end{matrix})(\\begin{matrix}6\\\\ 4-i\\end{matrix})", + "0db2429d12a77ce2.png": "y", + "0dbca76bb153be20.png": "q=[\\begin{matrix}u\\\\ d\\end{matrix}]", + "0dbeae2cc949957b.png": "D_{0}=(1,1494)", + "0dc20e49e40a8740.png": "e^{iH_{0}t_{1}/\\hbar}", + "0dc3206b3ed5ef55.png": "\\varphi", + "0dc33f4569224367.png": "V(r)=\\frac{1}{2}m_{0}\\omega^{2}r^{2}", + "0dc4e90870751f43.png": "\\omega_{\\mu}^{1}", + "0dcaeb4b79753841.png": "\\frac{(PV)}{N}=kT=E_{k}", + "0dcf55e0eb74014b.png": "log_{\\sqrt[\\varphi]{\\varphi}}(\\varphi)=\\varphi", + "0dd2936c3e882789.png": "f_{x}=\\frac{\\partial f}{\\partial x}", + "0dd4130a4da98b17.png": "A\\underline{\\delta}_{\\Phi}B", + "0dd6ed1afea7b866.png": "(pq|rs)\\in R", + "0dd9ab92734eef84.png": "(id_{\\alpha},id_{\\beta})", + "0de023f9b59281e0.png": "\\int dy=\\int f(x)dx", + "0decbd5f9050d146.png": "Q\\notin z", + "0df94bb963b33295.png": "Z", + "0dfd97347f080756.png": "\\sqrt[4]{2}=x-\\sqrt{2}", + "0e0ad2d133311957.png": "r=k_{1}[A]+k_{2}[A]^{2}", + "0e1b734e31b3a207.png": "-10,...,p_{n}>0", + "0e8be7be24445055.png": "x_{c}=1/\\sqrt{2+\\sqrt{2}}", + "0e91991927f35fa2.png": "\\overline{K}[C]", + "0e920e4673acc1c5.png": "f(x,y,z)=x^{5}y^{2}z^{3}", + "0e96740cecb9e4ca.png": "e_{k}=\\frac{1}{2}v^{2}", + "0e9800cd7e1d390a.png": "[\\begin{matrix}1&0\\\\ 0&-1\\end{matrix}]", + "0e9b0e9b73dc2696.png": "\\int_{0}^{1}\\frac{dx}{\\sqrt{x}}", + "0e9bdb39abbb0c46.png": "\\omega(z_{1},z_{2})=zJz^{t}.", + "0e9d9a134c06187f.png": "\\hat{d}", + "0ea112670c861a6e.png": "||\\vec{x}||\\le n", + "0ea46ba3cd745514.png": "\\tilde{H}=H_{0}+\\langle\\Delta H\\rangle_{0}", + "0ea4c9f48cad199c.png": "\\varphi", + "0ea830fb45d52c23.png": "\\int fdx", + "0ead5862e881309d.png": "\\frac{d}{D}", + "0eb5a3e5b38fe7a3.png": "Th_{\\Pi_{2}^{0}}(N)", + "0ec1dceda105bdf8.png": "\\int uvdx", + "0ec5f863484274c5.png": "exp_{2}^{i-2}(n^{O(1)}))^{\\Sigma_{j}^{P}}", + "0ec6f0e588d898d3.png": "K^{\\times}/(K^{\\times})^{n}", + "0ecabd06c3bdac40.png": "G,\\overline{G},\\tilde{G}", + "0eccf7769b91d2ab.png": "X:(\\Omega,F,P)", + "0ed006fc1d9281fd.png": "c,0\\le cT_{c}=1/(2\\sqrt{log2})", + "0f635915e44fca3e.png": "(5y^{4}-1)\\frac{dy}{dx}=1", + "0f6b06040b28145a.png": "\\delta\\int d\\tau=0", + "0f75c3a696cc02ec.png": "w\\sim N(0,\\alpha^{-1}I)", + "0f784403a41824e6.png": "Q_{H}=Q_{C}+W_{in}", + "0f784669779f8f1c.png": "[\\begin{matrix}1&0&0\\\\ 0&1&0\\\\ 0&a&1\\end{matrix}]", + "0f802fcc4e4188b2.png": "a_{n}=O(b_{n})", + "0f8877de9be4cf25.png": "\\hat{V}_{s}", + "0f8afec372072b28.png": "[n,n+(logn)^{2}]", + "0f8ddf90fedb8825.png": "\\int_{V}JdV=0", + "0f91ed331bbad6e1.png": "-\\vec{\\omega}\\times\\vec{R}", + "0f9bfdf5b93b3217.png": "[\\frac{\\alpha}{\\pi}]=[\\frac{\\alpha}{\\theta}]", + "0f9c81c0257377d5.png": "126", + "0fa0b8eeb5117711.png": "[\\hat{H},\\hat{L}_{z}]=0", + "0fa0eaa30b6554b8.png": "f^{*}=\\prod_{k=1}^{n}(X-\\alpha_{k}^{*})", + "0fb125c88591eb36.png": "\\frac{dX}{dt}", + "0fb650773a6d8bdf.png": "NE(X)", + "0fb888efe6cf421b.png": "[x_{w}y_{w}z_{w}1]^{T}", + "0fc2dedffb64cbdf.png": "\\hat{f}(n)", + "0fc645daa41b86c5.png": "ABA^{-1}B^{-1}", + "0fc7de0639a38512.png": "\\frac{40}{3}\\times\\frac{201}{16}", + "0fccb6614a05df0c.png": "f(x_{1},...,x_{n})=x_{i}", + "0fcd1979512cdfe1.png": "\\underline{\\underline{K}}=\\underline{\\underline{A^{T}KA}}", + "0fd6bee576a5ea81.png": "\\oint F\\cdot dl=0", + "0fd8e0e271b4305b.png": "Q(x)=\\prod_{n\\ge1}(1-x^{n})", + "0fda1eaa64211066.png": "(\\begin{matrix}n+x-1\\\\ n\\end{matrix})", + "0fdc0b1450ec6215.png": "\\hat{\\pi}", + "0fdc3a434a49b915.png": "Z=(\\begin{matrix}z&0\\\\ w&-z\\end{matrix})", + "0fe835441d4cad44.png": "\\overline{x}_{i}", + "0fec32b2a3832066.png": "\\iint f(x,y)dxdy", + "0feea4220047b543.png": "\\tilde{K}_{\\pm}", + "0ff00f1dea703841.png": "[\\begin{matrix}1&0&0\\\\ 0&1&0\\\\ 0&a&1\\end{matrix}]", + "0ff22c5d11c93abb.png": "(X-k)/\\sqrt{2k}", + "0ff28d9ed68264e3.png": "(\\forall x\\in V^{P})p\\Vdash_{P}f", + "0ff93f574ffe7cab.png": "N=(\\frac{Vf}{\\Lambda^{3}})e^{\\beta\\mu}", + "0ffa0621ad3d867a.png": "\\hat{X}(z_{1k},z_{2k})", + "0ffff5551007755a.png": "\\theta\\in[q_{i},q_{i}+1]", + "100199613b416600.png": "E_{0}=\\hbar\\omega/2", + "101551ec0d253eca.png": "\\frac{\\sum_{x\\in W}f(x)}{|W|}", + "101817c78aab5c03.png": "2x^{7}+x^{2}+1\\ne0", + "10184517494bb82b.png": "\\frac{dA}{dr}=C", + "1025bd7dbd00e9ec.png": "J=(\\begin{matrix}0&I\\\\ -I&0\\end{matrix})", + "1029b2418de32a5c.png": "(\\begin{matrix}a&z\\\\ \\overline{z}&c\\end{matrix})", + "1034379ceeabb1a1.png": "\\gamma(n)=\\prod_{p|n}p", + "1034662a2eae46a5.png": "m^{+}\\oplus l", + "10383c3a6a3c4f35.png": "H\\psi=i\\hbar\\partial\\psi/\\partial t", + "104c7022ee35cc67.png": "\\overline{I}=\\overline{\\overline{I}}", + "104d5a1c8234d935.png": "\\sum_{i=6}^{10}(\\begin{matrix}16\\\\ i\\end{matrix})", + "1053c17743a69652.png": "f_{d}\\approx2v\\frac{f_{t}}{c}", + "105498897c7c3405.png": "(n,k,2t+1)", + "1054f0bc9a42314d.png": "\\hat{p}^{k}", + "10645c5e41c70790.png": "\\overline{CD}", + "1071cde2c62ced98.png": "\\tilde{v}", + "1074dc32ffb6ac84.png": "\\tilde{p}", + "107693bab9cd6b9c.png": "-1^{\\sqrt{2}}", + "1077780567e332bd.png": "E[X_{\\tau}]\\ge E[X_{0}]", + "1079d96365be896d.png": "\\tilde{O}(n^{2})", + "107f2353667cb0a6.png": "\\frac{i}{n}x[n]", + "1080be6dd6bec0ad.png": "\\hat{u}=e^{-2\\pi y|\\xi|}\\hat{f}", + "1081ddf12d24b3c2.png": "\\Sigma|a_{n}|^{2}\\ne\\Sigma|b_{n}|^{2}", + "10839917821ee804.png": "a^{a}+b^{b}\\ge a^{b}+b^{a}", + "108d7c87dce20d7f.png": "\\hat{B}", + "1092529b34334526.png": "AM", + "10955fb7c2690503.png": "(id_{\\alpha},id_{\\beta})", + "109c57d0f4422ca8.png": "V_{Y0}t=h", + "109f05190fb80e19.png": "l^{*}=\\frac{l}{1-g}", + "109f3762e7fb6c5f.png": "\\sqrt{-3}", + "10a4ea01ae15086f.png": "x_{1},x_{2}\\in\\Omega\\\\ X", + "10a59eff9b09c474.png": "\\frac{d^{n}Y}{dx^{n}}", + "10a617b2245d1785.png": "\\tilde{p}(x)", + "10a86a9c3fa8cb87.png": "\\int kdx=kx+C", + "10b2d5bbac7f359c.png": "\\{\\begin{matrix}5\\\\ 5\\end{matrix}\\}", + "10b7339ab3fbdfb4.png": "A=(\\begin{matrix}2&0\\\\ 0&1\\end{matrix})", + "10b8287221808aad.png": "(\\begin{matrix}n\\\\ 2\\end{matrix})", + "10c0dcc7f5bb76ae.png": "H=\\frac{1}{2}(\\frac{1}{R_{1}}+\\frac{1}{R_{2}})", + "10c76cd0a22c0c60.png": "\\frac{dt^{2}}{dr^{2}}", + "10cacb3b1c7dc39b.png": "\\tilde{4}", + "10cf171e28ff0a91.png": "O(\\sum_{i=1}^{m}logd(f,a_{i}))", + "10cf9b4bf9f0d299.png": "\\sum_{n=0}^{225}(\\begin{matrix}225\\\\ n\\end{matrix})=2^{225}", + "10d17725afc8c7f5.png": "\\frac{dx}{dt}=c", + "10d44d194f743b98.png": "P^{2}\\psi=e^{i\\phi}\\psi", + "10d6f86259df1033.png": "\\hat{2}", + "10d9245d36051e2e.png": "A_{\\epsilon}^{n}(X,Y)", + "10dc7d606e6d0af9.png": "\\tilde{g}=F^{T}gF", + "10e0db6bcddd0842.png": "(d^{\\nabla})^{2}\\sigma=F^{\\nabla}\\wedge\\sigma", + "10e47cc14b660846.png": "p_{i}|\\phi_{i}\\rangle", + "10f3b5c7f077485c.png": "C_{\\tilde{Y}}", + "10f443ef6b54ef23.png": "\\tilde{Y}^{n}", + "10f7d4504bd3e3bb.png": "(\\begin{matrix}i\\\\ u\\end{matrix})", + "10f9d9c0d76bae14.png": "E[P^{(k)}]=-k\\alpha", + "10fa699d6aa84dd0.png": "\\frac{A}{RC}=\\frac{V_{out}}{RC}", + "11013d5a5262aaee.png": "\\int_{-\\infty}^{\\infty}", + "1101c4eb2ad38b70.png": "K=k^{2}B^{2}/\\mu_{0}\\rho:", + "11055ad5d3ede83e.png": "m=\\prod_{k=1}^{j}m_{k}", + "110b6c1040342fcb.png": "(\\tau_{1}^{-1},...,\\tau_{g}^{-1})", + "110d94ba244d18bc.png": "(\\sum\\frac{1}{n!})^{x}=\\sum\\frac{x^{n}}{n!}", + "1118049e524829ca.png": "p=\\frac{mv}{\\sqrt{1-(v^{2}/c^{2})}}", + "111d7acb4f3227e4.png": "\\frac{dM}{dt}", + "11200f7f5ce97f7d.png": "\\underline{\\neg\\psi}", + "11201972ed51e292.png": "\\int\\rho d^{3}x=1", + "112093aa841d6f44.png": "\\frac{D\\rho}{Dt}+\\rho(\\nabla\\cdot u)=0", + "112b29693ebef7a9.png": "\\sqrt{\\frac{1}{126}}", + "112d6b8643588124.png": "\\int_{a}^{b}f(x)dx", + "11305c592ceb50d9.png": "d=\\frac{ct}{2}\\sqrt{1-(\\frac{\\tau}{t})^{2}}", + "113082ab6ed2f7dc.png": "\\int_{h(C)}fds", + "11372d46c58a00c3.png": "\\int_{X}1d\\mu", + "113a6230f26580c0.png": "\\int_{0}^{t}Y(r)dr", + "113d828ca1b04b6b.png": "x.x+y.z-z.y", + "113fa477a848cb73.png": "\\int PdV+\\int VdP", + "1140ef5633f280a2.png": "\\hat{v}(x)", + "114181335d4ff4fb.png": "(\\begin{matrix}1&\\nu\\\\ 1&1\\end{matrix})", + "1150f660aa098571.png": "\\int_{X}1d\\mu", + "115208ec2d17de77.png": "Tr\\rho^{p}K^{*}\\rho^{1-p}K", + "11545553c39fce28.png": "(L_{X}g_{ab})_{;c}=0", + "115a631600fa6046.png": "\\frac{x-1}{x^{3/2}}=\\frac{x-1}{x\\sqrt{x}}", + "115b2f90a87bd430.png": "G", + "11648cc676f011ec.png": "argmax_{x\\in[x^{\\prime\\prime},x^{\\prime}]}f(x;s)", + "1166bf7b16563879.png": "\\eta_{e}=\\frac{\\sigma_{n}}{\\dot{\\epsilon}}", + "11687e63e40a180b.png": "D(f)\\mapsto M[f^{-1}]", + "1169ce71f45cf1ab.png": "=cos(x)+isin(x)", + "116d4d7dddd5a946.png": "X\\in C,Y^{*}\\in F", + "11737d1bf5841ad9.png": "sys^{2}\\le\\frac{\\pi}{2}\\cdot area", + "1176eceff7224d27.png": "|f_{n}^{\\prime}|>1", + "117a6c64eb129bf1.png": "\\lambda_{n}=(\\begin{matrix}n\\\\ 2\\end{matrix})\\frac{1}{N}", + "117cf2746ae2c4d2.png": "dx^{\\mu}=e_{(a)}^{\\mu}e^{(a)}", + "1182c7a44788160c.png": "[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "1185899ab1f7b731.png": "x=\\sqrt[3]{u}+\\sqrt[3]{v}", + "1185e76e53f357fb.png": "lim_{r\\rightarrow\\infty}\\int_{|x|>r}|f|^{p}=0", + "118a2ccc1e584daa.png": "\\frac{9(e^{10}-1)}{10}\\approx19823", + "118afa196b08b951.png": "2^{O(\\sqrt{k})}n^{O(1)}", + "118e0a0391e5bafd.png": "\\{X_{i},X_{j}\\}\\notin E", + "11904d74de341563.png": "\\mathbb{N}", + "1191941bb0c53155.png": "\\int Fdx", + "1193a03f9f881453.png": "\\sqrt{8}", + "119626aa65cf7951.png": "U_{E}(r_{ref}=\\infty)=0", + "11985941317b792a.png": "\\gamma=\\gamma^{o}(1-\\frac{T}{T_{C}})^{n}", + "1198a875bf1b708a.png": "F_{i},i=1,2", + "119b2991cc3ed8d1.png": "\\frac{U}{U_{v}}\\approx\\frac{m_{0}}{m^{*}}\\frac{m_{0}c^{2}}{E_{G}}", + "11a458d89027f194.png": "Im\\{x[n]\\}", + "11a472ae4acca47c.png": "\\frac{dP}{dw}", + "11a5a0db4414775d.png": "k[\\overline{X}]", + "11ab51523fd1efd8.png": "7=(3-\\sqrt{2})(3+\\sqrt{2})", + "11abc10ee54ff184.png": "\\underline{P}X=\\emptyset", + "11af6830667584d3.png": "\\int\\frac{dx}{lnx}", + "11b43736d796768a.png": "\\omega_{N}^{3(k+N/4)}=i\\omega_{N}^{3k}", + "11b6b47798390fd6.png": "MPC=\\frac{dC}{dY}", + "11bd11a090e62b13.png": "H(z)=\\frac{1}{1-az^{-1}}", + "11c6cf8883713ba1.png": "\\tilde{f}=|\\frac{\\tilde{d}}{2}|", + "11c9b0c404be8412.png": "\\Delta\\delta T=\\epsilon L_{\\xi}T_{0}", + "11d35fed84aa65b5.png": "L=q^{\\Omega(n)}", + "11de37bd7e6e3a5a.png": "(\\begin{matrix}n\\\\ 5\\end{matrix})", + "11e14d1e6e5c1d84.png": "n=(\\begin{matrix}2k-1\\\\ k\\end{matrix})", + "11e1c0b0bd3a845f.png": "\\tilde{x}^{2}", + "11e1e23e6ab3ce18.png": "(n_{o}p_{o}=n_{i}^{2})", + "11e48233c62f4ec2.png": "\\int_{0}^{x}1dt=x", + "11e77e44bcefac29.png": "\\frac{dp}{dr}", + "11ec18a5dfc558d8.png": "\\beta=(1-\\rho)\\sqrt{s}", + "11ed9584dd2b8865.png": "2^{O(\\sqrt{k})}n^{O(1)}", + "11eec6f20866a91e.png": "c_{ij}^{k}\\in Z_{\\ge0}", + "11f9c506baec28aa.png": "\\frac{d^{4}y}{dx^{4}}", + "12035aa806096f56.png": "L=u,v,...,w", + "12036dfdbf502b07.png": "\\frac{1}{n^{3}-n}", + "120591dd1a534fef.png": "C_{J}-", + "120af87e93157f29.png": "k=\\prod t_{i}", + "121534bbbf56d759.png": "G*\\underline{A}", + "1217b40b48428bcc.png": "\\int_{x}^{x}f(t)dt=0", + "1222d8736d496825.png": "\\frac{d^{2}y}{dt^{2}}", + "12240419790a9314.png": "\\frac{\\partial T}{\\partial y}<0", + "12364a38ed5e1d9a.png": "\\varphi_{F(p)}(y)=Q(p,y)", + "1237c6e2f94d8614.png": "c=\\frac{\\partial C}{\\partial m}", + "1242325d39cec2f3.png": "v=\\sqrt{\\frac{T}{\\mu}}", + "125191d0e05cad86.png": "|x|^{2}=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}", + "12524c8b96a8cc5f.png": "(\\begin{matrix}k-1\\\\ D-1\\end{matrix})", + "1256a94965000660.png": "\\frac{\\frac{7}{167}}{(454^{7}+6)}", + "125c12fd86949dec.png": "(n-1)|(m-k)", + "125d06b13c337df7.png": "\\overline{x}=\\lambda^{-1}", + "125f3db6ac067fc4.png": "\\frac{du}{dx}", + "12644b20421b3c7d.png": "u_{2}=[\\begin{matrix}0\\\\ 1\\end{matrix}]", + "12667421ae7254e9.png": "\\tilde{\\chi}", + "126ca28f8da703a5.png": "(m^{d})^{e}modn=m", + "126dff7aac8d375c.png": "\\frac{\\partial C}{\\partial r}", + "12704280eba4d628.png": "x_{n}/||x_{n}||", + "1273c320cc6b28e8.png": "\\int_{-r}^{r}|y-s|dx", + "127adead5e897a6b.png": "\\frac{dy}{dx}=x+y", + "12808c984988a956.png": "K=k^{2}B^{2}/\\mu_{0}\\rho:", + "12809b3507446c52.png": "G=(\\begin{matrix}1&0&0\\\\ 0&1&0\\\\ 0&0&-1\\end{matrix})", + "1284d550943953bb.png": "X=R-\\{0\\}", + "12950817d08ec965.png": "\\int x\\frac{1}{dx}=\\int\\frac{1}{x}dx", + "12aec08a9fdc4492.png": "X=\\prod_{i\\in I}X_{i}", + "12b22226f6ab7564.png": "\\overline{K_{0}}", + "12b9c4eb0ac0667e.png": "F=0.7tL(UTS)", + "12bd240cef6aaf9e.png": "\\mathbb{B}", + "12bd28ee8b74bce6.png": "N=max(m,n)", + "12c140ec49fe644b.png": "1.15m*c^{2}-mc^{2}", + "12d5df4887c32a98.png": "2(\\sqrt{xy}-\\frac{x+y}{2})", + "12d6117c72d1704c.png": "ae^{-kt}+3", + "12d8159f6e27a977.png": "\\{-1,0\\}\\cap\\{0,1\\}\\notin\\tau_{1}", + "12dbd3d1fdba9a9b.png": "\\lambda(r,\\theta)=e^{-r^{2}}", + "12de3cf953ddefa8.png": "I=\\int_{m}^{n}f(x)dx", + "12eeb2edef7c37e6.png": "\\hat{L}", + "12ef8c1b6553dd1f.png": "3k+1=2^{a}k^{\\prime}", + "12f064446e97de6e.png": "N=max(m,n)", + "12f7a49c67634273.png": "\\lambda Y(\\underline{k},\\omega)u(n)", + "12f7aeaabcf79f47.png": "\\tau(b^{2}+1)-2", + "12f86f33b88d0510.png": "s_{\\mu}*s_{\\nu}=\\sum_{\\lambda}g_{\\mu\\nu}^{\\lambda}s_{\\lambda}", + "12f8dff753c3c411.png": "\\lambda_{\\hat{\\beta}}", + "12f9493ea8fc2612.png": "n=|m|)", + "12fa1032603cbda7.png": "\\int_{0}^{1}f(x)dx=\\infty", + "12fa58b7fb151b32.png": "S_{0}+h\\nu_{ex}\\rightarrow S_{1}", + "12fbcfdf2960d7e0.png": "l", + "1306681ad68973fe.png": "\\langle\\frac{F}{||F||},\\frac{T}{||T||}\\rangle", + "130acba960b2089d.png": "5\\sqrt{2}", + "131778c514f3f433.png": "\\epsilon=2\\nu\\langle E_{ij}E_{ij}\\rangle", + "13188248fde64626.png": "P_{n}(K)=(P,G,\\in)", + "131c6f3bd4d97f6c.png": "N(\\overline{X},\\sigma^{2})", + "131cb015289ed015.png": "\\overline{W}^{s,p}(R)", + "1322eef8cdcf0573.png": "\\lambda_{\\hat{\\beta}}", + "1322f10fb4e8049e.png": "\\hat{\\phi}", + "132677212b84c6eb.png": "\\hat{p}^{k}", + "1328d623d8262855.png": "-a_{+}^{*}", + "13311224a9455943.png": "\\hat{S}_{a}", + "13338c208c474a85.png": "P-AP>0", + "133747918f0a4b75.png": "f_{5}(x)=log_{c}x", + "133bbe733599e5b2.png": "\\pi_{1}\\pi_{2}...", + "133cbe096ec6fe0a.png": "\\hat{f}(x)", + "133df54322e0dabc.png": "A\\overline{D}", + "133e3420959c8605.png": "\\hat{D}(\\alpha)|0\\rangle=|\\alpha\\rangle", + "13418d879e12bed9.png": "p=\\rho(\\gamma-1)e", + "134672e115e3c5fc.png": "y_{y^{2}}", + "13483b0b8d92a3b5.png": "\\Sigma a_{i}{x_{i}}^{m}", + "1349d1c61e1e40d8.png": "a_{s}(h)=\\sqrt{(\\gamma-1)h}", + "134b39c59e2d9f42.png": "1+x^{-14}+x^{-15}", + "134be8c02b23317c.png": "\\frac{d^{2}y}{d^{2}t}", + "134ce8ce821c7f86.png": "f^{-1}(]-\\infty,c])", + "134d50b4e12aeffe.png": "\\hat{v}_{i}", + "134f0f71c7d4250c.png": "x\\notin\\{y:d(x,y)>r\\}", + "13514b91ce60cdd1.png": "C_{\\beta}(s)=[\\begin{matrix}1&0\\\\ s&1\\end{matrix}]", + "1353ed3f229db1c2.png": "BA=(\\begin{matrix}1&0\\\\ 0&0\\end{matrix})", + "135d8fb6715e987b.png": "|\\psi_{y-}\\rangle", + "136345ccd9417dae.png": "\\frac{\\partial f}{\\partial x_{j}}(x)", + "1364a82045367999.png": "(\\begin{matrix}n\\\\ i\\end{matrix})2^{-n}", + "1367e777f8f67391.png": "L_{2}", + "136864b47cc63eb9.png": "(\\begin{matrix}p_{k-1}&p_{k}\\\\ q_{k-1}&q_{k}\\end{matrix})", + "136ec8e24b61ca2f.png": "dm=(\\frac{dy}{L})m", + "13711988df90ee19.png": "m\\frac{d^{2}x}{dt^{2}}=f(x)", + "137f4af3b75f9afd.png": "\\int_{0}^{T}dy_{2}dt", + "13802b59f8628cfe.png": "\\sum_{i=1}^{n}\\hat{\\epsilon_{i}}=0", + "138576772aaf6bcb.png": "u=2\\sqrt{-\\frac{p}{3}}", + "13890784173a6c42.png": "\\int sinx^{2}dx", + "1389c883677256d9.png": "(be)e=be", + "138e8907f9677858.png": "\\dot{m}=\\rho\\cdot A_{s}\\cdot b_{r}", + "1391d2edb886a83d.png": "a\\equiv\\frac{1}{x}(mody)", + "1393484d684389fc.png": "\\int_{\\mu^{\\circ}}^{\\mu}d\\mu=\\int_{P^{\\circ}}^{P}\\overline{V}dP", + "139382c40d5492a3.png": "\\frac{\\partial}{\\partial x}", + "13946984635f27e3.png": "\\theta/(\\theta+J-1)", + "1396039c6b10e347.png": "P(Y>n)\\le\\frac{E(Y)}{n}", + "1396176a00509c70.png": "y\\in\\overline{S}", + "139b3cc0846d9513.png": "T_{M}=\\tau_{N-1}-\\tau_{0}", + "139d48b78ba71c60.png": "AveP=\\int_{0}^{1}p(r)dr", + "139dd2cbe8e45c72.png": "0m\\Omega(r)", + "15da30d117036cc4.png": "\\prod_{p^{k}}f(p^{k})", + "15da484b53bd9c11.png": "L_{3}=\\frac{-K_{C}R_{S}}{sL_{M}}", + "15e4044df17040fb.png": "[f(\\theta_{i-1}),f(\\theta_{i})]", + "15e4f7aeb512f7ce.png": "\\frac{T}{100}=\\frac{4000}{100}=40", + "15e9f55cc29521af.png": "\\int f(t)dt=0", + "15f025c984b32b28.png": "(\\begin{matrix}5\\\\ 1\\end{matrix})=1\\times\\frac{5}{1}=5", + "15f2b74172a865f0.png": "\\sqrt{d}", + "15fc58a621a3f8d2.png": "\\hat{e}_{j}", + "15fdea12e32b441c.png": "(\\begin{matrix}n\\\\ 1\\end{matrix})_{F}=(\\begin{matrix}n\\\\ n-1\\end{matrix})_{F}=F_{n}", + "160bb79aecd6d084.png": "\\sum_{i=n}^{m}\\frac{(\\begin{matrix}i\\\\ n\\end{matrix})}{2^{i}}", + "16112aa98c7076df.png": "(a_{0},...,a_{N-1})", + "16124861671195bd.png": "FDR_{-1}", + "1619fab944921a69.png": "\\partial_{\\mu}\\hat{A}^{\\mu}", + "161ec483a5e75a7c.png": "\\mu_{0}\\epsilon_{0}=1/c^{2}", + "1621f447d25319d2.png": "\\int_{G}fd\\mu", + "1623795fb5f1557c.png": "\\hat{L}_{a}", + "1624e27a5c6a0989.png": "(\\begin{matrix}0&-1\\\\ 1&0\\end{matrix})", + "1627ea22fb3c038d.png": "\\hat{h}_{L}", + "162aebbefb7744c7.png": "E(B)=VF(B)V^{*}", + "162c4cfdbb709124.png": "\\dot{y}=\\frac{dy}{dt}", + "163bbda6cd9e2d32.png": "X\\backslash\\cup_{\\lambda\\in\\gamma_{k}}U_{\\lambda}", + "163d4b79e7f03944.png": "(\\begin{matrix}n\\\\ 1\\end{matrix})", + "163e432f1f18aa87.png": "2^{bh(v^{\\prime})-1}-1", + "163ee9a70730f59e.png": "S:C^{\\infty}([a,b])\\rightarrow R", + "164814b5984b7811.png": "h(x)|x^{N}-1", + "164b5df9508b5103.png": "-\\frac{3}{16}x^{2}-\\frac{3}{4}x-\\frac{15}{16}", + "1653f2583c35dc19.png": "(N^{\\prime}-1)!", + "1659f20cd048de75.png": "E[y]=\\mu=g^{-1}(\\eta)", + "165bca650891375c.png": "\\hat{K}_{G}", + "165d91365adc0857.png": "\\sqrt{n}/ln(\\sqrt{n})", + "166719ca34fb61a0.png": "\\nu^{h_{5}}", + "1674879bea3b8a32.png": "\\prod{A_{i}}^{\\prime}", + "16777cab28fdd00c.png": "\\int ln(3x-5)dx", + "167a74b19e214fd8.png": "\\forall i:V_{i}(P_{i})\\ge w_{i}", + "167fd231306ce316.png": "s_{\\lambda}s_{\\mu}=\\sum_{\\nu}c_{\\lambda,\\mu}^{\\nu}s_{\\nu}", + "16890f02ae10d65a.png": "10-10=0", + "169681c579f8771d.png": "\\tilde{H}_{r}", + "1699ce40305786c1.png": "\\nabla^{2}\\Phi=4\\pi Gm|\\Psi|^{2}", + "1699f91b07e4390a.png": "B=10log_{10}(b)", + "169fad9c3fedfcb5.png": "\\alpha_{f}<<\\theta^{\\prime}", + "16a7643d9bfef597.png": "\\frac{dy}{dx}=\\frac{x}{y}", + "16a87cf574e1db72.png": "\\frac{\\partial T}{\\partial x^{\\prime}}=\\frac{1}{v}\\cdot\\frac{\\partial T}{\\partial t}", + "16ade42e801de88f.png": "\\int_{0}^{L}F(x)dx", + "16b1057e95e8ac15.png": "\\int_{0}^{t}B_{s}^{2}dB_{s}?", + "16b523ccda1e4644.png": "f((\\begin{matrix}a&b\\\\ c&d\\end{matrix}))", + "16b739ab96c15474.png": "(\\begin{matrix}t\\\\ 0\\end{matrix})=1", + "16ba44a9a1164d36.png": "(\\begin{matrix}i&j\\\\ k&l\\end{matrix})", + "16bc42ffa92ad91b.png": "X\\rightarrow X^{\\prime},Y\\rightarrow Y^{\\prime}", + "16bfb0ddc32dc262.png": "1*1=\\sigma_{0}=d=\\tau", + "16c18db0fc9099ab.png": "|x|\\le1,|y|\\le1", + "16cb3d93997599fd.png": "\\{\\tilde{e}_{k}\\}", + "16cf8e2103200217.png": "sin(2\\pi ft+\\pi/2)sin(\\phi)", + "16d069454eeee47f.png": "\\int dy=y", + "16d475d86d126b35.png": "\\hat{\\mu}_{j}", + "16d49267c42fc4ad.png": "l^{t}\\tilde{\\beta}", + "16d58c2ce6a9ba2d.png": "X=s_{X}\\phi(x)^{r_{X}}", + "16e1644735db587a.png": "sin(x+y+z)", + "16f06f1edebbf786.png": "\\tilde{c}(\\Pi)", + "16f4781cade7f9c6.png": "\\hat{y}\\in\\{-1,1\\}", + "16f72ac03ff6086d.png": "\\int_{A}f(x)dx", + "16fa9e5079c78627.png": "\\int_{b}^{a}|f(x)|dx", + "1703878cdb1b6bcd.png": "z=a\\frac{sin\\sigma}{cosh\\tau-cos\\sigma}", + "170c6f6b28d6da7c.png": "(Z_{p}/mZ_{p})", + "1710a9627a96d0d9.png": "xD(1)=x*\\frac{d}{dx}(1)=0", + "171310ded69b5644.png": "\\frac{1}{q}=\\frac{1}{R}-j\\frac{\\lambda}{\\pi w^{2}}", + "171f35f7748f05af.png": "\\sqrt{x^{2}+y^{2}}-L=0", + "1720c1f3c3b073d6.png": "4^{2}+4\\cdot1+1^{2}=21", + "17250c69f6348140.png": "\\frac{dV}{dt}=Q_{0}", + "1728fc490ea5f3ca.png": "u^{\\prime\\prime}(x)-u(x)=0", + "1729dd00f9fdf71e.png": "h(r)=r^{2}\\cdot loglog\\frac{1}{r}", + "172bb9a2b7cd5929.png": "s\\{\\begin{matrix}5\\\\ 3\\end{matrix}\\}", + "172bc7d862104591.png": "Q:=\\bigcup_{\\sigma\\in\\sigma(T_{0})}Q_{\\sigma}", + "172c920bd8b61de2.png": "Q_{j,x}=\\int y_{i}dA", + "172fd1ae98771f0a.png": "\\int_{\\Omega}fw=0", + "173161751f109c2d.png": "\\overline{X_{j}}", + "1732433b5ebf08d6.png": "(\\begin{matrix}n\\\\ m\\end{matrix})", + "1732457be786103c.png": "\\hat{t}<0", + "1736da01cad6f41d.png": "g\\notin F", + "17392bcbf2774cd6.png": "\\emptyset\\notin P", + "173dfcd394b2d782.png": "sup_{n}|\\sum_{i=1}^{n}x_{i}|", + "173eb106d143dbdb.png": "\\frac{\\partial D}{\\partial G}<0", + "1740ecdb11656dfb.png": "S^{0}\\rightarrow S^{n}\\rightarrow RP^{n}", + "174347182f588344.png": "\\hat{p}^{k}", + "1744e968c858d454.png": "\\frac{\\partial Q}{\\partial t}", + "174de3a76d8d774a.png": "(\\begin{matrix}n+k-1\\\\ n-1\\end{matrix})", + "174fe9c91d26eade.png": "\\delta[\\rho-\\hat{\\rho}]", + "17581e52cea57488.png": "a_{C}=\\gamma\\frac{[C]}{[C^{\\ominus}]}", + "175af48df39886be.png": "K_{n}=C((T^{1/n}))", + "175b6a515a286100.png": "\\sqrt[3]{2}\\approx1.26", + "175d6991967de2b3.png": "\\Delta T(t)=\\Delta T_{0}e^{-t/\\tau}", + "175d6a06713e7422.png": "\\tilde{E}_{i}^{a}", + "17673ebc7aa5a782.png": "A_{f}=\\langle f|P\\rangle", + "17696a860a786b87.png": "v_{1}=(\\frac{\\sqrt{3}}{2},\\frac{1}{2})", + "176bec2f1d5d7e4b.png": "T_{0}=2\\pi\\sqrt{\\frac{l}{g}}", + "176dc27291b9b37a.png": "f(\\underline{m})=0", + "1776fef7190683be.png": "\\hat{\\omega}_{i}(t,\\omega)", + "1779d7489b63a039.png": "\\omega_{f}^{\\nu}", + "177a593fd5aab6f6.png": "ss\\{\\begin{matrix}2\\\\ 3\\end{matrix}\\}", + "177f7a6d970b01dc.png": "m(A)=\\int_{A}Xdn", + "177fc1183e4cf9e4.png": "L_{F}=ln(\\frac{F}{F_{0}})", + "1785afcd2e617e53.png": "c\\notin A", + "1788df7febc33fa3.png": "\\frac{\\partial\\rho}{\\partial t}+\\nabla\\cdot(\\rho v)=0", + "178a60daf9ceb63b.png": "\\frac{dL}{dt}", + "178af69d14afcc8b.png": "Pr(p)=W\\cdot m^{-N}", + "178f541b2fffac77.png": "|2l|=\\frac{2L^{2}}{mk}", + "1790489961e6989b.png": "[\\begin{matrix}8&-2\\\\ -4&6\\end{matrix}]", + "17a759b69f943e28.png": "\\tilde{A}_{6}", + "17a908e1183e3059.png": "\\tilde{Y_{k}}", + "17aa78c3e8be65e7.png": "S^{0}\\rightarrow S^{n}\\rightarrow RP^{n}", + "17ac3a819e27e62b.png": "J=(\\begin{matrix}0&1\\\\ -1&0\\end{matrix})", + "17b5fd794ca06249.png": "xT(3,1,x)=E_{1}(x)", + "17ba2811e719b4e1.png": "\\langle r|\\Psi\\rangle=\\Psi(r)", + "17bcb2a78a7bedc7.png": "(\\frac{N}{N_{0}})", + "17cca36495867177.png": "\\frac{d}{dr}B(r)=-DB", + "17ce9df68d87553c.png": "\\}", + "17d09c7696fc6229.png": "\\langle Q,\\Sigma,\\Gamma,\\delta,q_{0},F\\rangle", + "17d2dad8a91ff96f.png": "\\Phi=e^{B+i\\omega}\\Omega", + "17d714f972b8481f.png": "M,\\hat{d}", + "17d80313b82d1223.png": "X_{1}^{a_{1}}\\cdot\\cdot\\cdot X_{n}^{a_{n}}", + "17d931802083d98e.png": "(2e^{0i})^{0.5}=\\sqrt{2}", + "17e082990ff5758a.png": "C", + "17e0d573ca8dbcb8.png": "\\dot{\\tilde{\\mu}}=0", + "17e15ae2ee991398.png": "\\forall x_{1},...,x_{n}.F", + "17ea81be5925781c.png": "1:\\sqrt{\\varphi}:\\varphi", + "17eb0bdbf9dd9ecb.png": "f^{2}(dx^{2}+dy^{2})", + "17ee6a892c8c7dbb.png": "-\\lambda v=ma=m\\frac{dv}{dt}", + "17ef4dae612a3c12.png": "u=\\prod_{i=1}^{k/2}p_{i}", + "17f27b3b685e6384.png": "\\sqrt{-1}=\\sqrt{-1}", + "17f85b86984c3120.png": "\\frac{2m}{\\hbar^{2}}(V(x)-E)", + "17f9758261d00b1f.png": "[x;h]=0", + "17fa35b32ec0d26c.png": "2r=R\\sqrt{2}", + "180df9a36258e650.png": "\\hat{v}_{k}", + "180f1bdefe3acaa7.png": "\\hat{S}_{n}", + "1811ab92a55dd9fd.png": "\\hat{X}_{q}", + "1814ac489ed2069a.png": "\\tilde{c}(\\Pi)=(-1)^{k-l}c(\\Pi)", + "1816159c5afc4dc6.png": "(n-k)S", + "1816842eb585f1f6.png": "\\int|\\kappa(s)|ds", + "1816e6c5635e6948.png": "(\\frac{\\partial H}{\\partial T})_{p}=C_{p}", + "181784878fd09ca7.png": "\\sum_{amodn}\\chi(a)=0", + "181efa111aa2de68.png": "v_{(G;c)}(\\{1,2\\})=16", + "1820a76bf74d346a.png": "r>o+0.0005329", + "1824be82205660bc.png": "(F^{+})_{+}", + "1824bf129a9df19c.png": "d^{\\prime}([x],[y])=0", + "1825852d9280bafe.png": "\\lambda=c_{2}/(xT)", + "1826eaa40be24315.png": "2\\le a\\le\\frac{(b+1)}{2}", + "18306b7d06648ecf.png": "\\sum_{j=0}^{m}(\\begin{matrix}m\\\\ j\\end{matrix})^{2}=(\\begin{matrix}2m\\\\ m\\end{matrix})", + "183b66d1f21196a9.png": "a\\hat{x},a\\hat{y},a\\hat{z}", + "1842787e09fc2bd6.png": "=arctan\\frac{5}{12}", + "1843cf667f0957df.png": "c_{j,k}^{*}=\\frac{c_{j,k}}{\\lambda_{j}^{k}}\\Gamma(k)", + "184532bfb83d870d.png": "\\emptyset\\notin P", + "18456ede1d278fab.png": "(\\begin{matrix}0&1\\\\ -1&-1\\end{matrix})", + "184953a017f1135f.png": "-i\\hbar\\frac{\\partial}{\\partial x}", + "184c434f5bba5e37.png": "C\\propto(-\\tau)^{-\\alpha^{\\prime}}", + "1853bc9951b799f7.png": "(\\frac{ML}{T^{2}})", + "186820e072dc0b49.png": "d[x,x^{*}]", + "18695bbbde5d55b0.png": "\\partial_{\\mu}\\hat{A}^{\\mu}", + "1871635af970741d.png": "M_{ij}=\\int v_{i}v_{j}dx", + "1878233d43342e19.png": "\\hat{x}=i\\hbar\\frac{d}{dp}", + "187a4b2945de5752.png": "u(x)=\\frac{x^{1-\\gamma}}{1-\\gamma}", + "1884d2d214419a79.png": "b=\\prod_{p}p^{b_{p}}", + "188a81e8d66403d1.png": "\\frac{x^{\\prime2}}{25}+\\frac{y^{\\prime2}}{9}=1", + "189c574d64066c51.png": "F=Q(\\sqrt{m})", + "18a3e3d9553cd838.png": "\\frac{n!}{\\prod_{i=1}^{k}x_{i}!}", + "18a56404ad609e36.png": "\\int_{X}dxf(x)", + "18a5d32b3bd128fb.png": "[\\begin{matrix}0&-1\\\\ 1&0\\end{matrix}]", + "18aaf1b6d38aab61.png": "L_{*}x=b-Ux", + "18afc5a3fa4e2f53.png": "(\\begin{matrix}m+1\\\\ k\\end{matrix})", + "18b1f8205015212a.png": "G(\\tau=0^{-})", + "18b8f71c64a3b684.png": "\\tilde{C}_{4}", + "18c5f2db72be4070.png": "-na^{n}u[-n-1]", + "18c70560e351bfe5.png": "L(\\phi,\\partial_{\\mu}\\phi)", + "18ca60e6fe4703eb.png": "T^{\\prime}\\approx\\frac{1}{\\Delta f}", + "18ccf1a5a4b521f7.png": "\\tilde{t}_{i}", + "18cfb0bfa70ca2b1.png": "(\\begin{matrix}1&\\pi\\\\ \\pi&\\pi^{2}\\end{matrix})", + "18de6a5cc6bf57a8.png": "\\overline{12}_{24}+\\overline{21}_{24}=\\overline{9}_{24}", + "18dfaa1d791a5189.png": "\\gamma=lim_{\\epsilon\\rightarrow0}\\frac{lnf(\\epsilon)}{ln\\epsilon}", + "18e1c94ccc44e5c8.png": "[\\begin{matrix}k&0\\\\ 0&k\\end{matrix}]", + "18e57e8c1de4c166.png": "\\sum_{j=1}^{5}b_{ij}L_{j}=L_{i}", + "18e9deb20d9a6ee7.png": "\\int(sinx/x)dx", + "18ea550216583a53.png": "P_{4}=[\\begin{matrix}1&\\alpha\\\\ 0&1\\end{matrix}]", + "18eb4b547f31fa57.png": "[D,\\overline{S}]=\\frac{1}{2}\\overline{S}", + "18f05c6b96a263ea.png": "\\tilde{O}(\\theta dlog\\frac{1}{d})", + "18f3ded35b2c62f7.png": "b_{2}/b_{1}=m", + "18f767672bcdc419.png": "\\int d\\mu O_{i}Ge^{iS}", + "18fb5919e42386b8.png": "L(x,y;0)=f(x,y)", + "18fd3562ed91e72e.png": "C^{\\varphi_{\\mu}}", + "18ff1827ac2142c4.png": "2\\notin Y", + "18ff7ed313c7d593.png": "\\frac{d^{2}y}{d^{2}t}", + "1906737d6955bfc8.png": "(\\begin{matrix}4\\\\ 2\\end{matrix})=6", + "190d69ddea5f27aa.png": "U=(\\begin{matrix}0&1\\\\ 1&0\\end{matrix})", + "1912b72a8d9b769b.png": "F(\\nu)=\\frac{8\\pi h\\nu^{3}}{c^{3}}", + "191446c05e9b082d.png": "A\\notin D(u,p)", + "1917f8d2963d2447.png": "\\hat{V}(t)", + "191a6fb60c41a01c.png": "A\\overline{C}", + "1920cd5c6de7a079.png": "\\hat{R}", + "1922022d142cd7e4.png": "\\{\\begin{matrix}3\\\\ 7\\end{matrix}\\}", + "19227889b63c3d44.png": "\\int_{0}^{1}\\frac{dx}{\\sqrt{x}}", + "1922e7cf0ae0adda.png": "\\pi_{i+j}A", + "192c4d27a20060bf.png": "g^{\\prime}=gg^{\\prime\\prime}", + "192f7459aed9a061.png": "(\\begin{matrix}1\\\\ 0\\end{matrix})", + "19333586d3085d03.png": "W_{s}=\\int_{1}^{2}\\sigma_{s}dA", + "19337f8932483740.png": "f(0,\\overline{u})=g(\\overline{u})", + "1935d625c143daf0.png": "u=\\int u^{\\prime}dx", + "193820d5111704f7.png": "(\\begin{matrix}m-1\\\\ k-1\\end{matrix})/(\\begin{matrix}N\\\\ k\\end{matrix})", + "193cb8b307af102c.png": "\\frac{dJ}{dx}=\\frac{\\partial J}{\\partial x}-\\frac{\\partial R}{\\partial x}\\psi", + "1940022dda80bf9e.png": "\\int x\\cdot dx", + "1941b6da1d6ee171.png": "u=\\frac{\\partial\\psi}{\\partial y},v=-\\frac{\\partial\\psi}{\\partial x}", + "19461c16ecf3088f.png": "\\sqrt{n}\\in\\mathbb{Z}", + "194b20e277067b5e.png": "P_{n}=n(\\begin{matrix}n+1\\\\ 2\\end{matrix})-(\\begin{matrix}n+1\\\\ 3\\end{matrix})", + "194ba6e7fc8f6a4d.png": "V_{out-up}=-\\frac{V_{in}}{RC}t_{u}", + "194d7ee4248d6d55.png": "\\varphi\\wedge\\psi", + "19522c739403adb3.png": "L=\\frac{1}{k}L=I-\\frac{1}{k}A", + "1959b1966270d0e1.png": "R=\\frac{\\omega_{A}}{\\omega_{B}}=\\frac{N_{B}}{N_{A}}", + "195fe0839c03d193.png": "\\int_{2}^{5}x^{2}dx", + "19692f3e320f67ab.png": "\\tilde{\\theta}", + "196a6618630e7d11.png": "lnx", + "196b0640482692d3.png": "A\\notin D(u,p)", + "196b2952906ca316.png": "c\\notin A", + "196d0e2f85676696.png": "[\\begin{matrix}1&1\\\\ 0&1\\end{matrix}]", + "196d5a05202c9e85.png": "\\{\\begin{matrix}q+p\\\\ r\\end{matrix}\\}", + "196d787ed6ae5ccc.png": "-\\sqrt{x}", + "197275b8354415ae.png": "xT(3,1,x)=E_{1}(x)", + "197a3d7de5e27e26.png": "R(\\theta,d^{\\prime})0}w_{i}", + "1a6803e837c454bb.png": "\\int vdu", + "1a684ff5516ac019.png": "\\lfloor\\sqrt{n}\\rfloor", + "1a6dc5fc46eac658.png": "\\int_{0}^{T}PdX=nh", + "1a6f4c09f5ff2059.png": "\\prod_{x}f(x)", + "1a71fe1b4ba8c1e0.png": "\\frac{\\partial\\psi}{\\partial t}=P\\psi", + "1a754eb95960d03f.png": "(\\begin{matrix}c_{i}\\\\ i\\end{matrix})", + "1a7957b8bcc86404.png": "\\int d\\theta=0", + "1a7ad5cd43b9b255.png": "g_{j}=1\\pm\\frac{g_{S}-1}{2l+1}", + "1a7c1c6df95233c2.png": "f^{\\prime}(x)=-2xe^{-x^{2}}", + "1a7f1e26bf1db858.png": "E[\\hat{y}]", + "1a7f88c9ce105edf.png": "(\\begin{matrix}n+1\\\\ 3\\end{matrix})+1", + "1a7fcef8358d1928.png": "\\varphi", + "1a871943eb20d2aa.png": "\\sigma_{t}^{2}=p_{g}q_{g}f_{t}", + "1a8b0e254a98cc13.png": "[\\begin{matrix}0&1\\\\ 1&0\\end{matrix}]", + "1a904ad2e442c30c.png": "(\\eta,\\sigma)\\in P_{1}\\times\\Sigma", + "1a949a573f74816c.png": "s_{a}^{*}(t)\\cdot e^{j2\\pi f_{0}t}", + "1a971157c5b175c3.png": "\\prod_{k=1}^{n}k", + "1aa276d98aaeef0d.png": "[\\begin{matrix}1&1\\\\ 0&1\\end{matrix}]", + "1aa2fe8bce720cbc.png": "\\hat{i}", + "1aa7a486e438d6e3.png": "\\sqrt{\\pi}=\\pm\\sqrt{\\pi}", + "1ab75b69cc2e143c.png": "5\\le\\chi_{g}^{\\prime}(F_{4})\\le6", + "1ab9967d6033f648.png": "\\delta\\int ds=0", + "1abd29b4fba7ce08.png": "\\frac{-1+i\\sqrt{3}}{2}", + "1ac1012a345dc1e6.png": "B^{*}=\\frac{\\rho B}{2}=\\frac{\\rho C_{d}A}{2m}", + "1ac377532c76e11b.png": "\\tilde{g}=e^{2\\varphi}g", + "1ac656fd472c9eeb.png": "x_{1}(t)=A+w(t)", + "1ac85985118f8ea9.png": "AI=I_{w}-I_{o}", + "1ac95fd3a8cfc08d.png": "e^{-E_{a}/RT}", + "1ac9ea938032a159.png": "\\int_{E}\\varphi=\\infty", + "1acceea6d21fdfc8.png": "f^{\\prime}(x)=st(\\frac{\\Delta y}{\\Delta x})", + "1ad2fb499f0bda5b.png": "\\frac{d^{2}u}{dy^{2}}=\\frac{1}{\\mu}\\frac{dp}{dx}", + "1ad53002433c7061.png": "\\int wds", + "1ad680bf52e6f56b.png": "\\tilde{C}(u)=W(u)", + "1ad7abb5b926605a.png": "[\\begin{matrix}0&0\\\\ 0&1\\end{matrix}]", + "1ae6948c50ffbf03.png": "|\\Psi\\rangle=a|\\psi\\rangle+b|\\phi\\rangle", + "1afdc2233aeb3192.png": "x=y=\\frac{-i}{\\sqrt{2}}", + "1b0276b8bb43f48e.png": "\\int d\\mu O_{i}Ge^{iS}", + "1b028886c03bc8ee.png": "2x=O(x)", + "1b0995d4c63546a5.png": "I(\\hat{x},u)", + "1b18e1cf3e9066be.png": "V(+\\infty)", + "1b1b72e69eb94df2.png": "01(01)^{*}\\cup100^{*}", + "1b2a82e0a16aeef7.png": "\\frac{dV}{dt}=Q_{0}", + "1b2dcc2a22d37023.png": "C<D_{1}", + "1b45f43569ff66c8.png": "s=\\int\\frac{dt}{r(t)}", + "1b46fd2a6a240778.png": "(\\begin{matrix}n+2\\\\ 2\\end{matrix})-2n-1", + "1b4ab275915ef4e9.png": "m-2r<-1", + "1b4b6d541bea17a6.png": "|\\langle q|p\\rangle|^{2}=\\frac{1}{2\\pi\\hbar}", + "1b4d97c532af40fe.png": "k_{e}=\\frac{ln2}{t_{1/2}}", + "1b4db87705de356f.png": "\\frac{-1+i\\sqrt{3}}{2}", + "1b4ebd96ec876893.png": "\\frac{d^{2}u}{dt^{2}}=\\frac{\\Omega^{2}}{4}\\frac{d^{2}u}{d\\xi^{2}}(2)", + "1b5cbe55ac5b569c.png": "\\alpha=\\gamma^{2}\\frac{v^{2}}{r}", + "1b65f62d4f0d2459.png": "I(Y_{1};Y_{2};Y_{3})", + "1b67fb4bf771434e.png": "1-e^{-e^{2.6-0.00024K}}", + "1b70407e342e87e0.png": "p+B^{2}/2\\mu_{0}", + "1b7b027098e9e980.png": "K=\\int|\\kappa|ds", + "1b7b8fb8d3255270.png": "[\\begin{matrix}-1\\\\ 1\\end{matrix}]", + "1b7e750e266092ef.png": "y(x)=\\int g(x)dx", + "1b7fbf1de7bcedf8.png": "h_{g;k}", + "1b832ce565c44fd8.png": "A=\\frac{1+2\\frac{M}{C}}{1+2\\frac{N}{C}}", + "1b85824ad62260ce.png": "\\sqrt{4}", + "1b85ceb13a9d71dd.png": "\\int1d\\theta=0", + "1b87db40827fc205.png": "W=\\int Fdx", + "1b8a37737f1b564e.png": "M-\\overline{V}", + "1b8f7494b48c24da.png": "2^{m-n+c}", + "1b9a2b5d75619b71.png": "(X_{L}-T)^{T}R^{T}", + "1b9a97a761324cff.png": "\\hat{H}_{I}=\\sum_{i}\\hat{S}_{i}\\otimes\\hat{B}_{i}", + "1b9d26ab5792b09a.png": "(\\begin{matrix}n\\\\ n\\end{matrix})", + "1ba48dba30bbccf1.png": "2^{R}", + "1ba49b901eeb48d4.png": "[\\begin{matrix}a&b\\\\ c&d\\\\ \\end{matrix}]", + "1ba5057633f5f61d.png": "\\hat{H}_{0}^{\\prime}=\\beta p_{0}", + "1bad7517f375276a.png": "(\\begin{matrix}0&1\\\\ -1&0\\end{matrix})", + "1bb6f6261f72952b.png": "[0.1,1),[0.01,0.1)", + "1bb8daea38061621.png": "\\sqrt{S}", + "1bbf338a36f2b57f.png": "dF(u;\\cdot):X\\rightarrow Y", + "1bc0e8c2b3a96c90.png": "\\tilde{l}", + "1bc3a632b73cbf4e.png": "\\xi,\\mu_{\\xi}=\\mu_{\\xi,\\xi}", + "1bc402c323d756f1.png": "C_{pq}^{-}", + "1bc9193d4917752f.png": "S\\leftarrow S-\\{s^{\\prime}\\}", + "1bda2eec753468c8.png": "A", + "1bdc0da5c710fc99.png": "\\langle Ff,\\varphi\\rangle:=\\langle f,F\\varphi\\rangle", + "1bdcbd642cf889fd.png": "(\\begin{matrix}Z\\\\ I\\end{matrix})", + "1be117d80d874fac.png": "\\hat{v}(x)", + "1be427facf17a78c.png": "n\\ge\\frac{1+\\sqrt{4m}}{2}", + "1bea5e1efc8bcc18.png": "\\frac{\\partial Y}{\\partial K}", + "1bed6ad2fa106543.png": "\\int y^{2}dv", + "1bf476ba8f150b41.png": "\\int_{X}p(x)dx=1", + "1bf854fb9a74f395.png": "\\psi(R_{1}...R_{n})", + "1bfb2d372f9e0135.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "1bff30c0ed931002.png": "f_{ij}:V_{i}\\rightarrow V_{j}", + "1bfffe4a9939508c.png": "Q_{A}=10^{R_{A}/400}", + "1c077632416cb792.png": "[\\begin{matrix}a&r\\\\ d&s\\end{matrix}]", + "1c0ded184596da76.png": "t\\{\\begin{matrix}p\\\\ 2\\end{matrix}\\}", + "1c0f3faaf13a5dfc.png": "{(\\nu^{\\phi})}^{\\alpha}", + "1c0fe077af4ce0e6.png": "\\Gamma^{[k-1]}", + "1c117edef5b8bb93.png": "\\int_{-\\infty}^{a}", + "1c1249478aef8259.png": "[M]\\in N_{n}", + "1c18a8a465a37dba.png": "p(x)=\\prod_{j}(1-xX_{j})", + "1c1d33591cb30bb9.png": "v=(z^{\\prime}|x^{\\prime})", + "1c23516f30ff73d9.png": "\\frac{(O_{1}-\\mu)^{2}}{\\sigma^{2}}", + "1c31f6789e5107e9.png": "\\underline{S}_{\\lambda}", + "1c3b7dc45f4f2dd7.png": "AB=(\\begin{matrix}0&0\\\\ 0&1\\end{matrix})", + "1c3dfc565e9181cd.png": "(\\begin{matrix}n\\\\ n\\end{matrix})", + "1c3f154318972b5a.png": "\\overline{H}(y^{n}|x^{n})", + "1c400bab4d96598b.png": "b_{l}^{\\mu}", + "1c420121bb00b7c0.png": "K^{ab}[q]", + "1c450febb4503fe4.png": "F_{xx}(\\Delta x)^{2}", + "1c45bd337ebd7f03.png": "\\int dqE(q)=I", + "1c47d0e25880e204.png": "\\hat{T}_{\\pm2}^{(2)}=\\hat{a}_{\\pm1}\\hat{b}_{\\pm1}", + "1c491d7f184ed5d8.png": "\\sqrt{\\Pi}", + "1c4f532b00261e18.png": "(\\begin{matrix}p+q+3\\\\ 2\\end{matrix})", + "1c4fedd272805205.png": "O(\\sqrt{logy})", + "1c56d93ce39cd812.png": "{i^{y}}^{2}", + "1c59c9b9100ddbc1.png": "(-b+\\sqrt{b^{2}-4c})/2", + "1c5a1b90e7347cf5.png": "R[t]\\rightarrow S,f\\mapsto\\overline{f}", + "1c5b71ecd326ac62.png": "R^{+}\\subseteq G", + "1c61b04ada717167.png": "k[\\overline{X}]", + "1c6674a1b69941ea.png": "\\frac{d}{dt}log_{e}t=\\frac{1}{t}", + "1c74f9ae3636186d.png": "\\tilde{t}=\\sqrt{\\frac{g}{h}}t", + "1c7689655d9909b3.png": "\\frac{\\partial x}{\\partial y}", + "1c772c4352d5cc56.png": "T_{n}n!=n^{n-2}n!", + "1c7832b71d03a873.png": "N\\backslash S\\notin W", + "1c7aa62c51f6e935.png": "x\\mapsto xcos(2\\pi x)+1", + "1c83b5e1fdde89e7.png": "-\\frac{ln2}{4}\\gamma_{2}", + "1cfca0d15fdf7bff.png": "\\frac{\\partial f}{\\partial z}", + "1cff2c2625efec52.png": "\\frac{dx}{du}du", + "1d02f470a9f066a0.png": "s\\{\\begin{matrix}4\\\\ 4\\end{matrix}\\}", + "1d0c702dbe188920.png": "\\frac{dy}{dx}=-\\frac{1}{1+x^{2}}", + "1d0cd436f925acbf.png": "x_{i}\\notin D", + "1d0eac074508233b.png": "\\tilde{D}_{7}", + "1d137e60ae86c48b.png": "\\Delta\\lambda=\\lambda^{2}\\frac{\\delta D}{2D\\Delta D}", + "1d13bb8e37fc8468.png": "\\Rightarrow x=e^{-3W(\\frac{-1}{3})}", + "1d1dc6af7956b8a5.png": "p(\\cdot;\\theta+\\Delta)", + "1d20c07ad9fb41f9.png": "\\hat{\\phi}=Y_{D}\\circ F", + "1d2364435ba9d751.png": "C[x,y]/(x,y)\\cong C", + "1d24e2b0cac252d1.png": "|2l|=\\frac{2L^{2}}{mk}", + "1d250509eac83f36.png": "\\lambda\\langle f,f\\rangle=\\langle f,T_{K}f\\rangle", + "1d2892f417c135b1.png": "\\int_{0}^{1}\\phi(p)dp=1", + "1d28f6c39540db5e.png": "\\frac{\\partial Y}{\\partial\\beta}=Y_{\\beta}", + "1d2cc9435edc2db6.png": "ln(10^{10}A_{s})", + "1d2f08244f8f9969.png": "2.4(log_{2}n+m)", + "1d300b5f4d17d802.png": "x\\notin P", + "1d35593d9e27d913.png": "C=g^{r}modp", + "1d44938ba8e7fc4e.png": "\\frac{\\partial}{\\partial c}P_{c}^{n}(c)", + "1d45f56e0fc47332.png": "\\tilde{A}_{2}", + "1d49a02ca85aac1b.png": "\\sqrt{\\mu}", + "1d4bad3ca9db54e5.png": "f(\\underline{m})=0", + "1d53cf484aee925b.png": "x_{i}(i=1,2,...,n)", + "1d56635e15235574.png": "Sq_{p}^{2k(p-1)}=P^{k}", + "1d5a4914c603d1df.png": "v(t)=I\\frac{dl(t)}{dt}", + "1d5e3dbf10beabef.png": "z\\rightarrow-z^{5}+z_{0}", + "1d62eef7b83160fe.png": "(\\begin{matrix}n\\\\ 5\\end{matrix})", + "1d6f5d64dc2f82a4.png": "\\hat{V}(t)", + "1d76cec165ff2928.png": "\\underline{a}_{1},...,\\underline{a}_{r}", + "1d77939a755766c0.png": "c(k)=(\\begin{matrix}2k\\\\ k\\end{matrix})", + "1d7a42438148d7e4.png": "\\tilde{A}_{8}", + "1d7beae71ae145a6.png": "\\tilde{x}", + "1d7d1b5c78513151.png": "(n,k,2t+1)", + "1d7e1e173179044a.png": "|\\frac{y_{1}+y_{2}}{2}-x|^{2}\\ge\\delta^{2}", + "1d894f5589c22120.png": "b=\\prod_{p}p^{b_{p}}", + "1d89ffa52918b5f1.png": "M_{31}(R)", + "1d8c17ad7238add6.png": "P=-\\frac{\\partial F}{\\partial V}", + "1d9133fdc5064f1c.png": "\\int(u-v)dx", + "1d93e68049208c16.png": "(\\begin{matrix}n\\\\ t\\end{matrix})", + "1d97a8c258971853.png": "{k^{l}}^{f}", + "1d9ad3371d695bd7.png": "\\frac{dM}{dx}=V", + "1da1507517a82098.png": "\\prod_{i=0}^{k-1}(x-z_{i})", + "1da1a993126caad0.png": "B^{\\prime}\\in(\\begin{matrix}C\\\\ B\\end{matrix})", + "1da6de26145d0c56.png": "Hom_{D}(X,f(-))", + "1da9b5c462b9c411.png": "\\frac{\\partial n}{\\partial t}=-\\nabla\\cdot J+W", + "1dacfb3e3fdccdf1.png": "\\int\\frac{1}{x}dx", + "1db0763fdf055dba.png": "D=\\mathbb{Z}[\\sqrt{3}]", + "1dbbba37377b7438.png": "\\sum_{k=1}^{n}|b_{2k+1}|^{2}\\le n", + "1dbce9a72f82b246.png": "M=\\frac{m}{\\sqrt{1-v^{2}/c^{2}}}", + "1dc510444985bf50.png": "C_{p}=\\frac{(P_{m}-P_{s})L}{AE}", + "1dc55c24e13c3afa.png": "S=(\\begin{matrix}0&1\\\\ 1&0\\end{matrix})", + "1dc840dcc8c7a3d9.png": "G=\\prod_{i\\in I}H_{i}", + "1dcc3620178646d9.png": "[\\begin{matrix}I&C\\end{matrix}]X=b", + "1dce664f54b134c1.png": "262,144=2^{18}", + "1ddd85d5981a60f0.png": "x^{\\prime\\prime}x^{\\prime}=z\\frac{x^{\\prime}}{x^{2}}", + "1de41330835241a3.png": "I=\\frac{|E|^{2}}{2\\eta}", + "1de89929e22e7e74.png": "-\\rho_{\\infty}V_{\\infty}\\Gamma", + "1dea26ed09f4934b.png": "h_{n}=-\\frac{f(x_{n})}{f^{\\prime}(x_{n})}", + "1df251dcd35c645b.png": "\\int_{C}=0", + "1df5ce1f14d5150d.png": "g_{0}=1_{\\Omega^{\\prime}\\\\ U^{\\prime}}g", + "1df7c3e5f4fee82e.png": "(\\begin{matrix}13\\\\ 10\\end{matrix})=(\\begin{matrix}13\\\\ 3\\end{matrix})=286", + "1df943f38c1682a5.png": "\\sum F_{x}=0=R_{Ax}", + "1dfdce9a2add3b3a.png": "\\overline{w}_{g}^{j}=0", + "1dff01f3c718f34c.png": "\\hat{C}_{1}", + "1e00a9133d65f507.png": "F[X,Y]/(X^{2}-Y^{2})", + "1e01fc123f4ca1e9.png": "|\\overline{VU}|", + "1e0516bdaea44398.png": "[\\begin{matrix}2&p\\\\ q&2\\end{matrix}]", + "1e06827583031938.png": "(g(z))^{3}=(h(z))^{3}", + "1e09955500a7b3e1.png": "H\\sim\\hat{\\Sigma}^{1/2}", + "1e0df63c762e6f6b.png": "\\tilde{C}_{5}", + "1e0e52ef06a9dd65.png": "p_{(t_{1})}", + "1e109b0b95ec14f9.png": "\\int f(x)d\\alpha(x)", + "1e111c3b31cd0a63.png": "\\tilde{g}", + "1e17b61b5c2bbc7d.png": "I=\\int xcos(x)dx", + "1e1f339226fb765e.png": "\\frac{d}{dx}\\underline{x}^{-k}=-k\\underline{x}^{-k-1}", + "1e2226b1bbb4681c.png": "-N_{c}^{2}-1", + "1e249a92b7ad395a.png": "\\hat{\\varphi}=(-sin\\varphi,cos\\varphi)", + "1e274bf5fe1258b1.png": "\\tilde{\\phi}", + "1e2cc8a036409423.png": "\\frac{dx}{dt}=3", + "1e32f318317cbe3f.png": "0.5<\\frac{a}{L}<2", + "1e3b76097487f169.png": "\\int\\sqrt{1+1/x^{2}}dx", + "1e3f0aaf81ce6d8e.png": "\\underline{AB}", + "1e46bca4d198d879.png": "[[x,y],z]", + "1e484341fd071d47.png": "T>S(\\mu(0))/h", + "1e4bc61e0c0fd522.png": "\\int xcos(u)du", + "1e4dce6838890e1c.png": "F=\\nabla(m_{2}\\cdot B_{1})", + "1e51e90acf3e6821.png": "z(n;t)=O(n^{2-1/t})", + "1e541bacbdbf4f92.png": "\\frac{dx}{dt}=rx(1-x)-px", + "1e554f71b8345b07.png": "S=\\int Ldt", + "1e5580e005a700ee.png": "\\{\\begin{matrix}3\\\\ 5\\end{matrix}\\}", + "1e561a391b33f0a6.png": "(\\frac{x_{i}-\\overline{x}}{s_{x}})", + "1e5b2dccf5a4f659.png": "\\tilde{C}_{6}", + "1e5f4e24a4fe6791.png": "S=\\int_{M}BF", + "1e5f5bd7e565d154.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=0", + "1e664e9a2d912f6e.png": "\\frac{1}{2}v^{2}=U(x)", + "1e67db87c3441dd4.png": "\\tilde{C}_{n}", + "1e69506998390971.png": "N_{*}=\\sum_{n\\ge0}N_{n}", + "1e6da9f634242fae.png": "a=\\frac{3}{\\sqrt{3}}R=\\sqrt{3}R", + "1e6f70139e47c728.png": "E_{W}=\\frac{1}{2}w^{T}w", + "1e70f39fee684903.png": "\\sqrt{2+\\sqrt{2}}", + "1e786c73b2ea75d4.png": "(\\begin{matrix}2&0\\\\ 0&-e^{y}\\end{matrix})", + "1e81d51196d0d76e.png": "t=\\int\\frac{dy}{iy+F}", + "1e8829f6e9c1eb98.png": "F=S\\int udt", + "1e9079ee0eacf9f3.png": "K_{i}\\varphi\\Rightarrow K_{i}K_{i}\\varphi", + "1e90aaef47b0f48d.png": "A_{t}+F_{t}=0", + "1e9326ea9fd52e21.png": "jk=i\\sqrt{-1}", + "1e9444669f05099f.png": "J>1/2", + "1e98cc38723e1013.png": "\\int_{-3}^{4}f(x)dx", + "1ea0e694de4ea4d6.png": "[\\begin{matrix}-2&-1\\\\ -1&2\\end{matrix}]", + "1ea3db1692f301b4.png": "2^{-D^{\\epsilon}(\\rho||\\sigma)}\\ge\\frac{\\epsilon-\\delta}{\\epsilon}", + "1ea8759f12908703.png": "\\mathbb{J}", + "1eaa4ba9975f11cb.png": "F(x)=\\int f(x)dx", + "1eb36ada3f288f8e.png": "\\frac{d\\psi}{dt}", + "1ebf7235ae5b2531.png": "||C_{h}f||^{2}\\le||f||^{2}", + "1ec9d49cd9012807.png": "X\\leftarrow Y,Y\\\\ X", + "1eca371150af9010.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "1ecbbb1e70205bf2.png": "(\\hat{\\theta}-\\theta_{0})/SE(\\hat{\\theta})", + "1ed3a09842ed435f.png": "\\sigma:\\tilde{X}\\rightarrow X", + "1ed3b07cc31f90f0.png": "\\sqrt{\\delta}", + "1ed9d239d5e6a946.png": "\\alpha(z)\\approx(\\theta-\\beta)\\frac{D_{d}}{D_{ds}}", + "1edbfcc6d509ce84.png": "\\int_{1}^{\\infty}x^{-x}dx", + "1edf70c8be52a297.png": "\\sqrt{\\eta}", + "1ee099054c5eabbe.png": "\\frac{\\partial u_{i}}{\\partial x_{i}}=0", + "1eef0579fddee4e7.png": "2(\\begin{matrix}n\\\\ k\\end{matrix})", + "1ef5ad448ce97fae.png": "\\sqrt{\\Delta}", + "1ef9558a1aae7354.png": "|++\\rangle", + "1f034f536e1b7c44.png": "D_{q}f(x)", + "1f109591a14ea4e2.png": "\\frac{\\partial^{2}C}{\\partial S^{2}}", + "1f131144d951202c.png": "aR", + "1f1ce769dc98fc54.png": "\\Delta K=\\Delta\\sigma Y\\sqrt{\\pi a}", + "1f1e56574ef341eb.png": "\\{A_{i}\\}_{i\\in Z^{+}}", + "1f27abfc1244220b.png": "I^{0,q}\\rightarrow I^{1,q}\\rightarrow\\cdot\\cdot\\cdot", + "1f27c7c8b8a9cbea.png": "\\sum_{k=1}^{\\infty}\\frac{F_{n}}{5^{n}}", + "1f28f41fddd6988a.png": "\\langle\\rho=\\rho_{2},Z_{2}\\rangle", + "1f299630c9ffd9a4.png": "\\psi_{-}^{(0)}", + "1f2bbe59f4ac6c14.png": "\\frac{M}{p_{i}}\\ne O", + "1f309723a0092f61.png": "\\int-2r^{2}sin(u)du", + "1f31ab00b2f308a5.png": "v_{1}=[\\begin{matrix}1\\\\ 1\\\\ 0\\\\ 1\\end{matrix}]", + "1f3f623e85a4645e.png": "\\Sigma_{\\varphi}^{\\varphi}", + "1f4ca6b32c243671.png": "N_{0}-N_{1}+N_{2}", + "1f4ef3de089d242c.png": "\\tilde{C}_{4}", + "1f4f3b261d95a1c5.png": "((\\begin{matrix}2n-2\\\\ n-1\\end{matrix})/n!)^{2}", + "1f4f55c3c6152971.png": "\\frac{a}{2}+\\frac{a}{6}(\\sqrt{2}-1)", + "1f50fe67e55d1630.png": "1-\\int_{t-r}^{t}E(t^{\\prime})dt^{\\prime}", + "1f53908743c3d987.png": "f(D^{\\prime},r,w^{\\prime})", + "1f5464d8e15b0c96.png": "\\int cosxdx=sinx+C", + "1f552198e25d4ed0.png": "\\hat{x}_{1}", + "1f5710206652b5df.png": "\\int_{a}^{b}\\pi f(x)^{2}dx", + "1f58949e935b833d.png": "\\omega_{n}=\\frac{\\pi^{2}\\hbar n^{2}}{8L^{2}m}", + "1f59c2011265d3a2.png": "\\sqrt{d}", + "1f610a177b5ffdec.png": "(\\begin{matrix}n\\\\ 2\\end{matrix})p", + "1f6225ccbb01356c.png": "-\\sqrt{\\frac{9}{20}}", + "1f6286ba341db3ac.png": "s\\{\\begin{matrix}4\\\\ 3\\end{matrix}\\}", + "1f6ef5b6a327a30e.png": "\\overline{z}^{n}", + "1f73b3cfe7671b1c.png": "\\hat{H}^{n}(G,A)=H^{n}(G,A)", + "1f7df9aa1591a374.png": "cf(\\prod A/D)", + "1f807f5f72825cb2.png": "\\prod_{x}f(x)=F(x)", + "1f8130cbe5d4c366.png": "s(P,E_{i})=\\prod_{k}s(P,E_{ik})", + "1f8aac389eaa3216.png": "i_{b}=-E[\\frac{\\partial U}{\\partial\\beta}]", + "1f8ab5ba92377b4b.png": "\\frac{\\partial\\Phi}{\\partial t}=\\frac{1}{i\\hbar}H\\Phi", + "1f8c37dbe5e95f57.png": "\\tilde{O}(log^{4}q)", + "1f943cb745e6f97b.png": "\\underline{x}\\in\\mathbb{R}^{n}", + "1f98dfc4b3e398e2.png": "(\\sqrt[5]{\\frac{p_{f}}{p_{i}}}-1)\\times100", + "1f98ff7398bfae63.png": "j\\ne i,i+1", + "1fa4dd65a509f284.png": "r=\\{x|\\{x\\}\\notin u\\}", + "1fa695aa41fe3286.png": "I_{1},I_{2},...,I_{n}\\subset C_{1}", + "1fa97661cadff8b8.png": "\\Psi=\\frac{1}{\\sqrt{2}}(\\phi_{1}-\\phi_{2})", + "1fabc3880bd6bfda.png": "t\\sqrt{m}", + "1faf104dd53b1c5c.png": "P(G)(k)", + "1fba163e9a7d94f2.png": "V=(I-C)^{-1}Dp", + "1fc7d70b85025c2f.png": "x\\mapsto\\prod_{i=1}^{n}w_{x}(i)", + "1fcd74cc2ea36bb2.png": "0<\\mu<\\frac{1}{\\sigma^{2}}", + "1fd26f9f4980122f.png": "\\frac{x(x+1)}{(1-x)^{3}}", + "1fd751bc0260fed4.png": "(\\begin{matrix}7\\\\ 3\\end{matrix})=35", + "1fd78525212a2db7.png": "\\mathbb{W}", + "1fd8b71739a2d934.png": "minmax_{i,j}c_{ij}x_{ij}", + "1fdfaabc8571fd5f.png": "\\underline{X}:U\\rightarrow\\mathbb{R}^{n}", + "1fe1970b36fae519.png": "S=\\int_{0}^{T}E[s(t)^{2}]dt", + "1fe4ab1c592f30b9.png": "\\frac{dx}{dt}=r\\pm x^{2}", + "1fe656f1e565166f.png": "\\zeta_{L}(s)\\}", + "1fe962b8a172f73d.png": "\\lambda=\\int_{0}^{\\infty}\\frac{\\rho(t)}{t+2}dt", + "1feb7480c455f1c2.png": "d", + "1fed0d683228c4c4.png": "\\overline{k}", + "1ffa715add24dace.png": "\\int_{X}||f||_{B}d\\mu<\\infty", + "200313916ee75f17.png": "p_{k}(d\\sigma_{k}|\\eta)", + "2005aee902f722a9.png": "\\underline{P}\\equiv(P^{+},\\vec{P}_{\\perp})", + "2009a702703787d0.png": "\\hat{\\Sigma}_{/j,/j}", + "200f687f90ce52e0.png": "p_{1}=p(x_{0}+\\Delta x)", + "20126efc56e564fc.png": "a^{n}x+\\frac{a^{n}-1}{a-1}b", + "201623e5518da3c0.png": "\\int_{\\gamma}f(z)dz=0", + "2016d43b8e32f130.png": "\\int e^{ix}", + "201790e4ee4f5a70.png": "(\\begin{matrix}x\\\\ n\\end{matrix})", + "20184e26fcef2805.png": "\\bigcup_{f\\in F}f(U)", + "201b1eb1424206e2.png": "-2\\int Edl", + "201d7e674451c737.png": "(\\begin{matrix}R^{\\times}&R\\\\ 0&1\\end{matrix})", + "20206331ab8b249a.png": "\\frac{dy}{dt}", + "202309b51a73542e.png": "GF(q)^{n}", + "20290ac69b2f7433.png": "2\\sqrt{3}(1+4\\sqrt{3})", + "202bcf6201dbadf9.png": "(\\begin{matrix}N\\\\ 2\\end{matrix})", + "202fc5c1c8062a06.png": "\\frac{6}{(\\begin{matrix}49\\\\ 6\\end{matrix})}", + "20313860828e0bd4.png": "\\oint_{C}\\frac{e^{z}}{z^{5}}dz", + "203a53756db826ae.png": "\\sigma\\sqrt{r_{t}}", + "203be7ad080ba6f5.png": "S=\\int ds", + "203faf0a8ff6369b.png": "[\\begin{matrix}x&y\\\\ z&v\\end{matrix}]", + "204301f462607ab2.png": "t_{c}=\\sqrt{\\frac{a}{c}}", + "20463f22bb8ac5c2.png": "lim_{n\\rightarrow\\infty}\\int_{0}^{\\infty}e^{-e^{x^{n}}}", + "2048f7eb48aba192.png": "x\\in[a,b]\\cap N_{\\delta}(c)", + "204ddcbe47e1a886.png": "\\frac{dv}{dy}", + "2051278a43332079.png": "\\Sigma|a_{n}|^{2}=\\Sigma|b_{n}|^{2}", + "2051782314003a2d.png": "lim_{t\\rightarrow\\infty}\\overline{x}(t)", + "205ab5e04f43b5d5.png": "V=\\sqrt{P\\bullet R}", + "205bf152221eea07.png": "\\int Mds\\sqrt{v}", + "2064f4cffca4defd.png": "\\frac{|\\theta-\\mu|}{\\sigma}\\le\\sqrt{3}", + "2066709942424a21.png": "\\sum_{x\\in F}x^{i}=0", + "206e823d345694f2.png": "\\sqrt{0}", + "206fe707dc33cd8e.png": "\\frac{d\\phi}{dt}", + "2082b078adbe74c2.png": "\\prod_{i=1}^{m}Q(\\beta_{i}x)", + "2085e0c6a764141b.png": "(\\begin{matrix}m-1\\\\ k-1\\end{matrix})/(\\begin{matrix}N\\\\ k\\end{matrix})", + "208cb3c4fc57b36e.png": "M[\\begin{matrix}a_{1}\\\\ \\vdots\\\\ a_{n}\\end{matrix}]", + "209797e5b601822f.png": "H^{1}(X,O_{X})", + "20a4299506c008f6.png": "O(id^{2}+d^{3})", + "20a45ed5c271f540.png": "d^{2}\\le\\frac{\\pi}{4}area(S^{2})", + "20a80cdab09abc3e.png": "PG(2d+1,q)", + "20acbc10e5916491.png": "cend_{n}", + "20b5680e6b04b7d3.png": "\\mathbb{F}", + "20b5eb5a8a91ebd1.png": "s_{j}=[s_{j-1},x]", + "20b6113a44f3fd68.png": "{(D^{g})}^{3}", + "20ba95ace9fd8623.png": "\\Theta_{(\\varphi_{\\lambda})}", + "20be3ecd67cf592b.png": "\\Delta E=\\frac{(y_{2}-y_{1})^{3}}{4y_{1}y_{2}}", + "20c0ca25fcb18436.png": "(\\begin{matrix}\\alpha&\\beta\\\\ \\overline{\\beta}&\\overline{\\alpha}\\end{matrix})", + "20c75ed1326de4ff.png": "F^{(\\begin{matrix}l+d\\\\ d\\end{matrix})}\\rightarrow F^{|F|^{l}}", + "20ca6ba45fef7799.png": "|2\\Theta_{C}|", + "20cb9066436019bb.png": "\\hat{h}", + "20cf543460852244.png": "h^{\\prime}(x)=-\\frac{f^{\\prime}(x)}{(f(x))^{2}}", + "20d1a8568f8fb259.png": "r\\{\\begin{matrix}5\\\\ 3\\end{matrix}\\}", + "20de6fb9072e7670.png": "\\{i\\}=K_{i}\\prod_{j=1}^{N_{B}}\\{j\\}^{\\nu_{i,j}}", + "20e1d0cfe3355e6c.png": "(x,r)=(0,r_{o})", + "20e67af4b13165a9.png": "(\\begin{matrix}a&b\\\\ b&c\\end{matrix})", + "20e91117e854b8b6.png": "J_{1}(x)=x/2\\sqrt{2}", + "20f059e68be5a456.png": "M^{\\prime}:=M+D", + "20f4f3dafdd83745.png": "xa^{m}b^{n}yc^{m}d^{n}z", + "20f50e29f5e5d535.png": "(\\begin{matrix}0&1\\\\ -1&0\\end{matrix})", + "20f97191a11c731d.png": "\\|\\begin{matrix}x&y\\\\ z&v\\end{matrix}\\|", + "20fbea26fd24f5c7.png": "\\frac{dx}{dt}=r\\pm x^{2}", + "20fcadb5c1b3a3dc.png": "(2)_{t}^{2}(3)_{t}\\cdot(2)_{t}^{2}", + "2107ccebb2e9dd1c.png": "\\alpha s_{x}+\\beta s_{y}+\\gamma=0", + "210a5bfd9f1b09bc.png": "\\langle S_{i}S_{j}\\rangle=b^{2}\\delta_{ij}", + "210ea2c3e48139c7.png": "\\tilde{V}", + "210f2e97c9ab4999.png": "k", + "211103f70c689d69.png": "O_{i,j}=E_{i,j}\\forall i,j", + "211135cce13c1084.png": "[\\begin{matrix}3&0\\\\ 0&-2\\end{matrix}]", + "2116498deffaac64.png": "[\\begin{matrix}3&1\\\\ 0&3\\end{matrix}]", + "21180c50ce721313.png": "n^{*}=(-1)^{(n^{\\prime}-1)/2}n", + "21189f70a7fc47b9.png": "x^{p^{2}},y^{p}\\in G^{\\prime}", + "211951d6035d25be.png": "p_{i}\\in Ker(A-\\lambda_{i}I)", + "21198efea60649f2.png": "s\\{\\begin{matrix}2\\\\ 8\\end{matrix}\\}", + "211a64a238a976c9.png": "b(1-a-d)=0", + "211d7a94a9a6114d.png": "W_{i}^{*}=\\frac{Rgq_{bi}}{F_{i}u*^{3}}", + "212c10b6c2ac8d6f.png": "exp_{2}^{i-2}(n^{O(1)}))^{\\Sigma_{j}^{P}}", + "212d23ae227b38a8.png": "f(t)=-\\frac{\\partial S(t)}{\\partial t}", + "2130cfeb8cb4e331.png": "(3)\\frac{D}{P}=\\frac{ROE-g}{PB}", + "2131add6f5229488.png": "hu", + "2135606df71855c6.png": "x=\\frac{1}{|A|}adj(A)b", + "2135fc800fdca898.png": "(a^{b})^{c}\\ne a^{bc}", + "21398df609dd0259.png": "|\\Psi\\rangle=e^{T}|\\Phi_{0}\\rangle", + "213ed16d868be5a4.png": "1_{c}()", + "2143e6a82e73ac9f.png": "\\epsilon_{t-1}^{-}=0", + "2146ebcaa223bc11.png": "\\Delta_{call/put}(K,\\sigma)", + "214a929719493fba.png": "\\dot{a_{2}}=-2\\alpha", + "214c7d076630941b.png": "G*\\underline{A}", + "214cab2a9ac9cf39.png": "(\\begin{matrix}L\\\\ d\\end{matrix})", + "214df4fbba8d3731.png": "{\\xi^{\\delta}}^{5}", + "215130cf8b178dc9.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=\\prod_{p}p^{b(p,n,k)}", + "21587fe55f5a7a02.png": "\\hat{t}_{g}(t,\\omega)", + "216162cc1afd8be4.png": "\\frac{1}{2}(z+1)", + "2161f47312a6e664.png": "m_{H}=\\sigma_{0}\\sqrt{2\\lambda}", + "21644988ae33f063.png": "\\varphi_{i,j}(a^{\\prime})=b", + "216ae1a060f8bfb7.png": "-\\infty\\le max(1,1)", + "216b22a7c919e367.png": "\\int_{S}H^{2}dA", + "216ff7a6fa6f22da.png": "-g^{(k)}", + "2175ec2b80c29f1f.png": "[\\begin{matrix}1&3&2\\\\ 4&1&0\\end{matrix}]", + "217ad8478a9d1dac.png": "(A-B)\\sqrt{g}=1.", + "217ed7599bd2c8b2.png": "\\frac{\\partial}{\\partial T}\\epsilon", + "217f00956f5e50c1.png": "\\hat{t}_{i}", + "21829805972ade4b.png": "\\int1d\\theta=0", + "218421df4ee4aa8a.png": "\\tilde{u}_{i}", + "218846bfccdfa167.png": "|x|^{n}\\cdot exp(-\\lambda|x|^{\\beta})", + "218f7d8d6df8b299.png": "L_{X}=\\Lambda(T_{B})\\rho_{B}^{2}", + "2198b3dfab919816.png": "[q^{2},klogq]", + "219d267021dc2593.png": "x^{+}=\\frac{t+x}{\\sqrt{2}}", + "219df041ccbe801f.png": "\\frac{40}{3}\\times\\frac{201}{16}", + "21a5051c6a7cba85.png": "\\Psi(z_{u_{1}}...z_{u_{i}})", + "21a90582eef0fc99.png": "x\\mapsto\\prod_{i=1}^{n}w_{x}(i)", + "21aadeea51c101c4.png": "\\phi^{X_{t}}(z)", + "21ae2cbff37302ec.png": "M", + "21b04fb612fa0d9a.png": "dim\\hat{R}=dimR", + "21b0a17d30051b68.png": "\\tilde{A}_{n}", + "21b2300f1ebfb6d5.png": "\\overline{\\delta}=\\frac{\\sum c_{i}\\delta_{i}}{\\sum c_{i}}", + "21b46037da615225.png": "q=1+k_{3}(c-1)", + "21c45de64910a463.png": "\\begin{matrix}(1,2,3)&(1,3,2)\\\\ (2,1,3)&(2,3,1)\\\\ (3,1,2)&(3,2,1)\\end{matrix}", + "21c45fbcece5e661.png": "log(A(t)B)", + "21c914de62aad1cb.png": "\\int_{V}(\\epsilon_{ijk}\\sigma_{jk})dV=0", + "21ca5df938c07b53.png": "\\frac{\\partial\\rho}{\\partial t}+\\nabla\\cdot(\\rho v)=0", + "21cb68ed22937f6f.png": "X(t,\\omega;x_{0})", + "21cb7ddb85b00b4c.png": "x_{i}=[P^{i}(R)]", + "21dd8f156f46de6d.png": "P_{ij}=\\tilde{P}_{ij}logn/n", + "21de812da83311b5.png": "\\tilde{G}", + "21e70b71dbeeabea.png": "C_{*}(\\tilde{X})", + "21e75c9bc5dc02c2.png": "1-(1-\\alpha_{1})^{m}", + "21e9f0b40a93e9ed.png": "\\{\\hat{f}_{n}\\}_{n=1}^{\\infty}", + "21ef18fd3c9190aa.png": "1:\\sqrt{\\varphi}:\\varphi", + "21f13bbaa421c266.png": "1/|G|", + "21f6bee4beb7ef37.png": "\\int dy=y", + "21fa1328864b3492.png": "b_{\\mu^{7}}", + "21fdff56e8544320.png": "\\frac{\\partial^{2}f}{\\partial\\sigma^{2}}<0", + "22004caf9799d3ee.png": "\\tilde{S_{n}^{m}}=-\\frac{S_{n}^{m}}{\\mu R^{n}}", + "2200e8e36aba2ee5.png": "\\hat{D}(\\alpha)|0\\rangle=|\\alpha\\rangle", + "2204bb0fadcefb69.png": "\\frac{d\\mu}{dn}", + "2205d272cbd93035.png": "|S|\\le(\\begin{matrix}n\\\\ \\lfloor n/2\\rfloor\\end{matrix})", + "220798cf0ac8e072.png": "\\tilde{\\pi}", + "220bd5f40ea0e241.png": "||f_{n}(x)||_{B}\\le g(x)", + "220bf56059567b4d.png": "4^{-N}(\\begin{matrix}2N\\\\ N\\end{matrix})\\approx\\frac{1}{\\sqrt{\\pi N}}", + "220c11a4b7f8bb39.png": "(-1)^{\\frac{n}{2}}E_{n}", + "220c4399a5f414a3.png": "G=\\pi_{1}(Ff)", + "220e2053e0c840b8.png": "J_{l}^{\\delta}", + "221586a8e99c4050.png": "\\int_{i}^{\\infty}1/s^{2}", + "221fe5518f5eaa56.png": "R_{2}=(S-T_{1})\\times g", + "22207f864a5bd15b.png": "E\\{|y_{v}|^{2}\\}=1", + "22210a88a4d44e49.png": "x=\\sum f_{i}(x)a_{i}", + "222205de27b9ed50.png": "\\alpha_{mk}R^{k}y^{k}(1-y)^{m}", + "222599c928b8a8a3.png": "f_{s}\\sim\\int f_{s+1}", + "222d0342bb989a76.png": "\\frac{\\partial\\sigma}{\\partial x}+f=0", + "222e472dff0f838e.png": "E[\\hat{\\sigma}^{2}]=\\frac{n-1}{n}\\sigma^{2}", + "22301557dd291a25.png": "\\tau_{ij}=\\overline{u_{i}u_{j}}-\\overline{u_{i}u_{j}}", + "223339e8fa24cb1d.png": "\\sum_{n=0}^{\\infty}\\frac{n+1}{2^{n}}", + "2233c3f86233a790.png": "H_{1}(u)([p])=[q]", + "2239baeec78ab920.png": "\\hat{\\theta}=\\hat{z}", + "223bd758e4558689.png": "\\sum_{j=1}^{5}b_{ij}L_{j}=L_{i}", + "22409435d092aea6.png": "(\\begin{matrix}d\\\\ k\\end{matrix})", + "22439334f62a79a2.png": "\\{\\tilde{e}_{k}\\}", + "22459d0b612d911f.png": "(\\begin{matrix}d-1\\\\ n\\end{matrix})", + "224647ce3ef0fb8b.png": "\\{X_{i},X_{j}\\}\\notin E", + "224716aa9d5742b7.png": "A_{q}(n,d,w)", + "224c8998405f90b8.png": "\\overline{H}=G\\cdot exp\\overline{C}", + "225a5a8a4719c7f5.png": "-\\int E\\cdot dl", + "225f924920b63f74.png": "\\{\\frac{\\partial}{\\partial x^{1}},...,\\frac{\\partial}{\\partial x^{n}}\\}", + "22650e4e7a9538c4.png": "\\tilde{D}_{9}", + "22656da02fbf6d3f.png": "\\prod_{x}\\frac{x+1}{x}=Cx", + "226b42c3e8309586.png": "\\tilde{D}_{4}", + "226e5a3fd5fd6d5d.png": "\\overline{AC}", + "22717b7e35ce7bad.png": "M,\\hat{d}", + "22764aaf20863cf9.png": "\\hat{U}", + "2276568c7d99b45a.png": "FOV_{C}=\\frac{57.3d}{f_{T}}", + "227c00f393d4a82e.png": "c=\\sqrt{n}", + "227c177e3059638e.png": "\\hat{t},\\hat{\\omega}", + "227eaa30f3219cb3.png": "\\sqrt{-3}=\\pm\\sqrt{3}i", + "228645352b255ed5.png": "modl^{n+1}", + "2287ecff7290148a.png": "r", + "22a235622ca02daf.png": "\\prod_{i\\in I}M_{i}/U", + "22a3e8dfba4a0915.png": "(x\\in[0,1],y\\in R)", + "22a40d9417676e7e.png": "P=a^{n+1}r^{\\frac{n(n+1)}{2}}", + "22a8ca71aef2cb76.png": "\\frac{dG}{dr}=0", + "22add6a33e097729.png": "dm=(\\frac{dy}{L})m", + "22ae16d66289587d.png": "\\frac{d\\varphi}{dt}+c^{2}\\nabla\\cdot A=0", + "22b6cf3209805024.png": "f(r)=e^{-\\beta u(r)}-1", + "22bdfe88aff55b73.png": "[\\begin{matrix}0&1\\\\ 1&0\\end{matrix}]", + "22c4a0bc11023010.png": "G_{r}=G_{r}^{+}+G_{r}^{-}", + "22c785672b6f9a75.png": "(c:a:b)\\cdot\\tilde{ab}:2\\cdot m", + "22d0e989420982bc.png": "\\frac{\\partial u}{\\partial\\nu}(x_{0})>0", + "22d1852fba952a89.png": "\\prod_{d|n}\\Phi_{d}(x)=x^{n}-1", + "22dfd5eee4006996.png": "E_{k-1}e^{X_{k}}=Ee^{X_{k}}", + "22e24a22b0444c68.png": "\\pi<\\hat{1}", + "22e5506673b7f67c.png": "((\\lambda V.E)E^{\\prime})", + "22e7448112e0a2b9.png": "[\\begin{matrix}a&b\\\\ 0&0\\end{matrix}]", + "22e83f83f1332cfc.png": "[\\begin{matrix}p&t\\\\ q&u\\end{matrix}]", + "22ed30f6d3858594.png": "=\\int u+(-v)dx", + "22f7dd0b84b9f5fc.png": "F=\\prod_{i=1}^{K}f_{i}", + "22fbe303d4be5bb5.png": "P(z+\\zeta_{0})", + "23031dfc27d89602.png": "Qf=\\int fdQ", + "2308a4302c1994a2.png": "(\\begin{matrix}p_{k-1}&p_{k}\\\\ q_{k-1}&q_{k}\\end{matrix})", + "230ce81ea09f66e2.png": "\\tilde{A}^{AB}\\Phi_{n}^{A}\\Phi_{m}^{B}", + "230d21a502d54be5.png": "[n/n+1]_{g}(x)", + "2310896b189f8e3b.png": "\\hat{\\xi}", + "2313318ec2c0be14.png": "M<_{DM}N", + "231d2576161479cb.png": "l_{OB}\\cdot l_{OD}=k^{2}", + "231f7f0777e13ef0.png": "x<0;1", + "23270a78ea2cf6d4.png": "\\gamma(t)=exp_{p}(tv)", + "2328fbef0c2998c3.png": "\\frac{\\sqrt{3}}{4}a^{2}", + "232e12797b5fa802.png": "P(\\epsilon_{n}=\\pm1)=\\frac{1}{2}", + "232ed6a1b50d8e91.png": "x\\mapsto\\frac{1}{x},y\\mapsto\\frac{1}{y}", + "2336cba99d2a40e4.png": "E_{A}^{A}-E_{A}^{D}>U_{D}", + "23390ea8f4f699c0.png": "\\tilde{s}_{i}", + "233917b81dabbfae.png": "s\\{\\begin{matrix}7\\\\ 4\\end{matrix}\\}", + "233fc560ba20f1ba.png": "k^{0},k^{1}=k^{0}cos\\theta", + "2344c5f7fa51511b.png": "\\frac{\\partial f}{\\partial x}=0", + "2345377ad3686c6d.png": "H_{ij}=\\frac{1}{i+j-1}", + "23461fd6734db22c.png": "\\{y=\\frac{\\alpha}{\\beta},x=\\frac{\\gamma}{\\delta}\\}", + "2347d8acb8b3961f.png": "A=\\prod_{i=1}^{n}A_{i}", + "234e8400d6e784f1.png": "\\hat{\\nu}_{i}", + "23608c5eef861ab7.png": "t\\{\\begin{matrix}5\\\\ 3\\end{matrix}\\}", + "2361cca5418843aa.png": "\\int sinx^{2}dx", + "2364ef942ff3b74f.png": "(\\begin{matrix}m-1\\\\ k-1\\end{matrix})/(\\begin{matrix}N\\\\ k\\end{matrix})", + "2365d58a4b3e3130.png": "(x,y)\\mapsto(x,-y)", + "236aa3c6da5fc278.png": "(\\begin{matrix}4\\\\ 7\\end{matrix})", + "236cb987915a028e.png": "\\frac{\\partial f}{\\partial x^{i}}", + "2376d0b6ba3ceb92.png": "w(3)=\\frac{3}{\\sqrt{\\pi}}", + "237892c561c34cc9.png": "Pr(R_{i}<\\underline{R})", + "2378e4d4123de981.png": "\\mu_{t}=\\rho\\tilde{\\nu}f_{v1}", + "237b1455b5433b87.png": "\\dot{\\tilde{\\mu}}=0", + "237cac9612d69fc5.png": "\\tilde{F}_{4}", + "237f0212f0cb244a.png": "[g,g]", + "23825506736e84b9.png": "\\frac{\\partial(\\varphi f)}{\\partial x}+\\frac{\\partial(\\varphi g)}{\\partial y}", + "2382e0ff065cd7f8.png": "X^{(n+1)}=(X^{(n)})^{\\prime}", + "238366d7ee55f913.png": "\\frac{\\partial}{\\partial y_{1}}=X", + "238449fdd92095ae.png": "\\int_{0}^{x}f(t)dt", + "2388c33fb867a444.png": "e^{-}\\rightarrow e^{-}+Z^{0}", + "238c970afc293492.png": "\\tilde{\\chi}(t)=\\tilde{\\rho}(t)R_{0}", + "238f1ff748476d85.png": "\\frac{dx}{dy}=-\\frac{\\beta}{\\alpha}", + "238f947d9a6fe1fb.png": "[\\begin{matrix}H&H\\\\ H&-H\\end{matrix}]", + "23926fc33a8f1626.png": "\\rho g(r)dr=dn(r)", + "239e15831f5104b8.png": "f:R^{n+m+1}\\rightarrow R^{n}", + "23a09f58075b923c.png": "\\int\\frac{e^{x}}{x}dx", + "23a6621ad49c53e7.png": "F_{pq}(e_{p}^{\\prime}\\otimes e_{q})", + "23a683960af7deac.png": "L^{2}\\ge4\\pi A-A^{2}/R^{2}", + "23ac08b151937bfb.png": "n=2^{h+1}-1", + "23ad45f216da2dba.png": "\\prod_{v}(a,b)_{v}=1", + "23ae30e6557c09f9.png": "\\frac{\\partial\\rho}{\\partial t}+\\nabla\\cdot(\\rho v)=0", + "23b0ec60dc4485cf.png": "(1-\\Delta f)", + "23b19066eddbde79.png": "a=0.3+i0.3", + "23b4ce5836b091de.png": "x_{k}=[\\begin{matrix}x\\\\ \\dot{x}\\end{matrix}]", + "23b691415d4779e1.png": "t_{ij}^{(-1)}=\\delta_{ij}", + "23ba3e9dfa814cd4.png": "\\infty+-\\infty", + "23c0ae27a5fa085c.png": "H=(\\begin{matrix}1\\\\ 0\\end{matrix})", + "23c66e8d9e8d413b.png": "H_{1}(u)([p])=[q]", + "23c797088c72284d.png": "\\frac{\\partial\\Phi}{\\partial N}=\\frac{l^{2}}{6}\\nabla^{2}-f\\Phi", + "23d6d08a8d7e7528.png": "i=kmodm+1", + "23d802ddcc0f2b82.png": "\\rho^{\\prime\\prime}=\\sum_{n}P_{n}\\rho P_{n}", + "23d8c79bb9b93b30.png": "2^{n}=2^{2^{k}}", + "23dac14c69b799a4.png": "(\\frac{4}{264})^{10/197-\\sqrt{9}}", + "23dff4ee4ac32d95.png": "2^{o(\\sqrt{k})}n^{O(1)}", + "23e0443d5c2672e8.png": "A^{\\prime}(z)", + "23eec6ebfe5e6980.png": "B_{e}=\\overline{B}(R_{e})", + "23f4cee0a1e10c04.png": "\\hat{a}_{t}", + "2406e4431ecdfc3b.png": "Y=X\\tilde{B}+\\tilde{B}_{0}", + "2409303d4d9bc436.png": "", + "240dafd3aa3cd394.png": "\\nu^{h_{5}}", + "240f3dd27d696e8a.png": "\\hat{a}_{1}", + "24184e505c9ac9be.png": "R=\\alpha k^{\\alpha-1}", + "2418d12cc65773d2.png": "\\overline{huv}", + "2419594653e96f1c.png": "\\sum_{i=6}^{10}26^{i}10^{16-i}(\\begin{matrix}16\\\\ i\\end{matrix})", + "242eb2d427ae2acb.png": "-\\frac{dy}{dx}siny=1", + "2430d970f7ec8d21.png": "\\hat{e}", + "243246180e3870b1.png": "\\tilde{K}(p;T)=e^{-Tp^{2}/2}", + "243ac6032054f938.png": "\\int e^{-x}cos(x)dx", + "2442168cec5f7f55.png": "c=\\frac{d}{t}", + "2445299b72a900e8.png": "[\\begin{matrix}1&4&4\\\\ 3&5\\\\ 4&7\\\\ 6\\end{matrix}]", + "244714e2be656838.png": "(\\begin{matrix}4\\\\ 3\\end{matrix})=4", + "244752566c2906b9.png": "||.||_{1}=||.||_{\\infty}", + "2448cf38b73231ba.png": "\\{0,...,q-1\\}", + "244bc12d39e02590.png": "F[y]=\\int_{E}ytdt", + "244c2f562a60c4b2.png": "\\sqrt{7}", + "244d8a19ee0a62d8.png": "A_{i}\\subseteq A_{i+1}", + "244e072d3bca0c42.png": "T_{n}=\\frac{a+1}{D^{2}-\\frac{b-1}{n}}", + "24526832ddf20cd2.png": "F=\\sqrt{1-\\alpha}", + "24529f36b321903e.png": "\\sqrt{h}", + "24531b6ec94bc3fe.png": "\\phi(r,\\theta)=-\\frac{Q}{2\\pi}lnr", + "24538f7ccd15df31.png": "\\frac{d[C]}{dt}=k_{2}[A][R]", + "2461d6b18d413ee6.png": "\\frac{\\partial f}{\\partial z}=\\overline{z}", + "246248fdbc00f496.png": "J_{x,y}\\sim|x-y|^{-2}", + "246a4e7dc827dac8.png": "V^{C}:=V\\oplus V", + "24720bbadc050699.png": "f^{\\xi_{m}}", + "24764864c99334a4.png": "0.5<\\frac{a}{L}<2", + "247797fb05836876.png": "\\vec{g}-2\\vec{T}-\\vec{L}", + "2479644e836c5c1b.png": "\\langle\\cdot,\\cdot\\rangle:R^{n}\\times R^{n}\\rightarrow R", + "247a2119c488d08b.png": "\\tilde{E}_{6}", + "248025fc048f4d0a.png": "f(x)=\\sqrt{x}+\\frac{1}{\\sqrt{x}}", + "248c653042028139.png": "\\hat{f}_{i}", + "248cda1e8e2ecd3c.png": "L=\\frac{d^{2}}{dx^{2}}+u", + "248d715781559db4.png": "N=10^{a-bM}", + "2490d0f829511f84.png": "\\sqrt{2}k", + "2496044aace54f06.png": "g=\\prod_{i\\in I}(X-\\alpha_{i})", + "249cf76b40d2987a.png": "U:=U_{a,b,c,d}", + "24a075146cc24377.png": "(\\begin{matrix}1\\\\ 0\\\\ 0\\\\ -1\\end{matrix})", + "24a4631eab58935d.png": "G(t;\\mu_{1},\\mu_{2})", + "24a5d515afd7cd59.png": "|t|<1/2", + "24aa2729baac2dcd.png": "V_{\\Lambda}\\cong\\bigoplus_{\\lambda\\in\\Lambda}V_{\\lambda}", + "24ac17d9d16a954c.png": "x\\notin A", + "24ad46149cb5cc58.png": "(\\begin{matrix}n\\\\ t\\end{matrix})", + "24ae4021f1a1b6c8.png": "a=l\\cdot l=\\|l\\|^{2}", + "24b111dbb2ca9930.png": "-N_{c}^{2}-1", + "24b337fd8be244ef.png": "j\\mapsto(\\begin{matrix}0&1\\\\ -1&0\\end{matrix})", + "24b67f1a014fe6cb.png": "T_{ii}=3A+B", + "24b6f7d8522cee8d.png": "2((\\begin{matrix}n\\\\ 1\\end{matrix})+(\\begin{matrix}n\\\\ 2\\end{matrix})+(\\begin{matrix}n\\\\ 3\\end{matrix}))", + "24baa8f6f597e7bf.png": "H=k\\circ h^{-1}(z)", + "24bc905c40ff3598.png": "T_{\\mu\\nu}^{(vac)}=-\\frac{\\Lambda c^{4}}{8\\pi G}g_{\\mu\\nu}", + "24c34eaedf4143db.png": "C_{0...m_{j}...0}", + "24c36f56d90136d3.png": "\\prod_{p|n}f(p)", + "24c5df2cc6d71396.png": "S_{x_{B-l}}=I\\otimes S_{x_{l}}", + "24c5e7c43e5d75f7.png": "\\int_{\\gamma}D\\gamma", + "24ca2924c5dcc7ea.png": "e^{x^{2}-5x-7}-3=0", + "24d7928c33eeb963.png": "\\sqrt{2}W+X", + "24e522d51755fb56.png": "\\pi_{1}\\pi_{2}...", + "24e8b264d352299f.png": "min\\{e(u),c_{f}(u,v)\\}", + "24ea275c36ad2b33.png": "[\\begin{matrix}A&0\\\\ 0&B\\end{matrix}]", + "24ec68260f03477e.png": "F^{-1}(F(x))\\le x", + "24ef818ebdfde0bf.png": "t\\{\\begin{matrix}p\\\\ 2\\end{matrix}\\}", + "24f6bb7c617193e6.png": "(\\begin{matrix}-1\\\\ 0\\end{matrix})=1", + "24fd5ba5f438db30.png": "\\tilde{a}_{1},...,\\tilde{a}_{m/n}", + "250026bd73f6bb1f.png": "(-1,1)", + "25020f302721b30e.png": "O(\\frac{N}{L}log_{Z}N)", + "2502f9e1f029aa5c.png": "\\mu=5log_{10}(d)-5", + "250849f5a254be31.png": "\\frac{d^{k}f}{dx^{k}}(x)=0", + "2509e70b111c7254.png": "\\overline{K}[C]", + "250b55404848e2de.png": "[\\begin{matrix}L&M\\\\ M&N\\end{matrix}]", + "250d0979d676f9e4.png": "\\prod X_{i}", + "25190b441d336e81.png": "d_{\\zeta^{\\eta}}", + "251f8dd80df67597.png": "\\int\\frac{dx}{1+x^{2}}", + "252b585d0cbd1d1c.png": "\\sum_{i\\in F}N_{i}=M", + "25303b15dadf04ff.png": "D_{q}=\\frac{1}{x}\\frac{q^{\\frac{d}{d(lnx)}}-1}{q-1}", + "25360255bb3cc549.png": "t=t_{0},r=r_{0},\\theta=0", + "253742d3789a7c5b.png": "r=k_{1}[A]+k_{2}[A]^{2}", + "2538cee5f3076bcd.png": "\\int f(x)dx=F(x)", + "253b6caeac1d898a.png": "\\sqrt{E}", + "253e7bf5a2ceadd3.png": "\\psi", + "255394a3431c6a49.png": "\\Delta{\\Lambda^{\\mu}}_{\\nu}={\\Lambda^{\\mu}}_{\\rho}\\otimes{\\Lambda^{\\rho}}_{\\nu}", + "2553d804cb3d407e.png": "|E(\\theta-\\hat{\\theta})|<\\delta", + "2556dfe410c4399a.png": "G^{u}H/H=(G/H)^{u}", + "255a5fb495af4cda.png": "\\overline{w_{i}}", + "255a9418ca2008a4.png": "\\frac{1}{\\sqrt{1-x^{2}}}", + "255eb3db6d0da30d.png": "\\tilde{c}_{i}\\equiv t_{i}modv^{-1}F^{-}", + "255ebe8e0364e195.png": "(\\begin{matrix}n\\\\ 1\\end{matrix})", + "255f4817758e94f1.png": "\\tilde{R}", + "2565877c0a512daa.png": "y\\in\\overline{S}", + "256a25c6612a8f41.png": "(n+1)p-1\\notin\\mathbb{Z}", + "256b9ff438982f07.png": "\\frac{337m}{11}-2=x", + "25705b83684bc2df.png": "\\frac{d^{2}u}{dx^{2}}-u=0", + "257b72c67d7815f7.png": "\\langle\\frac{F}{||F||},\\frac{T}{||T||}\\rangle", + "257e9a325348ae7e.png": "[\\begin{matrix}1&0\\\\ \\frac{1}{R}&1\\end{matrix}]", + "257f5a8030596316.png": "\\underline{u}\\in U", + "2581fa534a5b0230.png": "[\\begin{matrix}1&0\\\\ -sC&1\\end{matrix}]", + "25851dc0f2dab895.png": "\\lambda_{2}=3-\\sqrt{5}", + "2589680d0174f734.png": "\\Pi_{f}=1-e^{-BR}", + "258bce796f254a09.png": "Y(t):=y[X(t),t]", + "25929680026b3c80.png": "G^{*}(f)=G^{\\prime}+jG^{\\prime\\prime}", + "259f61d5075f1406.png": "[\\tilde{A}^{AB},H^{(0)}]\\ne0", + "25a04d9b8b6993f4.png": "T(p)=\\frac{1-z_{a}}{1+z_{a}}", + "25a6d12bcc84244a.png": "\\hat{Y}_{i}", + "25a8adf91ff9143b.png": "\\sqrt{x-1}+\\sqrt{x}", + "25b01ccacbd3de7f.png": "z=\\prod_{p_{i}\\in P}p_{i}^{a_{i}}", + "25b28a329057825f.png": "T^{*}=\\frac{(T-T_{o})}{(T_{s}-T_{o})}", + "25bd620dcce70d73.png": "(\\begin{matrix}8\\\\ 3\\end{matrix})", + "25beb7f734947912.png": "\\sqrt{31}\\times\\sqrt{31}", + "25c0cfb0eebbceaa.png": "(\\begin{matrix}14\\\\ 5\\end{matrix})=2002", + "25c3c21214191773.png": "\\phi_{0}=[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "25c67e61a3f9cd17.png": "N=\\pm1,\\pm2,...", + "25c80f86df1c5dc1.png": "\\tilde{C}_{2}", + "25c953e252714bc3.png": "E_{u}[Y_{t}(u)-Y_{c}(u)]", + "25cbc75125f6413f.png": "(-2\\sqrt{\\frac{2}{5}},0,0,0)", + "25cce2b211953239.png": "||\\cdot||_{1},||\\cdot||_{2}", + "25ceeefd79f1e948.png": "\\underline{r}", + "25d219fd8c019df4.png": "ab<0,c>0", + "25d60b79d14f9f9f.png": "\\frac{dx}{ds}=a", + "25d7039cdb9840dd.png": "2\\tau_{0}/n_{\\tau}", + "25d7948b5155ffa5.png": "[\\hat{T},\\hat{H}]=0=[\\hat{H},\\hat{T}]", + "25dd35a0ac27cb33.png": "(\\frac{n}{2}-1)", + "25dec3196edcacac.png": "\\hat{L}_{z}", + "25e122ca17ef179f.png": "\\prod_{i\\in I}X_{i}", + "25e71d143b1508f5.png": "\\frac{dE}{dx}=0", + "25f4b808519cd132.png": "\\lambda_{i_{1}},...\\lambda_{i_{n}}", + "25f663ab2fbcaf21.png": "S=-(\\frac{\\partial F}{\\partial T})_{V}", + "2610e106abfe1378.png": "L=q^{\\Omega(n)}", + "2616e97cfba5caa9.png": "\\tau_{g}^{\\delta}", + "262a5286ba24b4a8.png": "C_{pq}^{-}", + "262ecf439b7cc8de.png": "\\frac{1}{c^{2}}\\frac{\\partial^{2}\\varphi}{\\partial t^{2}}-\\nabla^{2}\\varphi=0", + "2632a59af48918f3.png": "U^{\\prime}=U\\cdot\\sqrt{\\frac{1+\\beta^{2}}{1-\\beta^{2}}}", + "2637ab8e591c158f.png": "|0\\rangle=(\\begin{matrix}1\\\\ 0\\end{matrix})", + "263808c3274fad03.png": "x=y=\\frac{i}{\\sqrt{2}}", + "2641b90c7cdbfc4e.png": "0\\le\\underline{d}(X)\\le\\overline{d}(X)\\le1", + "2649ac42aebe45a9.png": "d_{\\hat{K}}", + "265040f04c202f40.png": "c(k)=(\\begin{matrix}2k\\\\ k\\end{matrix})", + "2654f3e993d00dd4.png": "\\sqrt{K}", + "2655f50a5dce8f0e.png": "\\hat{p}^{k}", + "2656068de98c6433.png": "\\hat{q}_{o}", + "265dffad05ab2fcf.png": "\\frac{dM}{dt}", + "265eb975eaa7ae58.png": "\\sqrt{(x-y)^{2}}=|x-y|", + "2661214c87f43ef4.png": "2\\sqrt[3]{x}=16", + "26620dc8b50716a0.png": "f=f_{0}(1+\\frac{v}{c})", + "2664c52caf5458e6.png": "\\delta\\int d\\tau=0", + "26693677ff2f56ac.png": "h_{k}=f_{-k}", + "266b5780b398ba76.png": "\\frac{ds}{dt}=0", + "2674a9294884b4a9.png": "F_{r}=\\int dF_{r}", + "26792144c4d81afd.png": "\\hat{L}_{z}", + "267c946ec7f33414.png": "\\int fd\\mu", + "2682b77cfa6cc178.png": "\\tilde{X}^{n}", + "2683c84fd6fd29de.png": "\\int cos^{2}xdx", + "2685c61224fa0327.png": "\\sum_{k=0}^{\\infty}\\langle f,e_{k}\\rangle e_{k}(x)", + "268f46c4e23a2f5c.png": "\\frac{f(x)}{g(x)}=\\frac{\\sqrt{x-3}}{x^{2}-9}", + "2691514e6098b5ee.png": "\\frac{1}{\\rho(s)}=\\kappa(s)=\\frac{d\\theta}{ds}", + "2696f7848adf178e.png": "lim_{x\\rightarrow0}f^{-1}(x)=-\\infty", + "26975aac0eeed139.png": "P=[\\begin{matrix}1&0\\\\ 0&0\\end{matrix}]", + "269bbb5f26a85d02.png": "r=\\sqrt{x^{2}+y^{2}+z^{2}}", + "269c73b6a6f4a528.png": "c(k)=(\\begin{matrix}2k\\\\ k\\end{matrix})", + "26a07f351af682cb.png": "x\\leftarrow\\frac{a+bx}{1+x}", + "26a464320e2f0782.png": "U_{\\rho}=v_{r}-v_{r}^{\\prime}+\\frac{ra_{r}^{\\prime}}{c}", + "26a57cc55fd75f96.png": "P^{(k)}=\\sum_{i=1}^{k}U^{(n-i)}", + "26a8185ea2c67d4f.png": "x_{3}=\\alpha_{j}(\\alpha-r)+\\delta", + "26ac086c66cf3616.png": "x\\in[-2,-0.5]", + "26aeebbd48294401.png": "g(X)=\\frac{dF_{1}(X)}{dX}", + "26b0dd3d94e419a4.png": "I_{r,r-1}=[\\begin{matrix}I\\\\ O\\end{matrix}]", + "26b23b623af27736.png": "\\tilde{E}_{6}", + "26b616c88e104eaf.png": "[\\begin{matrix}1&R\\\\ 0&1\\end{matrix}]", + "26ba3a0ec620a008.png": "<<...>>", + "26c2d6b8910e5c0f.png": "\\overline{f}=[\\begin{matrix}u\\\\ -v\\end{matrix}]", + "26c4e19f5f2e1092.png": "F[x,y]=\\int_{E}xydt", + "26c4fedb6892ddcd.png": "E[(X-\\mu_{X})^{2}]", + "26d1ea797f642209.png": "\\delta_{\\overline{k}}<0", + "26e12a2d2576e253.png": "d\\tilde{n}/d\\eta", + "26e1fc3c68ce2bdf.png": "L_{3}+-4L_{2}\\rightarrow L_{3}", + "26e2c62283bfed30.png": "[\\begin{matrix}k&0\\\\ 0&k\\end{matrix}]", + "26e5a82fb0cc43a6.png": "\\int_{0}^{x}1dt=x", + "26ecc38f7a2909ce.png": "|-\\rangle", + "26f8fe47767740df.png": "\\int_{S}1dS", + "26fbe653c2e7f0dd.png": "\\tilde{W}_{t}=W_{t}-[W,X]_{t}", + "26fe449f5cd63546.png": "\\phi(E_{i})\\subseteq F_{1-i}", + "2708684ab6116fc6.png": "\\tilde{t}", + "270f31ee18231017.png": "2\\dot{\\psi}=-\\dot{\\phi}cos\\theta", + "2711b351440168df.png": "\\hat{\\phi}=Y_{D}\\circ F", + "27137a9d9e4b7da4.png": "B=[\\begin{matrix}0&A^{*}\\\\ A&0\\end{matrix}]", + "27147fd29d074763.png": "c=\\frac{d}{t}", + "271f44d8ab908028.png": "(\\begin{matrix}R^{\\times}&R\\\\ 0&1\\end{matrix})", + "2720653c70002875.png": "[\\begin{matrix}3/2&0\\\\ 0&3/2\\end{matrix}]", + "2734fe80c744d169.png": "A=\\frac{\\sqrt{3}}{4}a^{2}", + "273849a61f399e95.png": "\\hat{f}^{s}", + "273d399a84a57c0b.png": "\\frac{\\partial f}{\\partial\\overline{z}}", + "2756905d98388afd.png": "\\int_{X}f(x)dx", + "27587649e4a33ffc.png": "U_{ij}(N)=k_{e}\\frac{e_{i}e_{j}}{r_{ij}}", + "2759b450f2cc8b40.png": "\\int\\frac{e^{x}}{x}dx", + "275e085caf38a717.png": "0=1", + "27609a93563518f9.png": "r(\\underline{x},t)", + "276f8b0544cb0166.png": "|a_{n+1}|>|a_{n}|", + "27718a69a0b3e905.png": "S_{a}=x+\\overline{X}a", + "277ac02087e48c2c.png": "\\sigma_{j}^{2},j=1,2,...", + "277c032caf5d50af.png": "D=\\{x^{2}+y^{2}\\le4\\}", + "277d01faef356dca.png": "\\frac{dB}{dz}", + "27809cc78e3678c7.png": "e[n]=x[n]-\\hat{x}[n]", + "27861461a3394e92.png": "NE(X)", + "27861de23914eb15.png": "N=\\frac{f}{(\\hbar\\omega\\beta_{c})^{3}}\\zeta(3)", + "27861e413f5db2ef.png": "\\}", + "27877946111f7db6.png": "\\frac{\\partial r_{i}}{\\partial\\beta_{j}}", + "2791102e2696b171.png": "f_{*}(L_{X})", + "2792d2c606ffd702.png": "\\int_{L}^{*}", + "2795b325d5923dbd.png": "Z(C[S_{n}])", + "279958705ce21d8d.png": "\\tilde{Z}_{0}", + "279a6ae0c7019893.png": "\\hat{h}(\\xi)=\\frac{1}{|a|}\\hat{f}(\\frac{\\xi}{a})", + "279e031d13935351.png": "\\overline{C}", + "27a1513ef5c73b81.png": "\\tilde{R}", + "27a1bd67eb88da86.png": "\\Phi_{11}=-2m/r^{3}", + "27a420d38da99d1a.png": "(Q^{*},\\cdot)", + "27ad8701bb5bd8ef.png": "(X_{1}+\\cdot\\cdot\\cdot+X_{n})/\\sqrt{n}", + "27b2f81d9701f597.png": "\\frac{-1+i\\sqrt{3}}{2}", + "27bb4c32f899a7df.png": "T\\ne\\overline{U}", + "27bd40fc1d70714c.png": "[\\begin{matrix}c&-s\\\\ s&c\\end{matrix}]", + "27bdff854c1f6703.png": "(r\\times v)_{z}<0", + "27c05be6d068d60a.png": "\\hat{\\mu}=\\frac{\\sum_{i}x_{i}}{n}", + "27c2825b96a64bf1.png": "\\{P_{\\alpha}[\\cdot]\\}", + "27c63707524b9198.png": "N_{L/K}(L^{\\times})", + "27da9dd463254b54.png": "\\tilde{V}", + "27df7f64c71785fb.png": "D\\{J\\}\\subseteq\\tilde{D}", + "27dfbeb2e9ec052b.png": "\\sigma^{\\mu\\nu}\\equiv\\frac{i}{2}[\\gamma^{\\mu},\\gamma^{\\nu}]", + "27e4ab061bb2cd05.png": "A^{2}S^{2}|F(q)|^{2}", + "27eac9fb781467fd.png": "m\\ge(\\begin{matrix}k\\\\ 2\\end{matrix})", + "27eda9fb91ef6ba6.png": "\\tilde{B}_{n}", + "27ee2ea5c1ca0752.png": "\\int_{1}^{0}\\frac{dt}{t}=-\\infty", + "27f146f1b785b9fd.png": "b,Ab,...A^{n-1}b", + "27f42f50add6f4f7.png": "(\\begin{matrix}2&-2\\\\ -2&2\\end{matrix})", + "27f67feb126c050f.png": "a\\approx\\sqrt{\\frac{l_{1}^{3}}{24(l_{2}-l_{1})}}", + "27fbc6c62b117435.png": "||v||^{2}=\\langle v,v\\rangle", + "27ff63facabadfd1.png": "\\Omega^{\\prime},\\Omega_{0},\\Omega_{1}", + "2801fe659a821230.png": "\\hat{N}_{C}", + "2803b367664a4e7e.png": "M=(Q,\\Gamma,\\delta,q_{0},g)", + "28047be5985996c4.png": "[x_{w}y_{w}z_{w}1]^{T}", + "2806bc8fb4181638.png": "a^{\\prime}=\\lambda_{1}a+\\lambda_{2}b", + "280b2fc0ba2378de.png": "Z_{L}=\\frac{V}{I}=j\\omega L", + "280c028601783730.png": "B=\\frac{\\sqrt{m-1}}{Q}", + "280d777f1bfffab1.png": "E(S)=a_{1}M", + "28104402bad2a2f7.png": "E_{p}=k_{B}T", + "28178607d7165296.png": "\\psi(R_{1}...R_{n})", + "2818580a128f9404.png": "cosx=1-\\frac{x^{2}}{2}", + "2821a7a5bf058ac7.png": "x^{d_{\\sigma}}", + "28223132801c06ca.png": "(\\begin{matrix}n\\\\ k\\end{matrix})_{q}", + "282498691dab8300.png": "\\tilde{q}\\tilde{\\overline{q}}\\rightarrow q\\tilde{N}_{1}^{0}\\overline{q}\\tilde{N}_{1}^{0}\\rightarrow", + "2824bda21c23e8f1.png": "C=\\epsilon_{r}\\frac{A}{4\\pi d}", + "2831258ae8f3746a.png": "c_{g}=\\frac{1}{2}\\sqrt{\\frac{g}{k}}=\\frac{1}{2}c", + "2833fbf5b18832b1.png": "angle(x_{1}):=\\theta", + "283822fd372aa412.png": "\\hat{p}=1", + "2838f2dcde6e7bdd.png": "p:=|X^{+}|", + "284116236c16f911.png": "H(e^{i\\omega})", + "2844a6ac8f68f7a5.png": "\\hat{y}", + "2846e8783bd585d9.png": "\\sigma_{j}^{2},j=1,2,...", + "284c1520ae492230.png": "\\pi(p^{*})-p^{*}y^{*}(p)", + "28508428bc39706a.png": "U_{j}=(1+t_{j}^{\\prime})\\alpha", + "2852830ed65e5071.png": "\\{-2,-1,1,2\\}", + "2852904d1da44e97.png": "a_{n}=1-\\frac{1}{10^{n}}", + "2857c92e2d677e10.png": "P(M>a)", + "285a3e76bc5baca0.png": "[\\begin{matrix}-\\alpha-1\\\\ -\\beta\\end{matrix}]", + "285fcf6edb4ebf7b.png": "\\delta=\\hat{h}(n)-h(n)", + "286734d40247fc45.png": "u_{\\eta^{r}}", + "287243327b5a2674.png": "E_{n}=\\hbar\\omega(n+\\frac{1}{2})", + "287321a9adf00135.png": "C_{\\tilde{Y}}", + "2873a1339cb93b49.png": "\\int VdP", + "2877cd4448139eef.png": "(C_{\\bullet}(X),\\partial_{\\bullet})", + "287a2cc8b8f67b2e.png": "F=\\frac{B^{2}S}{2\\mu_{0}}", + "287f55dab027bba7.png": "h(a_{i})-th", + "28842de4052a6179.png": "2+\\sqrt{5}", + "2889d8ddfe92dfd3.png": "g(x)=\\prod_{i}h(x_{i})", + "288d7dde61dcc3aa.png": "\\frac{d}{da}", + "288f72649bff200b.png": "J_{a},a=1,2,3", + "288fc7373b3b6da7.png": "[X]:=[X,X]", + "2894283cd6aaf86c.png": "\\hat{M}", + "289fe096ac15433d.png": "NE(X)", + "28a34f8a750c11d6.png": "0=1", + "28a3fca7a1019c57.png": "[h_{i},f_{j}]=-c_{ij}f_{j}", + "28a58e726373e3db.png": "A=(\\begin{matrix}1&2\\\\ 3&4\\end{matrix})", + "28a6407e226a8805.png": "s_{x}^{\\epsilon}", + "28ab3bc348b99ad6.png": "[\\begin{matrix}1&\\frac{1}{sC}\\\\ 0&1\\end{matrix}]", + "28b14d73f508c8f7.png": "n!+1=m^{2}", + "28b180d4404dd335.png": "W=\\int pdV", + "28bb81c8a276a200.png": "r_{i}=a\\frac{\\phi^{2}}{2\\sqrt{3-\\phi}}", + "28c30d9e5877793e.png": "\\frac{0}{\\sqrt{\\frac{0}{u^{2}}-0}}", + "28c857497a866d72.png": "[\\begin{matrix}U_{1}\\\\ U_{2}\\end{matrix}]", + "28c87a374430b391.png": "|t|^{2}=t\\overline{t}", + "28c90d5944d996e8.png": "(\\begin{matrix}c_{i}\\\\ i\\end{matrix})", + "28d43e749ced08ab.png": "\\prod_{n=1}^{\\infty}a_{n}=a_{1}a_{2}a_{3}\\cdot\\cdot\\cdot", + "28dd1fcd2497b098.png": "\\lambda_{j}-\\alpha\\mu_{j}", + "28df58c06188e098.png": "|\\overline{AJ}|=\\frac{2}{\\pi}r", + "28dfbb80dd3367d1.png": "\\frac{\\partial L}{\\partial t}=0", + "28e6568e95ec9085.png": "\\sqrt{\\Delta}", + "28ead017aa9a9431.png": "3\\sqrt{x}", + "28ec8b9a0b02f15f.png": "0\\le\\frac{x^{2}}{x^{2}+y^{2}}\\le1", + "28f0f8b4eb89ee7b.png": "Z(s)=\\sum_{i=1}^{\\infty}e^{-\\lambda_{i}s}", + "28f18dbe5d3b61ee.png": "-j\\sqrt{\\frac{1}{2}}", + "291e2fb082f2ce5d.png": "v=\\int\\frac{dv}{dx}dx", + "2922bdeed4456c49.png": "\\nu=\\rho\\phi_{0}/|B^{*}|", + "292993f0bb24f522.png": "\\sum_{k=0}^{n}(\\begin{matrix}n\\\\ k\\end{matrix})p^{k}(1-p)^{n-k}=1", + "292e3f2b57ccf22b.png": "\\sqrt{1+tan^{2}\\theta_{o}}", + "2930a9af6ae50a01.png": "\\int_{0}^{3}|x^{2}-4|dx", + "29385dfa18dd6b58.png": "m1", + "2cdddf04e950a255.png": "x_{0}=\\frac{S^{2}-1}{S^{2}+1}", + "2cdf28655d0d4125.png": "(\\begin{matrix}x^{\\prime}=x(1-y)\\\\ y^{\\prime}=-y\\rho(x-1)\\end{matrix})", + "2ce1053f5c7ec410.png": "\\chi_{+}(1)\\chi_{-}(2)", + "2ce3221e6b72feae.png": "P=K\\rho_{c}^{1+\\frac{1}{n}}\\theta^{n+1}", + "2cedf949bffe4c87.png": "(\\begin{matrix}x&y\\\\ -y&x\\end{matrix})", + "2ceeb6f46cddf9e0.png": "\\sqrt{2}-1", + "2cf0549cfbb9aba8.png": "\\hat{e}(s_{0})", + "2cf3873cd5158f68.png": "\\prod_{p\\le x}\\frac{p-1}{p}", + "2cfa537ac2311763.png": "-\\frac{1}{10}\\pi^{2}-ln^{2}\\phi", + "2d07d7f89120fefd.png": "\\tilde{\\Gamma}", + "2d0b40c061134bb5.png": "V_{D}=V_{DD}-IR", + "2d0cdb43d5f3736a.png": "\\{H_{i}\\}_{i\\in Z^{+}}", + "2d0cde9b84e7e9ef.png": "\\bigoplus M_{i}", + "2d1185a48535391d.png": "[\\begin{matrix}p&t\\\\ q&u\\end{matrix}]", + "2d14a29172e3bb5d.png": "\\frac{4\\pi R^{2}}{(4/3)\\pi r^{3}}f(R)dR", + "2d163672d018a0ad.png": "\\tilde{Q}_{4}", + "2d16bec873e3768e.png": "B[i]=1", + "2d1a80d9bdbf985c.png": "\\hat{H}=1+\\frac{1}{2}(slope)", + "2d1deeb3bd1946ca.png": "\\chi_{0.50}^{2}", + "2d1df64117c2798d.png": "\\mu(E_{n_{k},k})<\\frac{\\epsilon}{2^{k}}", + "2d22c4c6fe0f6313.png": "\\frac{\\partial\\varphi}{\\partial t}(x,t)=F(\\varphi)", + "2d23c1a8da239f72.png": "C=(\\begin{matrix}1&i\\\\ i&1\\end{matrix})", + "2d2c19ba146c6439.png": "s=\\int\\frac{dt}{r(t)}", + "2d2e57673309fe67.png": "\\delta=-A^{2}-A^{-2}", + "2d326305dc98375d.png": "\\frac{\\lambda}{\\mu}+\\pi_{0}\\frac{\\rho(c\\rho)^{c}}{(1-\\rho)^{2}c!}", + "2d328c39152b49b4.png": "P(n,x):=P^{n}(x)", + "2d33c448862fc911.png": "T=\\frac{m\\overline{v^{2}}}{3k_{B}}", + "2d34c9cd0b1093b1.png": "\\frac{dr}{dt}=Ar", + "2d3c14614d6c6ad5.png": "\\sum V_{i,j}", + "2d4bb1b75a7ebd2d.png": "N=max(m,n)", + "2d4f1be24d01f831.png": "(\\begin{matrix}1&d\\\\ 0&1\\end{matrix})", + "2d5efac9946f1b73.png": "s_{\\overline{n}|i}=\\frac{(1+i)^{n}-1}{i}", + "2d687415167974b3.png": "\\overline{z}^{n}", + "2d6938a5362dbeb4.png": "Y=P_{x}\\cdot x+P_{y}\\cdot y", + "2d6b489e80c5557c.png": "\\frac{dS}{dt}=L", + "2d6d6625e9f59cb2.png": "2\\pi/c_{ij}", + "2d73b3672466c824.png": "W=\\int PdV", + "2d7964ca6e85ceba.png": "X_{m}=\\{e_{i}|x_{m}\\in e_{i}\\}", + "2d829b3164a31d71.png": "\\tilde{\\nu}_{e}", + "2d82ea974334c623.png": "\\frac{d}{dx}", + "2d861e6c3291e064.png": "\\tilde{H}/\\tilde{H}^{\\prime}\\simeq H/H^{\\prime}", + "2d8a7ba7253a4fc3.png": "T_{n}n!=n^{n-2}n!", + "2d9539e2e6ed8ece.png": "[\\begin{matrix}4&4\\\\ 6\\end{matrix}]", + "2da07dc05b454b2b.png": "7-5\\sqrt{2}=-0.07106...", + "2da5187be949fdb9.png": "o", + "2daa970984336a06.png": "\\delta\\int2T(t)dt=0", + "2dad02a266383810.png": "\\overline{C}_{1}", + "2db1c21d91c7fc6b.png": "\\tilde{u}\\in L^{2}(\\mathbb{R}^{n})", + "2db74499b591830f.png": "N[\\frac{I(T_{M})}{I(T_{0})}-1]", + "2dbc0d0812cf8e6a.png": "x", + "2dbc34dd0031b38f.png": "sr\\{\\begin{matrix}4\\\\ 3\\end{matrix}\\}", + "2dc816d7875ddcf4.png": "U", + "2dc960d20731a724.png": "Pr(X=0)=1-p", + "2dcbc26b31ff08b4.png": "-e,\\sqrt{2},3,\\pi", + "2dcc72302a5e1fb4.png": "(22)k^{c}\\nabla_{c}\\hat{\\omega}_{ab}=0", + "2dce263e011a94d0.png": "S_{k}=(\\begin{matrix}m\\\\ k\\end{matrix})\\frac{(m-k)!}{m!}=\\frac{1}{k!}", + "2dce4aadaece98e7.png": "\\theta_{min}\\approx\\frac{CD}{AC}=\\frac{\\lambda}{W}", + "2dd0acc922b56a19.png": "(\\begin{matrix}a\\\\ b\\end{matrix})", + "2dd5fc6b806302df.png": "S_{ab}=\\hat{S}_{ab}+\\hat{s}_{ab}", + "2ddf0fbd723a4539.png": "\\frac{F_{2n}+F_{n}}{2}", + "2de1b3709ec9c1bd.png": "g(x)=c+\\sum_{j\\in Q}x^{j}", + "2de96b71d31c5475.png": "Y", + "2dea9596aef40690.png": "-Q_{b}=\\chi\\epsilon_{0}", + "2ded16a892d9d8a5.png": "(\\pm\\sqrt{2},1)", + "2dedd85a1c4d0a36.png": "A_{1}=B_{1}=0", + "2df63865df3dc8a9.png": "T_{0}^{2}(q)=\\frac{\\sqrt{6}}{2}q_{zz}", + "2df71072ff1bf66d.png": "\\prod_{k=1}^{n}a_{k}^{j_{k}(g)}", + "2dfd209c9db2f0fb.png": "S=-mc\\int ds", + "2e05c4f579c76fad.png": "\\hat{G}", + "2e0613c2df33d258.png": "P=1.854kd^{n-2}", + "2e074b74e3c3798f.png": "U=[\\begin{matrix}U_{1}&U_{2}\\end{matrix}]", + "2e0806612b15fce4.png": "R_{l}^{pp}(r)=R_{nl}^{AE}(r)", + "2e0c4c8b78127c7c.png": "\\sqrt{\\psi}", + "2e0ed49f46d3025f.png": "v\\notin N(T\\backslash S)", + "2e124b2444cb448b.png": "\\hat{Z}", + "2e171d1d93a70240.png": "\\tilde{T}_{M}^{ab}", + "2e196dfcd9fadeba.png": "G_{liquid}m\\Omega(r)", + "2e496b1b5513f71c.png": "U=[\\begin{matrix}M\\\\ N\\end{matrix}]", + "2e51db837a2010d6.png": "\\rho(r)\\sim e^{-2Z_{\\alpha}r}", + "2e55f2ed90d089b1.png": "\\sum D^{2}=ND_{o}", + "2e5bac13d9b69ca2.png": "\\int_{S}H^{2}dA", + "2e5f9417ac4545dc.png": "\\partial_{t}L=\\frac{1}{2}\\nabla^{2}L", + "2e60b8352d6d23a0.png": "\\gamma=\\gamma^{o}(1-\\frac{T}{T_{C}})^{n}", + "2e66689c4c150333.png": "\\frac{-1}{ln(1-p)}\\frac{p}{1-p}", + "2e691ece7abf8e40.png": "B=\\frac{\\sqrt{m-1}}{Q}", + "2e6aa1d9b3781216.png": "n\\#=6<16", + "2e6dbc9f33fc5b80.png": "d_{i}|d_{i+1}", + "2e6fb1e140e407db.png": "\\sum_{i=1}^{k}\\sum_{w\\in V}f_{i}(s_{i},w)", + "2e730b5dd2025325.png": "f(t)G(t)+g(t)F(t)", + "2e775372ed1c399e.png": "\\hat{H}", + "2e7a60e92d21f829.png": "\\{a,b,n-2,1\\}", + "2e7dad865670c17e.png": "\\prod A_{i}", + "2e811197380430aa.png": "x\\rightarrow\\frac{x}{\\sqrt{a}}", + "2e822ef194c47d22.png": "[\\begin{matrix}1&1\\\\ 0&1\\end{matrix}]", + "2e8378000c0ee2cf.png": "\\sqrt{\\frac{27}{70}}", + "2e84fa11244d723b.png": "[\\begin{matrix}A&U\\\\ V&C\\end{matrix}]", + "2e85d9afe3789444.png": "\\int_{a}^{b}\\cdot\\cdot\\cdot dx", + "2e903886ac8a6b97.png": "H_{3}\\longrightarrow H_{3}^{+}+e^{-}", + "2e910d9d610e5712.png": "O(kn+1.274^{k})", + "2e9177dba70afaf8.png": "|\\psi_{y-}\\rangle", + "2e9994fb65408bf5.png": "\\hat{y}\\in\\{-1,1\\}", + "2ea1426f37707877.png": "(L_{X}g_{ab})_{;c}=0", + "2ea1cac71cc0083b.png": "(\\begin{matrix}n-k\\\\ k\\end{matrix})", + "2ea3dba905b2c4e8.png": "\\frac{\\partial u}{\\partial\\nu}(x_{0})>0", + "2ea81225a5016f41.png": "\\frac{d}{dx}", + "2eac6b7e66fc4725.png": "z_{n}=re^{\\frac{2\\pi in}{N}}", + "2eade847f0461be7.png": "v=\\sqrt{\\frac{2q}{\\rho}}", + "2eae76ed47840fb1.png": "Z(s)=\\sum_{i=1}^{\\infty}e^{-\\lambda_{i}s}", + "2eae8985afff35c2.png": "\\int_{0}^{1}-ln(x)f(x)dx", + "2eaf02c3b01430ec.png": "\\frac{du}{ds}=0", + "2eb16bc55277a15a.png": "c^{\\prime},(v\\ll c^{\\prime})", + "2eb35cfdb38a6667.png": "\\frac{\\partial C}{\\partial\\sigma}", + "2eb5bffda56fea15.png": "\\frac{dE}{ds}=\\frac{dR}{ds}N(s)", + "2ebaf5fa47b12dee.png": "\\frac{1}{q}=\\frac{1}{R}-j\\frac{\\lambda}{\\pi w^{2}}", + "2ebcfbc3883e4f59.png": "W=\\int_{a}^{b}PdV", + "2ec5f1c8e78f0911.png": "|4d,m_{2}\\rangle", + "2ec70128a3964337.png": "v=\\sqrt{\\frac{2eU}{m_{0}}}", + "2ec86cde2ecaebae.png": "c^{\\prime},(v\\ll c^{\\prime})", + "2ec9b653470cb6c4.png": "\\overline{d}(A)", + "2ed0b82cd4d947f3.png": "O(|w_{k}|^{2})", + "2ed415449af1d45f.png": "\\frac{d}{dt}log_{e}t=\\frac{1}{t}", + "2ed54c4762cedb22.png": "\\prod_{i\\ne\\beta}X_{i}", + "2edaccab2f73b294.png": "\\sigma_{n}(A)=1/2", + "2edf40d2e393fb53.png": "T_{0}+1,T_{0}+2,...,T", + "2ee2503760a948d0.png": "\\hat{e}_{z}", + "2ee26568f8a8102f.png": "\\gamma(n)=\\prod_{p|n}p", + "2ee858921e265373.png": "c^{(1)}(t),c^{(2)}(t)", + "2ee96e902faa8c7c.png": "\\alpha_{i}^{2}=\\beta^{2}=I", + "2eece627a082fcbc.png": "x\\notin L", + "2eeebde22731c8d4.png": "\\prod_{s\\in S}(1+X_{s})", + "2ef84f2e5fe3a6dc.png": "\\frac{K_{i}}{K_{d}}=\\omega_{0}^{2}", + "2f08af5913e4e7eb.png": "\\{\\begin{matrix}7\\\\ 7\\end{matrix}\\}", + "2f0ec30d9552afdd.png": "c\\sqrt{n}", + "2f18858389b36ed5.png": "V(x)=-\\int w(x)dx", + "2f18ba47d494f8e2.png": "\\rho_{(z_{\\nu})}", + "2f1a7d0fffa348a5.png": "\\sum_{i=1}^{N_{\\lambda}}m_{i}=N_{v}", + "2f1d82ae2e9fa339.png": "(\\sqrt[5]{\\frac{p_{f}}{p_{i}}}-1)\\times100", + "2f1f0d82e1f3ba63.png": "*1=\\{*0\\}", + "2f223a11f687a358.png": "\\int_{0}^{t}p^{\\prime}(s)p(t-s)ds", + "2f2778bc15e4a65a.png": "\\tilde{M}", + "2f2c745f587f3da8.png": "\\hat{I}_{\\pm},\\hat{U}_{\\pm}", + "2f2c8b8bc9808ad7.png": "A^{-1}JA=J", + "2f2dc8a9c3fa55e9.png": "H_{f}(a)=f^{-1}(a).", + "2f33581d689e404d.png": "\\frac{d^{2}y}{d^{2}t}", + "2f36b8c80ec4d09c.png": "S=\\int_{a}^{b}x^{x}dx", + "2f3b2f7dade9dfc9.png": "R[R],G[G]", + "2f3fcf023753c16c.png": "\\{i,j\\}\\notin E", + "2f471d2b6d4db45b.png": "\\int_{S}fd\\mu", + "2f49b821cf97d387.png": "\\int_{a}^{b}k(s)ds", + "2f4a36e8076b93af.png": "((\\begin{matrix}2n-2\\\\ n-1\\end{matrix})/n!)^{2}", + "2f4b7f65aed081db.png": "\\zeta_{R}(s)=\\sum_{z=1}^{\\infty}\\frac{R(z)}{z^{s}}", + "2f4ef22777084827.png": "bk_{B}T-2a", + "2f5273c54d17dbfa.png": "G=\\int_{0}^{T}k(t)x(t)dt", + "2f53b729538ba0a5.png": "\\frac{3+103^{285}}{141^{295}}", + "2f54c9af0e5dc9d1.png": "x+y=-13", + "2f56f4ecd86df384.png": "\\tilde{w}=f(\\tilde{X},\\tilde{Y})", + "2f595632ba78be74.png": "1-1/e", + "2f5d314608e1b6e7.png": "\\pi\\int_{l_{1}}^{l_{2}}f(x)^{2}dx", + "2f60b2de24259419.png": "\\theta_{min}\\approx\\frac{CD}{AC}=\\frac{\\lambda}{W}", + "2f677174235012f9.png": "\\Delta T(t)=\\Delta T_{0}e^{-t/\\tau}", + "2f6795b243734524.png": "10^{1,000,000n}", + "2f6a0129830827a0.png": "(c:a:a):4_{2}\\odot\\tilde{ac}", + "2f6a0a7daadfbf8b.png": "n=n_{0}-\\frac{4n_{0}}{m^{2}}", + "2f6e43526429dcf3.png": "p=-\\frac{1}{\\sqrt{3}}z", + "2f6f2b8d06b09f17.png": "|0|<|1|+|-2|", + "2f740ff613b3faaf.png": "\\frac{dy}{dt}", + "2f744f1805e3b8fc.png": "{(\\nu^{\\phi})}^{\\alpha}", + "2f74774c3b68b72d.png": "I(t)=I_{0}\\cdot e^{-\\frac{R_{2}}{L}t}", + "2f76a00c99d5b084.png": "|\\overline{AJ}|=\\frac{2}{\\pi}r", + "2f7e8f08030271c7.png": "\\hat{H}", + "2f85b146f240b79a.png": "\\hat{q}", + "2f85d0e0e6c8ccf5.png": "||x||>\\gamma_{2}", + "2f8ac07a397277c4.png": "\\hat{P}^{2}", + "2f8da195910fc49c.png": "(\\begin{matrix}m\\\\ n\\end{matrix})", + "2f8ddfa1d81ba73d.png": "\\sum_{k=1}^{n}F_{k}^{2}=F_{n}*F_{n+1}", + "2f927b0c348c2634.png": "\\underline{x}_{0}", + "2f93f3667124328b.png": "A(<\\lambda)", + "2f967d56c973c8a4.png": "P^{D}(\\tilde{t}_{i})", + "2f9a2bf6a7dd618a.png": "(\\begin{matrix}0&-1\\\\ 1&0\\end{matrix})", + "2f9c070f5b759339.png": "L(M=i)=[m\\le i]{(\\begin{matrix}i\\\\ N\\end{matrix})}^{-1}", + "2fa21b82c3342652.png": "V_{D}=V_{DD}-IR", + "2fa8f483ee52ecbc.png": "|arg\\sqrt{-\\mu_{j}}|<\\frac{\\pi}{4}", + "2fac583eb3eb429c.png": "y^{2}=b^{2}-\\frac{b^{2}x^{2}}{a^{2}}", + "2fade6590cdb2c5c.png": "\\frac{db}{dt}=\\frac{1}{3}", + "2fae5d1f65515fd3.png": "\\prod_{i\\in I}R_{i}", + "2fb2754d9cec2c2a.png": "\\overline{op_{1}}", + "2fb3c7d855be5421.png": "\\tilde{A}_{8}", + "2fb659ecf3c5aa1a.png": "N\\models\\varphi(\\underline{\\#(\\theta)})", + "2fbc0022364b6baa.png": "\\hat{S}_{N}", + "2fbc243919b63349.png": "\\gamma_{m}^{j}", + "2fbfe1dacba023b2.png": "V_{j^{n}(\\kappa)}", + "2fc3897974419339.png": "\\dot{m}_{out}=K\\cdot C(4)", + "2fc4aca5dff7c84a.png": "m(t)=\\frac{1}{2(t+1)}", + "2fc4dcf0b30c0030.png": "\\tilde{O}(n)", + "2fc4eadae38990b6.png": "[\\begin{matrix}0&-1\\\\ 1&1\\end{matrix}]", + "2fc7f9515db83296.png": "\\int_{|z|=r}f(z)dz", + "2fca3209128cf7ac.png": "E=1-\\frac{T_{Low}}{T_{High}}", + "2fcd840c05379e3d.png": "(\\begin{matrix}2n\\\\ n\\end{matrix})=\\sum_{i=0}^{n}(\\begin{matrix}n\\\\ i\\end{matrix})^{2}", + "2fd4528f9e77d3ce.png": "a/\\sqrt{a^{2}}", + "2fd84b73d657f4ca.png": "\\frac{dh}{dt}", + "2fd84f38f9301111.png": "log\\hat{\\lambda}\\approx Z\\sqrt{4/D}", + "2fda90452408af80.png": "A=\\underline{m}", + "2fdab8df85049eed.png": "H=(\\begin{matrix}1&-1\\\\ -1&1\\end{matrix})", + "2fdfa01e3ee17d47.png": "E_{p,q}^{2}=H_{q}(F)", + "2fe001220659dfe1.png": "\\Xi_{q}^{z}", + "2fe1069314a9327d.png": "E\\{\\hat{x}-x\\}=0", + "2fe249e961a88e04.png": "-\\frac{1}{10}\\pi^{2}-ln^{2}\\phi", + "2fe41b0fe993ddf2.png": "\\neg\\psi\\vee\\neg\\varphi", + "2fe45d122523d22e.png": "\\bigcup_{i}F_{i}(\\lambda)=I(\\lambda)", + "2fec63cefc210bcc.png": "p=-\\frac{\\partial U}{\\partial V}", + "2fee5032084ff53f.png": "\\overline{\\theta}_{n}=\\int_{-\\infty}^{\\infty}tdH_{n}(t)", + "2ff326f502f18d38.png": "D_{n-1}=\\sum_{j=1}^{n-1}\\frac{\\partial}{\\partial x_{j}}", + "2ff3f6439c43f96f.png": "c^{\\aleph_{0}}", + "3001fd7c37198b30.png": "\\tilde{r}", + "30035b5ed4bf1bc7.png": "\\tilde{\\sigma}", + "3004a0dec6aabaa4.png": "\\hat{p}=1", + "300662483ed99896.png": "M=(\\begin{matrix}1&-1\\\\ 0&0\\end{matrix})", + "300da92d5a21b2a1.png": "\\sqrt{i}=\\pm(1+i)/\\sqrt{2}", + "3010fb7e69d9e4cc.png": "\\sqrt[3]{0.125}\\cdot10^{-e^{\\pi i}}", + "30244fd7560719be.png": "\\frac{\\partial f}{\\partial y}", + "30246d8c411dc847.png": "\\hat{t}", + "30262b663de923e2.png": "\\int f(x)d\\alpha(x)", + "3027243c7f82eb67.png": "2^{\\aleph_{0}}", + "3033e3bd8c56064b.png": "\\tilde{A}_{4}", + "3035228607538023.png": "u\\notin\\Phi(V)", + "30380a28d3e2c7bc.png": "0\\le\\underline{d}(X)\\le\\overline{d}(X)\\le1", + "303ad345047d84e8.png": "x+y,xy,-x", + "303f000d364a206e.png": "J=[\\begin{matrix}0&1\\\\ -1&0\\end{matrix}]", + "3040317ea853fe14.png": "|A|-1", + "3043e4dad8c08886.png": "AM", + "304b140333d652de.png": "X=e^{\\mu+\\sigma Z}", + "304c5bf04f2b2f83.png": "(p_{1},p_{2},p_{3},E)", + "304fde49e2e3b479.png": "h(z)=h_{1}(z)(z-c)", + "305c0bbe921b6510.png": "S_{gen}^{\\prime}=\\frac{Q_{2}^{\\prime}-Q_{1}^{\\prime}}{T_{surr}}", + "305e508956ce573c.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=(\\begin{matrix}n-1\\\\ k\\end{matrix})+(\\begin{matrix}n-1\\\\ k-1\\end{matrix})", + "3063f950bdd1c86f.png": "\\frac{\\partial V}{\\partial h}=0", + "30662a2f5ba0ffa8.png": "\\hat{\\epsilon}=\\frac{D_{0}}{E_{0}}=|\\epsilon|e^{-i\\delta}", + "306ae54a258751ee.png": "k=\\frac{\\partial^{2}V}{\\partial Q^{2}}", + "3071b8fc7636c822.png": "\\frac{F}{\\epsilon^{D}}\\cdot\\epsilon", + "30774785ebc549b9.png": "\\int\\frac{\\delta Q}{T}", + "30779912a05570ec.png": "\\epsilon_{0}(\\rho,R,L)", + "307dd1616181b024.png": "\\sqrt{\\tilde{p}}-\\sqrt{\\tilde{q}}=\\sqrt{r}", + "307ffcc255cb91b2.png": "z=sqrt((-1/3)^{2}-1)", + "308310879777a87f.png": "(x*(x*y))*y=0", + "308a06e7a5445a04.png": "n_{sp}=\\sum y_{i}", + "308ba1bec068e8bf.png": "(5+4)-(2+3)", + "308e8a56d16a46de.png": "\\int I(q)q^{2}dx", + "308e97148ad3a4e1.png": "\\frac{De}{Dt}=T\\frac{Ds}{Dt}-p\\frac{Dv}{Dt}", + "308f4a7c1a601b9e.png": "(\\begin{matrix}r^{-1}&0\\\\ 0&r^{-1}\\end{matrix})", + "3090f2aeb24835d4.png": "\\chi_{+}^{-k}=\\delta^{(k-1)}", + "30990e1c6ecf322a.png": "\\bigcup_{i}A(x)\\oplus t_{i}=R", + "3099431e3fcf807f.png": "\\int\\Delta f=0", + "30997e4e027d30e3.png": "S", + "309cd4385254112a.png": "f(\\langle x_{0},1\\rangle)", + "309e0e502b8cc062.png": "P(D)y=f(x)", + "309f2c6017173335.png": "[A]-[B]+[C]=0", + "30a267036f6286f4.png": "\\int d^{4}p/(2\\pi)^{4}", + "30abf68a88205735.png": "R_{fu}=-C_{R}\\rho m_{fu}\\frac{\\epsilon}{k}", + "30addf9aa19a89c6.png": "(P,M)\\rightarrow^{*}M^{\\prime}", + "30af0fbcc4adcd49.png": "\\int_{S}1dS", + "30b22599459ef04d.png": "sl_{3}(K)\\oplus sl_{3}(K)", + "30b86c7bcd9a8dd7.png": "[\\begin{matrix}3&7&2\\end{matrix}]", + "30c36d0e3e6da77d.png": "(\\begin{matrix}m\\\\ n\\end{matrix})", + "30c38f2ef67410f4.png": "10^{-12}W/\\sqrt{Hz}", + "30c7eb771ce73d6f.png": "\\epsilon=2\\nu\\langle E_{ij}E_{ij}\\rangle", + "30cbf045fbfcf58b.png": "S=\\int ds", + "30cdd952af688f6d.png": "[\\begin{matrix}b/d&p\\\\ c/d&q\\end{matrix}]", + "30d13c92851cc44f.png": "\\int dx=x+C", + "30d2d65e6f6d8bbb.png": "\\frac{ds}{dt}", + "30de697180179c1b.png": "-i\\hbar\\frac{\\partial}{\\partial x}", + "30e31402ad5c75b0.png": "B=\\prod B/I_{i}", + "30eb07fa4fa03d14.png": "B(z)=1+zB(z)^{2}", + "30eb8b32bf1860e7.png": "P\\hat{B}+\\hat{B}P=0", + "30ec5ccbb1cdf32d.png": "S=\\sum_{n=0}^{N}(N-n)", + "30ed878ef7f1745f.png": "A_{1}=\\frac{P}{\\sqrt{2}}", + "30eef1dc93922a91.png": "Qf=\\int fdQ", + "30f0f5343528f4e5.png": "L_{\\rho}(\\gamma)=L_{\\rho^{*}}(\\gamma^{*})", + "30f358debe306899.png": "W=\\int Fdr", + "30f60904fc42455d.png": "(\\begin{matrix}2\\\\ 6\\end{matrix})", + "310005f30916c47b.png": "\\int_{X}fd\\mu", + "3110880970621b95.png": "\\frac{e^{hk-\\lambda e^{h}}\\lambda^{k}}{k!}", + "31218661eeaa6ba8.png": "(\\begin{matrix}m+1\\\\ k\\end{matrix})", + "31245334addcbf1f.png": "k=0,.....,n-1", + "312b1a8b3dbc0e86.png": "\\theta_{k}^{b}", + "312de4d5b84f9ec1.png": "z^{3}-z^{2}-z-1=0", + "312e679ca813c9ed.png": "B_{p}=\\langle s,h_{p}\\rangle", + "3131ea4fc32757a7.png": "P_{\\mu}P^{\\mu}|\\phi\\rangle=M^{2}|\\phi\\rangle", + "31350484a696793d.png": "2+\\sqrt{2}+\\sqrt{6}", + "3137c805d194867e.png": "Q:2^{X}\\longrightarrow2^{R^{n}}", + "3138c892b131e0e7.png": "L\\in S_{2}^{P}-SIZE(n^{k})", + "3138ded4c4c8fe51.png": "f=\\frac{\\omega}{2\\pi}=\\frac{1}{2\\pi\\sqrt{LC}}", + "313c932f97f0b100.png": "(\\begin{matrix}X+n-1\\\\ n-1\\end{matrix})", + "314235193833f006.png": "\\frac{\\partial B}{\\partial G}", + "3143e398adfbe9dc.png": "\\hat{\\omega}_{i}(t,\\omega)", + "31444b5f7cb0cce3.png": "\\hat{a}_{2}", + "31452385053804d4.png": "(\\begin{matrix}i&0\\\\ 0&-i\\end{matrix})", + "31488db381841c4e.png": "L_{n-l-1}^{2l+1}(\\rho)", + "314e49f06926c7d5.png": "\\frac{\\partial X_{M}}{\\partial x_{n}}", + "3150721195d2c3f8.png": "S\\approx L_{ISCO}+S_{1}", + "315c5ea70ff50657.png": "Y=\\{Y_{1},Y_{2},..,,Y_{l}\\}", + "3160414d73d29e86.png": "\\alpha\\approx\\frac{at_{0}\\Delta_{SO}}{\\Delta_{BG}}", + "3164a7b2b91ac13c.png": "\\sqrt{2}a", + "3166065e31df0b2e.png": "Y=\\{Y_{1},Y_{2},..,,Y_{l}\\}", + "3166c532c041126e.png": "T=\\frac{P/B}{k_{B}}", + "3167353287f74069.png": "\\nu=0,\\pm1,\\pm3,\\pm4", + "316822464a8bc7f4.png": "\\frac{dy}{dx}", + "31683e134f190fe6.png": "Q=D", + "31728028e4c6d5e9.png": "X:=\\bigcap_{n=1}^{\\infty}X_{n}", + "3173586e7a47458f.png": "A=[\\begin{matrix}2&1\\\\ 1&2\\end{matrix}]", + "31737ff0d8216052.png": "\\partial C/\\partial Y_{d}=b", + "31744598baea6e22.png": "W=\\int_{1}^{2}Fdx", + "318157f8e3c6ba6c.png": "\\int_{E}|f|<\\epsilon", + "3181eee2685004a6.png": "\\frac{y^{\\prime}}{x^{2}}-\\frac{2y}{x^{3}}=0", + "318659efcf070cb6.png": "R_{0,1}=2.405", + "318df792db87330a.png": "R=[\\begin{matrix}W&X\\\\ Y&Z\\end{matrix}]", + "318f2994adcd31a6.png": "sin\\alpha=(\\frac{w}{l})", + "319101d5bdf8ad71.png": "\\frac{\\partial\\nu}{\\partial S}", + "3191eaeff97b2621.png": "G=\\int_{0}^{T}S(t)x(t)dt", + "31939ec9aee8391e.png": "u_{J}(x,y)=x^{a}y^{1-a}", + "3193e450894b5d34.png": "\\frac{d}{b}=\\frac{c}{a}=k", + "319dcaaf76aa63f2.png": "xa^{m}b^{n}yc^{m}d^{n}z", + "319f2931bf50d4cc.png": "(\\begin{matrix}4\\\\ 2\\end{matrix})", + "31a2685966359e08.png": "x\\mapsto\\prod_{i=1}^{n}w_{x}(i)", + "31a2c5d8b7721169.png": "\\frac{(2b^{2}+2c^{2}-a^{2})}{4}", + "31a5b369a4ee2d3c.png": "q_{y=0}=1-\\hat{y}", + "31af108f231a2121.png": "\\int_{\\gamma}f(z)dz=0", + "31b42dd753caab16.png": "\\rho g(r)dr=dn(r)", + "31bdba329df76a3d.png": "\\hat{t},\\hat{\\omega}", + "31c0b6722b2c4e46.png": "\\int_{1}^{\\infty}x^{-x}dx", + "31c6581176b78741.png": "V_{Y0}t=h", + "31c784415693763f.png": "\\hat{\\rho}", + "31c8bbcb4db8d494.png": "\\pi_{i+j}A", + "31d14bb5d21338f3.png": "f(u)=\\beta_{1}+\\beta_{2}e^{-u}", + "31e08a4b29c6a8b9.png": "p_{s+1,l}(z)", + "31e341b0f3c87a74.png": "\\int_{0}^{\\infty}\\frac{sin(x)}{x}dx", + "31ed63232097ee64.png": "B=(\\begin{matrix}0&1\\\\ 0&0\\end{matrix})", + "31edff5ee612d0db.png": "(\\begin{matrix}k\\\\ 2\\end{matrix})-m", + "31efbb8ae280d6a0.png": "E_{p,m}=\\frac{1}{2}LI^{2}", + "31f594cf7f3b6c29.png": "((a,b),[\\infty])\\notin I", + "31fd559ed617f335.png": "-\\overline{u^{\\prime}v^{\\prime}}", + "32028679be2cf633.png": "W(dx)=dx/(\\pi x^{2})", + "3215b7957c753e37.png": "\\int_{X}dxf(x)", + "321c6db6b777ba0f.png": "P=\\frac{E}{t}=\\frac{1}{2}A\\rho v^{3}", + "3224f086b456e697.png": "\\int\\frac{dx}{lnx}", + "32289b04639d787e.png": "\\Delta\\vec{F}=A\\Delta\\vec{p}", + "322c77efb1125fb7.png": "(\\begin{matrix}1&2\\\\ 2&4\\end{matrix})", + "3230b385cff24662.png": "\\alpha\\rightarrow\\beta_{1}|\\beta_{2}", + "3234d80bdbe148fa.png": "(\\begin{matrix}S_{11}&S_{12}\\\\ S_{21}&S_{22}\\end{matrix})", + "3236c09239667f3a.png": "k\\notin S", + "323c4e4d8d657b23.png": "w^{\\prime\\prime}=\\frac{d^{2}w}{d^{2}x}", + "324a1cc792f548f9.png": "H_{i+1}/H_{i}", + "324abc6fa28e94ba.png": "\\frac{d^{n}}{dx^{n}}", + "324b9bd8a0c71bc4.png": "(\\begin{matrix}n\\\\ 4\\end{matrix})", + "3258ba3d4ce98b43.png": "x,x-20", + "3259159125852e61.png": "\\hat{\\alpha}>0", + "325b80620dd60db4.png": "-D_{1}\\frac{\\partial C_{1}}{\\partial x}", + "325c531a2b421e2f.png": "\\overline{M}=|M|e^{i\\theta}e^{-i\\phi}", + "325dd4083494dac9.png": "v_{(G;c)}(\\{1,2\\})=16", + "32683988a79f0d61.png": "A\\underline{\\delta}B", + "326adc20cb2f651f.png": "-j\\frac{\\sqrt{2}}{2}", + "326b7ec7189943ef.png": "X^{u5}", + "326cf648363dd46a.png": "i=\\frac{d}{1-d}", + "327c47a40b631c05.png": "J=\\int f(t,x,y)dt", + "3289b09b32b6ea4e.png": "P_{TOT}=\\frac{3V_{P}^{2}}{2R}", + "329075579159f5f3.png": "S=\\frac{\\pi}{3}k_{B}^{2}Tn(E_{F})", + "32930126f5244eef.png": "E(\\underline{x}|y)", + "32930b6f2e3dcb87.png": "\\sqrt{-1}", + "32958b2fd5d57f38.png": "\\theta_{0}=2\\pi r_{0}^{2}H_{0}", + "3295bc3090c080ee.png": "(r\\times v)_{z}<0", + "3299a22f1bb0a0c5.png": "A_{1}=B_{1}=0", + "329daa0cf64528b6.png": "f^{*}(x)-L", + "329dfd9ab8d6698f.png": "(\\begin{matrix}4\\\\ 2\\end{matrix})", + "32a640b5e4ee8117.png": "\\sqrt{\\eta}", + "32ae8ad07351b689.png": "\\{(x_{j_{n}},f(x_{j_{n}}))\\}", + "32b0bc9fe74e5c43.png": "E=\\int Fudt", + "32b73ea41b526ee7.png": "I>10^{-1}", + "32ba21c2600a39ec.png": "[\\begin{matrix}4&4&7\\\\ 6\\end{matrix}]", + "32d4c515d69edc19.png": "\\frac{P_{f}}{P}=\\theta", + "32d51e9d1b2e5516.png": "n=(\\begin{matrix}2k-1\\\\ k\\end{matrix})", + "32d969a015c56650.png": "k", + "32ed32f2f4d42521.png": "\\overline{O_{R}P}", + "32ed62c5ce66e93a.png": "EC=(\\begin{matrix}I_{r}\\\\ 0\\end{matrix})", + "32ef4a652fbe674d.png": "U=\\int f(v)E(v)dv", + "32f2a7873a503251.png": "\\sqrt{\\pi}=\\pm\\sqrt{\\pi}", + "32f48c283b7be2dc.png": "\\tilde{\\psi}(t)", + "32f84f40bfb7af87.png": "R(r,s)\\le(\\begin{matrix}r+s-2\\\\ r-1\\end{matrix})", + "32f9489163c48810.png": "\\nabla_{i}\\nabla_{j}\\varphi=\\nabla_{j}\\nabla_{i}\\varphi", + "3309db66324c8a33.png": "\\frac{d}{da}", + "330aa9ffffcb64fb.png": "\\hat{2}", + "3310f01e1dbc9e86.png": "\\tilde{A}_{9}", + "33141771f5893107.png": "e=\\sum_{n=1}^{N}(z_{n}-\\hat{z}_{n})^{2}", + "331735c2b0d3d90f.png": "E_{e}^{-}=X", + "3317b5587b06ba29.png": "G_{k}(s)=\\frac{k-1+s}{k}", + "3317cceb7ef763f0.png": "R_{U}\\in R_{U}\\iff R_{U}\\notin R_{U}", + "3318f299c6842f19.png": "n^{\\underline{n}}=n(n-1)(n-2)\\cdot\\cdot\\cdot1", + "331a96068a72bee0.png": "c_{w}=(\\frac{\\lambda_{1}-\\lambda_{2}}{\\lambda_{1}+\\lambda_{2}})^{2}", + "331c4928b7530066.png": "2r(X)+r^{\\prime}(\\sqrt{X})", + "331f8a1d1b993fe2.png": "\\{1,x_{0},x_{0}^{2},...\\}", + "331ff50b4a6532b5.png": "F=\\prod_{i=1}^{K}f_{i}", + "33211393b306f241.png": "PQ", + "33255bcf1d88c019.png": "N=[\\begin{matrix}A&B\\\\ 0&C\\end{matrix}]", + "3326207c50bd7ac4.png": "\\int f(t)dt=0", + "332d950e5abdd07a.png": "7-5\\sqrt{2}=-0.07106...", + "332dc85a6b3abeec.png": "\\omega=\\frac{\\partial u}{\\partial z}", + "332f6c34d402cbc1.png": "\\nabla F=\\underline{0}", + "333234c439ca1ad1.png": "L_{n}(x)=L_{n}^{(0)}(x)", + "3332f18f874805ff.png": "2\\pi/c_{ij}", + "3337827343da9a83.png": "(\\begin{matrix}x&y\\\\ z&v\\end{matrix})", + "333c3febf5e68490.png": "\\lambda=\\sqrt{\\frac{r_{m}}{r_{i}+r_{o}}}", + "33418be88e0505c1.png": "G=(\\frac{c^{3}}{M_{U}})t", + "3344be711db985c3.png": "argmax_{W}\\prod_{v\\in V}P(v)", + "33454d522cd6aac2.png": "\\tilde{G}_{2},\\tilde{F}_{4},\\tilde{E}_{8}", + "334591348a551ee2.png": "L_{1}:U_{1}\\rightarrow C", + "334e32fe73154bc0.png": "S\\subset[\\omega_{1}]^{\\omega}", + "334ea33bd76a726f.png": "q=\\hat{q}", + "33539fb19082afdf.png": "u_{g}=\\frac{1}{f}\\hat{z}\\times\\nabla\\phi", + "33574d8ba61e17ee.png": "\\frac{dX}{dt}", + "3366529fc1bb5c2a.png": "H^{1}(X,O_{X})", + "33693aa20270a056.png": "\\underline{w}=(s_{i_{1}},s_{i_{2}},...,s_{i_{l}})", + "3369e8131b1ba65a.png": "\\frac{W^{2}}{L\\lambda}\\ll1", + "336b5abfbff9f03d.png": "A||_{+}B", + "336b8a36b92e1ca3.png": "F^{*}(s^{*})", + "3380a2d493974727.png": "F(\\nu)=\\frac{8\\pi h\\nu^{3}}{c^{3}}", + "3380cc87292a393c.png": "\\hat{v}_{i}", + "33821ab367bfda86.png": "M=(\\begin{matrix}-i&i\\\\ exp(it)&exp(-it)\\end{matrix})", + "3386cf23a3c879f2.png": "\\mu_{ij}^{0}:=exp(\\beta Q_{ij})", + "338797c132fb92c9.png": "\\frac{dR}{dP}=0", + "338d2a39b3197124.png": "\\hat{f}(x)", + "33903917ebaf62e3.png": "\\hat{f}=e^{-\\pi\\xi^{2}}", + "3390c598be2aaf68.png": "\\overline{MR}", + "3393499f769d871d.png": "Y=\\hat{X}\\beta+noise", + "33951f4d81ed329f.png": "\\tilde{L}_{i}", + "3397c0392f075607.png": "p(\\cdot;\\theta+\\Delta)", + "339d99382667dbee.png": "(A\\backslash Y),B,C", + "339e460b32d50d19.png": "y^{\\prime}=(y_{1}^{\\prime}...y_{N}^{\\prime})", + "33a0a6bdd3e25083.png": "x^{(s)}exp|\\alpha^{(s)}|<1", + "33a3d13ffdd6a171.png": "g_{j}=1\\pm\\frac{g_{S}-1}{2l+1}", + "33a4168daf9d509e.png": "\\mathbb{E}", + "33a5ad6604543f8c.png": "\\frac{1}{\\frac{1}{88}-\\frac{1}{365.24}}\\approx116", + "33acd53314415649.png": "\\}", + "33b7b6312b53a4aa.png": "-\\lambda v=ma=m\\frac{dv}{dt}", + "33bf0b8046bca7d0.png": "FV(xy)=\\{x,y\\}", + "33c0074de5cb3a41.png": "(\\begin{matrix}0&-1\\\\ 1&a\\\\ \\end{matrix})", + "33c1103ca9d956b7.png": "\\Sigma r(Q_{0}+\\Delta Q)^{n}=0", + "33c12017ef3c8732.png": "(A\\backslash Y),B,C", + "33caa9f06d86c3e5.png": "-D_{1}\\frac{\\partial C_{1}}{\\partial y}", + "33cc2e96191942f2.png": "P_{2}=(1/10)-\\epsilon", + "33cce06265de1551.png": "\\varphi\\vdash\\neg\\psi", + "33d422ec0a626de1.png": "(\\begin{matrix}13\\\\ 4\\end{matrix})", + "33d437cc1a2fda68.png": "\\{\\begin{matrix}3\\\\ 7\\end{matrix}\\}", + "33d9b63fb23e6d37.png": "J^{2}=j(j+1)I_{2j+1}", + "33dc20ad0ab3361a.png": "[\\begin{matrix}2&2&4\\\\ 3&5\\\\ 6&6\\\\ 8\\end{matrix}]", + "33e9440b820872db.png": "=60\\int_{0}^{2\\pi}d\\theta", + "33e99f8e59aa4bb8.png": "(f(-t)=-f(t))", + "33ef53eba68ad9cc.png": "\\epsilon\\sim exp(1)\\cdot q_{sig}\\cdot\\epsilon^{\\prime}", + "33efb6ac9c5f0ac0.png": "\\frac{dL}{dt}", + "33f373b1ff4614ed.png": "G(\\tau=0^{-})", + "33f67e792bd9a386.png": "2^{7}+17^{3}=71^{2}", + "33f8f0b601991f41.png": "(-3)!!=-1", + "33f92b5ee3f76cb1.png": "\\overline{z}=\\frac{1}{N}\\sum_{n=1}^{N}z_{n}", + "34047231892b7746.png": "\\int_{0}^{\\infty}f(x)dx", + "3406865e7d938e9d.png": "s=\\int\\frac{dt}{r(t)}", + "34092a1dde36e3b8.png": "N_{3}(k)=4\\pi k^{2}", + "340e8ebbafa57c07.png": "\\tilde{w}(t)", + "3413770847bc463b.png": "Y^{l}=Y_{1:ymid}", + "3413bd7a07b690ba.png": "\\varphi", + "3414491a9f664332.png": "H[w_{1},...,w_{n}]|J|", + "3415cf2832129663.png": "f(x)=C_{1}e^{-\\pi x^{2}/\\sigma^{2}}", + "3415da5c86679f51.png": "|A_{i}|=r^{l_{n}-l_{i}}", + "341a366da497cc34.png": "\\frac{d}{dz}w=w", + "34219f81e15b779d.png": "\\frac{5}{36}+\\frac{1}{24}\\sqrt{15}", + "3424588af1ce1331.png": "\\hat{t}<0", + "342f08fdeb6431d9.png": "\\partial_{y}=\\frac{\\partial}{\\partial y}", + "342f7341e21e4872.png": "\\frac{d\\rho}{dr}=-\\frac{\\rho(r)g(r)}{\\Phi(r)}", + "3431c1113ebebedf.png": "V=(\\begin{matrix}1&-1\\\\ 0&1\\end{matrix})", + "3439dcf65c84f547.png": "\\frac{dt}{dU}=0", + "344348d977f24af3.png": "(v^{\\prime}-1)^{m}=v^{k}", + "34447c2538f0464d.png": "\\bigcap\\{\\overline{B}_{0}:B_{0}\\in B\\}", + "3445453e686f33db.png": "(10^{n}-1)*7/9", + "34467f6803171918.png": "\\hat{m}_{-}", + "34490d04894d19ce.png": "\\hat{r}", + "34503aa0e406bd99.png": "Rv_{i}=\\tilde{\\lambda}_{i}v_{i}", + "3452d2c948cd2cfb.png": "\\tilde{X}^{n}", + "3452d3c16538e118.png": "var(p)=\\frac{p(1-p)}{n}", + "3458c21f007dce7a.png": "\\sqrt{c}", + "345d153e3f81f22e.png": "\\vec{C}\\rightarrow\\vec{t_{1}}", + "34616ac160875b80.png": "x=f^{k}(y)", + "3464b8925250824a.png": "n=\\prod_{i}p_{i}", + "3466540475a8fe77.png": "\\hat{h}", + "346826f2b0bb3a61.png": "[\\begin{matrix}1&0\\\\ 0&1\\end{matrix}]", + "3469a95f6ae4d3d2.png": "d_{e}(x_{e}+1)", + "346fb2dee480a04d.png": "\\underline{x}_{0}", + "347b0c79c3452621.png": "v(t)=I\\frac{dl(t)}{dt}", + "347dac75be74394f.png": "G(y)=\\int_{0}^{y}g(z)dz", + "347f6ad0b8f8beaa.png": "X=[\\begin{matrix}A&0\\\\ 0&D\\end{matrix}]", + "348044e41c7c4924.png": "\\tilde{\\eta}", + "3482225dfda96779.png": "\\tilde{X}\\rightarrow X", + "349acc95428b355f.png": "3n(n+1)^{2}", + "349afd5e606bb403.png": "q=p^{v_{p}(q)}\\frac{r}{s}", + "34ae3d4705ce109d.png": "C(v)=\\sum_{j=0}^{N-1}a_{j}a_{j+v}", + "34b488d7a9c5449f.png": "\\overline{M}", + "34b8f8b4fafa6b90.png": "0\\notin S", + "34bd38e18f59bb34.png": "F_{D}=\\frac{3\\pi\\eta Vd}{C_{c}}", + "34c3ae4015f0e899.png": "p=\\gamma(u)m_{0}u", + "34cbecdbc2ff8650.png": "\\prod_{n}(z-c_{n})", + "34d65cdf6a8d26e9.png": "(\\pi_{n}(t);n=1...N)", + "34d8056d62e414b4.png": "C_{E_{2}}^{J}=-\\epsilon_{1}^{1}\\epsilon_{2}^{3}/D", + "34e217de3566067f.png": "(m-M)_{0}=", + "34ec64715bbf0e8b.png": "8", + "34ee5d1a2dfd11e8.png": "A[v_{1}v_{2}]", + "34f03ad901dde533.png": "\\{(x_{n},f(x_{n}))\\}", + "34f0a1b5b361d61e.png": "F=\\sqrt{1-\\alpha}", + "34f15a318688acfd.png": "P_{C}^{\\prime}/a_{LC}^{\\prime}", + "34f855829f68db06.png": "f(x):=\\int_{0}^{x}\\omega", + "34f9990ef220cf87.png": "2^{-D^{\\epsilon}(\\rho||\\sigma)}\\ge\\frac{\\epsilon-\\delta}{\\epsilon}", + "34fbf375c515ba9a.png": "\\nu^{h_{5}}", + "34fea17c2d350ee3.png": "f(3,0.5)=0", + "34ff1e505b24b7f8.png": "f(t,n)=\\sum_{i=0}^{n}(\\begin{matrix}t\\\\ i\\end{matrix})", + "350919654f59bd0a.png": "j\\notin S", + "350f07f95f65f4b0.png": "J=-D\\frac{\\partial C}{\\partial x}", + "35134cb242d835da.png": "a_{\\overline{q}_{j}}", + "351b97726a7a37cf.png": "5x^{4}y-10x^{2}y^{3}+y^{5}", + "35231ea3f2f14996.png": "m=5/2+3/\\gamma_{2}", + "3524c00a6ade8017.png": "2^{2^{\\aleph_{0}}}>2^{\\aleph_{0}}", + "3525c640342da92e.png": "\\tilde{G}", + "353608a6728186b5.png": "c_{j,k}^{*}=\\frac{c_{j,k}}{\\lambda_{j}^{k}}\\Gamma(k)", + "3536f78d3beccca1.png": "f_{CC}(\\theta;\\mu,\\gamma)", + "353858015a1df7d9.png": "-m+\\frac{n}{2}1", + "3751218635f218e0.png": "u^{n_{w}}", + "37521487a270fd24.png": "A1:=28.552", + "3752ee30f3c620c1.png": "\\overline{ab}\\approx dx+\\frac{\\partial u_{x}}{\\partial x}dx", + "3752f258f38606b2.png": "\\sqrt{z}", + "375602eb2225870c.png": "P(X_{n}\\rightarrow X)=1", + "375b7280c8e8551b.png": "\\beta^{2}=var[U^{(i)}]", + "375cdfe17b6641bf.png": "\\int\\frac{dx}{S}=\\frac{2S}{a}", + "376106a0af70edc8.png": "(\\begin{matrix}a&b&b\\end{matrix})", + "3763eae900828f66.png": "\\sum_{n=0}^{\\infty}\\frac{n+1}{2^{n}}", + "37643a35a559dfd2.png": "\\omega^{2}=\\omega_{p}^{2}+k^{2}c^{2}", + "37646ed753b5c83f.png": "\\frac{\\partial q^{i}}{\\partial x_{j}}", + "376b507e578a4beb.png": "2^{n}(an+1)", + "376e460da11ce478.png": "M=\\frac{1}{9}[\\begin{matrix}1&1&1\\\\ 1&1&1\\\\ 1&1&1\\\\ \\end{matrix}]", + "376e889609791c70.png": "\\overline{O}=O", + "37739bfd4641fc7f.png": "(x+y)^{n}=\\sum_{k=0}^{n}(\\begin{matrix}n\\\\ k\\end{matrix})x^{n-k}y^{k}", + "377a717b2a239044.png": "D_{0}=(1,1494)", + "3780d44bc939a973.png": "T=\\sqrt{N_{0}/2^{k}}", + "3782d3e79e8b091e.png": "\\tilde{A}_{9}", + "378bbc703fe88bbf.png": "T_{\\hat{\\alpha}\\hat{\\dot{\\beta}}}^{\\hat{\\mu}}=2i\\sigma_{\\hat{\\alpha}\\hat{\\dot{\\beta}}}^{\\hat{\\mu}}", + "378edcce868a818c.png": "x=\\sqrt{y+(1/4)}-(1/2)", + "378f4a3c54637b72.png": "c\\sqrt{n}", + "3795e8c563b804f8.png": "(m-3)^{2}=\\frac{25|m|}{2}", + "379831ad1280754d.png": "(\\begin{matrix}2\\\\ 6\\end{matrix})", + "3799fbc0d149b148.png": "=\\prod_{k=1}^{n}[k]_{q}", + "379a82c12cc53c54.png": "s\\{\\begin{matrix}6\\\\ 3\\end{matrix}\\}", + "37a3baef98f554c2.png": "A=\\frac{1+2\\frac{M}{C}}{1+2\\frac{N}{C}}", + "37a51fdeb24c05fd.png": "dx_{u}:=\\prod_{j\\in u}dx_{j}", + "37a5b446c6f3e421.png": "(a/l)(\\nu/\\omega_{0})", + "37a8d24464d28790.png": "dS=\\frac{dQ}{T}", + "37b20dc4077e9daa.png": "\\frac{K_{i}}{K_{d}}=\\omega_{0}^{2}", + "37b246ff5457cd72.png": "w_{i}=\\frac{\\partial R}{\\partial a_{i}}", + "37bacc16e0acae19.png": "\\sqrt{K}", + "37bde400509421be.png": "r\\dot{r}=-\\frac{\\kappa}{2}r^{2}", + "37bf52bbe82c54e9.png": "(\\begin{matrix}m\\\\ r\\end{matrix})_{q}", + "37c34a9408b5d961.png": "(\\begin{matrix}x&y\\end{matrix})", + "37c3eac57401dad8.png": "g=\\epsilon_{0}\\chi^{(m)}H", + "37c77760758711f1.png": "\\alpha^{\\prime}(0):=v", + "37c7d43bf0875893.png": "e^{it^{T}\\mu-\\sqrt{t^{T}\\Sigma t}}", + "37ca9c029bf277f1.png": "\\mathbb{A}", + "37cc3862fcd008c9.png": "E=0,t_{B}=", + "37d6ea15f09d1d78.png": "\\int_{0}^{x}1dt=x", + "37de304613a8f7fb.png": "\\sum_{k=1}^{n}|b_{2k+1}|^{2}\\le n", + "37e067a94eb0ca93.png": "N_{\\alpha}^{l}", + "37e0d8f4b176db14.png": "\\tilde{F}_{4}", + "37e87ce83fc118e6.png": "\\langle r|\\Psi\\rangle=\\Psi(r)", + "37effc0a51de9aaf.png": "O((n/\\sqrt{\\epsilon})logn)", + "37f041060a2682a7.png": "AB=(\\begin{matrix}4&6\\\\ 6&2\\end{matrix})", + "37f5c8397b982f08.png": "2+2\\sqrt{2}", + "37f6fa659874d96e.png": "\\frac{\\partial T}{\\partial y}<0", + "37f94364881b6b17.png": "\\sum_{i,j\\in N_{i}}d(\\vec{x}_{i},\\vec{x}_{j})", + "37faee3eaf49daf0.png": "f_{S^{i}}^{\\lambda}", + "380072a81f076984.png": "\\sum_{n=0}^{\\infty}a_{n}x^{n}\\sim\\frac{1}{1-x}", + "380830df3b83b8b9.png": "\\hat{y}_{i}", + "3808fba4eee9b10a.png": "\\int dV|\\Psi|^{2}=N", + "380977021b828388.png": "B=\\frac{\\mu_{0}}{4\\pi}\\oint\\frac{Idl\\times\\hat{r}}{r^{2}}", + "3810333a50d02021.png": "\\{\\begin{matrix}5\\\\ 3\\end{matrix}\\}", + "38117ef970e02208.png": "\\frac{\\partial\\sigma}{\\partial K}", + "3812f92edeba292e.png": "\\int xcosxdx", + "38142b3c01ad3aee.png": "\\hat{v}^{*}", + "38160be30e36f34c.png": "1,\\frac{1}{2},\\frac{1}{3},\\frac{1}{4}", + "381b72a0f430980b.png": "C_{x}\\rightarrow C^{\\infty}(S_{i})_{x}", + "381de0bc70502ed1.png": "X_{\\mu>m-\\epsilon}", + "381f9c3fd4fe9067.png": "1/\\sqrt{2}(\\pm1,\\pm1,0)", + "382574fb6cccc3bc.png": "n=\\frac{i-r}{||i-r||}", + "382e5e678be9b9e2.png": "m=(n^{\\prime}-n)", + "38308a19019f60cb.png": "lim\\int f_{n}=\\int f", + "3833f83ec095324e.png": "{\\omega^{\\hat{m}}}_{\\hat{n}}", + "3834176b42b28439.png": "\\hat{R}_{m}", + "3834a627dd2369b4.png": "\\hat{f}(x)", + "38371facaa813340.png": "\\int pdq=nh", + "383d7f112181d1a8.png": "\\int f_{n}\\le\\int f", + "3840d7e6ce2aa876.png": "{\\lambda_{a}^{b}}^{\\prime}", + "3843498648734ed6.png": "A_{k+2}=(2k-\\lambda)A_{k}", + "3843e951e85ca06c.png": "|f^{\\prime}(p)|", + "3846563815e31394.png": "\\int cosxdx=sinx+C", + "384700fabda87a81.png": "log_{2}(26^{n^{2}})", + "384edee978137420.png": "\\frac{\\sqrt{2}}{12}", + "385096cfbb80a6fe.png": "\\hat{n}_{b}", + "3851fba43e47f93a.png": "H_{*}(C_{f},pt)=0", + "385bbb747337e46f.png": "\\int x^{k}d\\mu(x)=m_{k}", + "385f6f823bfb5f47.png": "\\hat{A}_{0}[f^{2}]", + "3863d80042285c0b.png": "\\sqrt{\\frac{1}{-1}}=\\sqrt{\\frac{-1}{1}}", + "38646004786ac7f1.png": "s\\{\\begin{matrix}7\\\\ 3\\end{matrix}\\}", + "3866a20eecbbc730.png": "-1=g_{\\mu\\nu}\\dot{x^{\\mu}}\\dot{x^{\\nu}}", + "3867eff89a1360f7.png": "\\overline{i}", + "386d4a6ad311667c.png": "\\frac{dP}{d\\tau}", + "3870bcb4bd89a930.png": "J^{(\\zeta_{9})}", + "387fa40fff77166c.png": "\\frac{3}{5}(N_{p}+N_{n})^{2/3}", + "3880dbd2f8f3fa0b.png": "\\{1,2,3\\}\\notin\\{1,2,3\\}", + "3884154a89137af8.png": "x\\mapsto\\prod_{i=1}^{n}u_{x}(i)", + "3884df47ef0c1c7e.png": "\\frac{f^{(n)}(b)}{n!}=a_{n}", + "3888ed06ed950e91.png": "\\Sigma_{i}=\\Sigma_{j},\\forall i,j", + "3891bf18b120e01f.png": "H_{*}(C_{f},pt)=0", + "389c951dc10915eb.png": "\\eta_{Carnot}=1-\\frac{T_{cold}}{T_{hot}}", + "38a72719629b8afa.png": "\\overline{L}^{\\dot{\\alpha}\\dot{\\beta}}=T^{\\dot{\\alpha}\\dot{\\beta}}", + "38a7339fd80f9bbd.png": "R_{E}=c/\\sqrt{4\\pi G\\rho}", + "38a7498ac2a2d07f.png": "\\hat{U}|\\psi_{i}\\rangle", + "38abfed21b36d591.png": "\\tilde{P_{n}}(x)", + "38ad7764bc550408.png": "\\alpha\\circ\\phi(g)=\\psi(g)\\circ\\alpha", + "38aded41e1eff9ae.png": "\\eta_{Carnot}=1-\\frac{T_{cold}}{T_{hot}}", + "38af6021d30711ae.png": "\\frac{2\\pi s}{h}\\frac{rh}{2}", + "38b7521a4711e4bd.png": "B_{v}=B-\\alpha(v+\\frac{1}{2})", + "38b9f3fde9847a0a.png": "m_{\\tilde{t}}", + "38ba50c9ec4a6c34.png": "Ff\\in L^{1}(R^{n})", + "38c91d02ebebaba7.png": "W\\underline{A}", + "38d08218b0a37c90.png": "2r(X)+r^{\\prime}(\\sqrt{X})", + "38d2946f97e6ba1c.png": "a^{i}b^{j}(ba)^{k}", + "38d6d41e5105bfe0.png": "A_{n}=[n,n+1)", + "38dd15648cb7d8f5.png": "[\\begin{matrix}4&7\\\\ 3&5\\end{matrix}]", + "38e4f75d4c6e8b7d.png": "\\int u(x,t)d\\mu", + "38e7a19b435d6b4f.png": "\\hat{T}(x)^{-1}\\hat{H}\\hat{T}(x)=\\hat{H}", + "38ea0b11e7a741eb.png": "v_{1}=(\\begin{matrix}1\\\\ 0\\end{matrix})", + "38eaed7825ba675c.png": "\\dot{y}=\\frac{dy}{dt}", + "38ef49d199e6ef62.png": "\\frac{d^{2}w}{dz^{2}}=f(z)w", + "38efa3e836b2eb1d.png": "\\pi_{i}\\ge0,\\sum\\pi_{i}=1", + "38f029dd9bfba97b.png": "Eq.2\\frac{d\\theta}{dx}=\\frac{M}{EI}", + "38f9900acd266c9b.png": "B_{\\rho}^{\\eta}", + "3900957519d42ee7.png": "\\frac{dx}{dt}=r\\pm x^{2}", + "390cb1f0387198c9.png": "-\\sqrt{\\frac{2}{35}}", + "390f41761c81a08e.png": "e_{a}=\\frac{\\partial}{\\partial x^{a}}", + "39129d8611caf215.png": "P=(I_{n}-A)^{-1}U", + "39148da012e4ea51.png": "(\\eta,\\sigma)\\in P_{1}\\times\\Sigma", + "391c97dead698532.png": "F(\\underline{x},-)", + "391e1b18a53a0025.png": "S:C^{\\infty}([a,b])\\rightarrow R", + "3920b70f784db815.png": "\\vec{\\rho}=(A^{T}A)^{-1}A^{T}\\vec{p}", + "39260bba68c50b88.png": "\\int_{-r}^{r}|y-s|dx", + "39274ea3cbf721f4.png": "\\int\\Psi\\Psi^{*}dV=N_{s}", + "392d4fa4718edcde.png": "b^{(t_{j})}", + "392faa3d4157ba02.png": "H_{i}=\\langle h_{i},G^{\\prime}\\rangle", + "3934b4860e6f9b17.png": "\\prod C", + "39361124c6dd868a.png": "\\tilde{Q}_{4}", + "3938a857112f80e8.png": "\\hat{\\beta}_{L^{*}}", + "3938c28a3f321f37.png": "rect(.)", + "3938c98d91c225ab.png": "\\hat{t}", + "39390f9072e379ee.png": "\\sigma_{xx}-\\sigma_{xz}+\\sigma_{xy}", + "393b1f6a0af0bded.png": "(\\begin{matrix}p&q\\\\ nq&p\\end{matrix})", + "39466cb791d38e99.png": "\\gamma_{n}=-\\Omega_{n}(1-\\delta_{n})", + "394999d12da38645.png": "\\tilde{R}", + "394bf9dcb82bb833.png": "\\lfloor\\sqrt{n-1}\\rfloor", + "39506852f2994a05.png": "E=mc^{2}+\\frac{p^{2}}{2m}", + "3950e7adb9024e74.png": "\\int_{\\gamma}z^{1/2}dz", + "3952d81ce8f44195.png": "\\int_{a}^{b}f(x)dx", + "395b781cd8687b82.png": "E[\\epsilon_{n}\\epsilon_{i}]=\\sigma_{\\epsilon}^{2}", + "395d1716ea36ce7e.png": "\\hat{N}_{C}", + "397841129ab9bcf9.png": "(\\begin{matrix}n\\\\ p\\end{matrix})", + "397a1d1938a57ad2.png": "Y_{t}=\\int_{0}^{t}H_{s}dX_{s}", + "397f1dd5252d9c29.png": "\\tau=\\mu\\frac{\\partial u}{\\partial y}", + "39814a06db06aa16.png": "(\\overline{m_{1}})", + "398575813770c0bf.png": "3n(n+1)^{2}", + "398fc339e74e6535.png": "B(z)=\\prod_{n}B(a_{n},z)", + "39914be543fe5c82.png": "R", + "3991e41ca52d3236.png": "(A^{*}f)(u)=f(Au)", + "39939b733b329c72.png": "|E\\cup E^{\\prime}|>1", + "39942d40cfeaa34e.png": "\\tilde{\\phi}\\circ\\omega_{G}=\\omega_{H}\\circ\\phi", + "3998257d8d144262.png": "s\\{\\begin{matrix}3\\\\ 4\\end{matrix}\\}", + "399b2efc71a09bf7.png": "\\hat{A}_{i}", + "399c97664aa094cc.png": "\\tilde{u}(t)", + "39a21828129baaae.png": "d_{e}(x_{e}+1)", + "39a36f53b17bd0eb.png": "4-2\\sqrt{3}", + "39a5359dffafa52f.png": "\\beta=\\frac{\\partial f}{\\partial y}", + "39a59f31a5cd6df4.png": "ML", + "39ac68085e7a1d39.png": "\\psi", + "39af59fa7f5433d8.png": "\\sqrt{\\phi}", + "39b6fa5681b00c8b.png": "\\vec{h},M", + "39b994c597381448.png": "F_{S}^{-1}:S\\rightarrow S", + "39bca8e3d04267bb.png": "(\\begin{matrix}8\\\\ i\\end{matrix})", + "39bdebee2419e39d.png": "y_{p}(x)=c_{1}e^{r_{1}x}", + "39c25de407d03373.png": "I\\subset Z[\\eta]", + "39c8b7fab5ad4529.png": "T(p)=\\frac{1-z_{a}}{1+z_{a}}", + "39cab02d5d6400c1.png": "\\lambda(s)=f_{s}^{\\prime}(0)", + "39d42ec16388f190.png": "F^{u_{u}}", + "39d665856a664ef6.png": "a=\\int\\frac{da}{dt}dt", + "39d7d01e667e019b.png": "a=\\frac{a^{\\prime\\prime}}{p^{\\prime\\prime}}", + "39da44ca330eac07.png": "\\Sigma=\\sum_{j=1}^{3}S_{j}\\sigma_{j},(4)", + "39e40f684089fc5a.png": "\\{A_{i}\\}_{i\\in Z^{+}}", + "39e8288222dfe861.png": "\\partial_{t}L=\\frac{1}{2}\\nabla^{2}L", + "39ed9fa40cf62bed.png": "|q\\overline{q}\\rangle", + "39f75e7c907bf742.png": "\\Sigma_{y=0},\\Sigma_{y=1}", + "39faf8ce316d6191.png": "\\int_{G}fd\\mu", + "39fb2032619976d6.png": "\\frac{1}{2}\\sqrt{r-r^{2}}", + "39fc826796b144b5.png": "\\int_{0}^{1}n(x)dx", + "3a011510cdb7edec.png": "X^{1-o(1)}", + "3a0bc1f99247676c.png": "n!+1=m^{2}", + "3a0cafd4281d8db4.png": "0\\notin\\Phi", + "3a14a4941a370c23.png": "\\frac{dr}{dt}=Ar", + "3a1a7c09c1eca60d.png": "\\tilde{B}_{7}", + "3a1cbc0df31746a6.png": "F_{r}=\\int dF_{r}", + "3a1e02d2449731c4.png": "v=\\{\\begin{matrix}1\\\\ -1\\end{matrix}\\}", + "3a2ef369ee61090a.png": "0=x-12", + "3a30689415075e16.png": "\\int ydA=0", + "3a33abe34a2309e1.png": "\\sum_{n=1}^{\\infty}(-1)^{n}\\frac{1}{n}", + "3a3abf4b15e3d242.png": "A=T_{a}P_{a}^{\\prime}+E_{a}", + "3a3e18fcf4d45125.png": "Q=\\frac{X_{L}}{R}=\\frac{\\omega L}{R}", + "3a3f6968a665e3f1.png": "\\Delta\\alpha=\\frac{1}{k}\\frac{\\partial\\phi(x)}{\\partial x}", + "3a40acde3ded23ff.png": "A=[\\begin{matrix}3&-2&1\\\\ 1&-3&2\\\\ -1&2&4\\end{matrix}]", + "3a40aef9573eca71.png": "\\hat{K}(n)", + "3a4743c3b8bd5fc0.png": "y=k-\\sqrt{r^{2}-(x-h)^{2}}", + "3a4baaf8f6b38111.png": "a_{1},a_{2},...,a_{n}\\in Z", + "3a4db690acadaf2e.png": "C_{2}(q,q^{\\prime},\\Delta\\phi_{q})", + "3a53f8dc80abc6dc.png": "\\hat{I}_{3}", + "3a5574770e101561.png": "|\\overline{VT}|", + "3a5ece3b172429ae.png": "\\frac{1}{c^{2}}\\frac{\\partial^{2}\\varphi}{\\partial t^{2}}-\\nabla^{2}\\varphi=0", + "3a73d58afd2adb71.png": "MPS=\\frac{dS}{dY}", + "3a774762e95b6242.png": "prox_{\\varphi}:H\\rightarrow H", + "3a7908d86dc9f4e4.png": "1^{1}\\cdot2^{2}\\cdot3^{3}", + "3a7bc5e238b9c427.png": "\\overline{f}=\\hat{f}", + "3a7df06584d5aa23.png": "\\tau_{\\alpha,\\beta}=\\varphi_{\\beta}\\circ\\varphi_{\\alpha}^{-1}", + "3a8b01068ed70003.png": "x^{2}+\\frac{b}{a}x+\\frac{c}{a}=0", + "3a8d5a723ea9310d.png": "aR", + "3a8ec5e36dfe98be.png": "\\int_{t-r}^{t}E(t^{\\prime})dt", + "3a92b80e8ab29d44.png": "\\vec{E}+\\vec{v}\\times\\vec{B}=\\vec{J}/\\sigma", + "3aa0074809e88e7d.png": "\\int xsinx^{2}dx", + "3aa31cb54d24f875.png": "\\tilde{x}(t)", + "3aa827e60466c570.png": "u=\\frac{x-b}{c\\sqrt{2}}", + "3aabc82360bd949a.png": "2x+3|8x-4", + "3aad062b952ec842.png": "\\int_{1}^{x}\\frac{dt}{t}", + "3aae0c1855f1dadb.png": "Q(\\zeta_{p}+\\zeta_{p}^{-1})", + "3aae1a65eb54655e.png": "\\frac{dM}{dx}=V", + "3aaea04013aafdc3.png": "(\\begin{matrix}a&b\\\\ b&c\\end{matrix})", + "3aaf4c0bf8b622ad.png": "(\\begin{matrix}a&b\\\\ b&1-a\\end{matrix})", + "3ac1e58c9fd5a651.png": "f_{x}=\\frac{\\partial f}{\\partial x}", + "3ac2e05516a3dc96.png": "\\hat{H}(t)", + "3ac6e7f95a49a731.png": "(\\begin{matrix}n\\\\ 0\\end{matrix})", + "3acb7d7cd7504f53.png": "L(Y,i)=M/P", + "3acd3f6b10d0d059.png": "\\hat{W}", + "3acd5039249c7256.png": "\\rho_{g}(X)=E^{Q}[-X]", + "3ad06a4eeec5dd09.png": "U(\\alpha^{*},\\tilde{u})\\subseteq U", + "3ad3bc1d0740d027.png": "f:n^{\\alpha}f_{,\\alpha}>0", + "3ad710b91bfe2234.png": "P_{-(1/2)+i\\lambda}^{\\mu}(x)", + "3ada03b6e163405a.png": "2\\cdot(\\begin{matrix}12\\\\ 4\\end{matrix})=990", + "3adfb21e5a1b085e.png": "\\int\\frac{dx}{1+x^{2}}", + "3ae22f9c026ef740.png": "C_{Y}W^{T}=C_{YX}", + "3ae2a953c8b0d893.png": "sys^{2}\\le\\frac{\\pi}{2}\\cdot area", + "3ae47790f00d53c8.png": "P_{l}^{m}(cos\\theta)", + "3aeb579900f1fc55.png": "\\overline{D}f=0", + "3aee6da11ee6cad7.png": "\\sum_{k=0}^{n}k(\\begin{matrix}n\\\\ k\\end{matrix})=n2^{n-1}", + "3af54d9f4ed4d120.png": "\\tilde{O}(log^{3}n))", + "3affca23498fed00.png": "B(x;r)\\cap B(y;s)", + "3b00dc2c20bbf547.png": "||P_{n}-P||_{C}=1", + "3b03be81fd1743fb.png": "p=\\rho(\\gamma-1)e", + "3b0ea66813026ead.png": "a\\notin A", + "3b166c8a8430558b.png": "w^{\\prime\\prime}\\notin W^{p}", + "3b18e598e874ce0a.png": "\\frac{\\partial L}{\\partial\\dot{x}}", + "3b1aca54a0107747.png": "P(A>O_{j})", + "3b1ad9ba371d6b1f.png": "\\tilde{h}_{u},\\tilde{h}_{d}", + "3b1c8a6f2f5c03b4.png": "\\hat{\\beta}=(\\overline{y/x})", + "3b24853a157fb7fa.png": "(\\begin{matrix}-1\\\\ 0\\end{matrix})", + "3b26d0f6d56effc8.png": "\\int_{\\Omega}u_{j}u_{j}=1", + "3b2801118099c270.png": "\\sqrt{x}", + "3b287dc78cdd2ed5.png": "\\overline{w_{i}}", + "3b2bc086d61ecc11.png": "b=\\sqrt{c^{2}-a^{2}}", + "3b2be76d6fde08fd.png": "p_{\\mu}\\mapsto p_{\\mu}-qA_{\\mu}", + "3b3369b78ab5481b.png": "(\\frac{\\partial S}{\\partial E})_{x}=\\frac{1}{T}", + "3b33f1f19a2ab222.png": "\\frac{\\partial f}{\\partial y}=\\beta", + "3b351a4a96e7babf.png": "2\\sqrt{1-\\frac{x^{2}}{4}}+2", + "3b3c6a03dcc329f1.png": "(\\begin{matrix}6\\\\ 5\\end{matrix})", + "3b3e47233b3731cd.png": "\\prod_{i}A_{i}", + "3b4187c070323800.png": "\\prod_{k=1}^{n}a_{k}", + "3b4456ca6bb79e0e.png": "c_{\\epsilon}^{\\rho}", + "3b44d027c54ae0b7.png": "\\tilde{E}", + "3b46b157b982ae17.png": "q_{y=0}=1-\\hat{y}", + "3b4d89b07ba00c81.png": "\\hat{f_{j}}", + "3b502128bd53543f.png": "[\\begin{matrix}ac\\\\ bd\\end{matrix}]", + "3b5036d87b067cb4.png": "\\frac{\\partial^{2}U}{\\partial g^{2}}<0", + "3b5bb8214a172ba1.png": "1/2\\ne2/1", + "3b5f15b8ff209d1b.png": "D^{2}=\\frac{P}{S}\\propto3dB", + "3b600fa42e029e76.png": "\\frac{1}{\\sigma_{i}+n\\lambda}\\sim\\frac{1}{\\lambda n}", + "3b665685481af882.png": "\\frac{d^{2}y}{dt^{2}}", + "3b6e547fa5ebf1bf.png": "v(\\infty)=A_{2}=V_{S}", + "3b6fdaee2c19547d.png": "\\hat{S}_{M}", + "3b71a5e58dfe88d0.png": "\\tilde{\\mu}", + "3b71d951a01547b5.png": "\\Gamma_{ij,k}^{(0)}", + "3b7472e42d978489.png": "K_{n}=C((T^{1/n}))", + "3b7a18122163ed26.png": "\\int_{1}^{2}F(x)dx=0", + "3b853b1793991759.png": "\\int_{0}^{1}2x^{3}+3dx", + "3b85ab258cf373cc.png": "n+(-\\infty)=-\\infty", + "3b8b62f4b80153cd.png": "V=CR^{2/3}S^{1/2}", + "3b8f50e6677cfdd4.png": "{\\xi^{\\delta}}^{5}", + "3b917f11e1fa6e7c.png": "\\frac{1}{X}\\sim lnN(-\\mu,\\sigma^{2})", + "3b9380555b6495e1.png": "(1\\pm i)/\\sqrt{2}", + "3b94c238f204d925.png": "\\int_{M}A\\wedge dA", + "3b94e4d68f53f49c.png": "2+15\\sqrt{\\frac{2}{17}}", + "3b953dfdc09039a0.png": "[\\begin{matrix}1&0\\\\ -sC&1\\end{matrix}]", + "3ba24409d7296d04.png": "H(\\tilde{x}|\\alpha)", + "3babfd1242a9965e.png": "xa^{m}b^{n}yc^{m}d^{n}z", + "3bb07f4aadf4d784.png": "\\cup_{n=1}^{\\infty}A_{n}\\in\\Sigma_{0}", + "3bb1d77f4b9a87ec.png": "i=1-\\frac{n-1}{n}\\alpha", + "3bb2980144834ceb.png": "Y", + "3bb64bb52000ba9e.png": "\\frac{\\partial\\Pi}{\\partial x_{j}}", + "3bb89fda45f9be9a.png": "\\partial_{y}=\\frac{\\partial}{\\partial y}", + "3bbad32518095b37.png": "\\tilde{b}", + "3bc04570684f89a4.png": "tr=det_{I}^{\\prime}", + "3bc2a1adf037bee2.png": "\\beta=(g_{im}\\cdot1)/n", + "3bc5b4f9e763e167.png": "\\frac{1}{1-e^{\\frac{S\\times(1-S)}{3^{N\\cdot1}}}}", + "3bcc2100c9c50764.png": "0.5<\\frac{a}{L}<2", + "3bd16a82ed7574db.png": "\\frac{1}{N}\\frac{dN}{dt}=\\frac{ln(\\frac{1}{2})}{T_{1/2}}", + "3bd72fb2471e4dc5.png": "(\\prod_{i=N-1}^{0}T_{i})\\vec{0}", + "3bdc4ce874464645.png": "\\hat{p}", + "3be0127fc51cb384.png": "I(X_{i};X_{j(i)})", + "3be01366dce7b3fe.png": "\\frac{du}{ds}=0", + "3be25a7d73244b54.png": "n=\\int fd^{3}v", + "3be2a31ca6f1d90a.png": "\\int_{now}^{\\infty}\\frac{cdt}{a(t)}", + "3be3a7785c50cd30.png": "\\frac{\\partial^{2}C}{\\partial S^{2}}", + "3be4a8bcf7cb86e9.png": "\\frac{\\partial U}{\\partial p_{i}}", + "3be7659f879f52e7.png": "\\tilde{D}_{8}", + "3be7dca3dc763ca5.png": "\\frac{dy}{dx}", + "3bed2e0e40cc29c8.png": "I=\\sum m_{j}{r_{j}}^{2}", + "3bf06c326688ceaa.png": "P_{i,i-1}=P_{i,i+1}=q_{i}", + "3bf0b1dbd40659d8.png": "a_{n}\\rightarrow\\sqrt{S}", + "3bf3ddcdd574ba0a.png": "\\frac{dy}{y}=-f(t)dt", + "3bf513ac9d312207.png": "|t|1", + "3ce88da064ce1720.png": "\\tilde{f}_{i}\\tilde{e}_{i}", + "3ce981f7fc80ce9a.png": "\\lfloor\\sqrt{n-1}\\rfloor", + "3cee20a3ad9e19eb.png": "\\int_{Z}i^{*}\\alpha", + "3cfb7080e79ab633.png": "-A=\\overline{A}+1", + "3d16d5e0c963b3c7.png": "\\pi_{n}(X,p)\\cong\\langle S^{n},X\\rangle", + "3d18a29378dd400d.png": "\\hat{S}(n)", + "3d19658e31ae2b18.png": "P=x_{3}^{3}+x_{1}x_{2}+7", + "3d1eb1c755fb6f73.png": "Slope=-\\frac{\\Delta H}{R}", + "3d200827f703ea88.png": "0+0=1+1=0", + "3d2356fdc0a1fefa.png": "F:[g]\\rightarrow\\Lambda^{1}(M)", + "3d237e2e0d3cb031.png": "\\tilde{K}_{\\pm}", + "3d24f24ed27bacee.png": "\\prod_{k=1}^{x}f(k)", + "3d257d28f224453b.png": "\\sum_{i=1}^{\\infty}\\frac{3}{10^{i}}", + "3d264ef76a17cd0d.png": "MPM=\\frac{dI}{dY}", + "3d29da9cb69f88c6.png": "\\underline{\\underline{K}}=\\underline{\\underline{A^{T}KA}}", + "3d2c5f72ef383177.png": "\\frac{1}{2}(a+b)c_{0}", + "3d30548808dd7384.png": "R=\\int_{0}^{\\tau}X(s)ds", + "3d334e8dfd4ebda8.png": "A_{eff}=\\frac{P_{o}}{PFD}", + "3d36eda29ff2742f.png": "y=k-\\sqrt{r^{2}-(x-h)^{2}}", + "3d388ad77a6ba419.png": "-\\frac{dN}{dt}=\\lambda N", + "3d418330fc85d8bc.png": "\\frac{\\phi(r)}{r}=\\phi(\\frac{1}{r})", + "3d43c531ffcdc602.png": "\\frac{dS}{dt}=L", + "3d5155bd70c54933.png": "e\\notin S", + "3d5179294b3bd60d.png": "(\\begin{matrix}0&0\\\\ 0&e\\end{matrix})", + "3d561b1168fa994b.png": "s=(a+b+c)/2", + "3d5b15983fa6594f.png": "\\tilde{x}_{0}\\in\\tilde{M}", + "3d5e584f5609b4d9.png": "c(k)=(\\begin{matrix}2k\\\\ k\\end{matrix})", + "3d6bf03b083f6d54.png": "R_{01}=\\frac{W}{{I_{1}}^{2}}", + "3d6c10f8381f560c.png": "|x-\\sum_{n=0}^{N}x_{n}|\\rightarrow0", + "3d6f39aa93d0cb94.png": "\\hat{t},\\hat{\\omega}", + "3d735b1c57c3077d.png": "(\\tau_{h}S)[\\varphi]=S[\\tau_{-h}\\varphi]", + "3d78f78f8250fe15.png": "0<\\mu^{-1}<\\lambda<1", + "3d7c980cb9c9690b.png": "(\\sum\\frac{1}{n!})^{x}=\\sum\\frac{x^{n}}{n!}", + "3d7d0c9860b79d7d.png": "\\tilde{r}", + "3d7d88e3708a1db1.png": "m_{B}/m_{A}B", + "3d7f28679cf79413.png": "\\int xe^{2x}dx", + "3d804e60eca519ff.png": "G=6.7\\times10^{-11}", + "3d8690db8b0c84b2.png": "h_{f}=f_{D}\\frac{L}{D}\\frac{V^{2}}{2g}", + "3d86a043b665970f.png": "u_{g}=\\frac{1}{f}\\hat{z}\\times\\nabla\\phi", + "3d883ece1a82f50f.png": "T_{q}^{(1)}=\\sqrt{\\frac{4\\pi}{3}}rY_{1}^{q}", + "3d8a069931e4c724.png": "\\frac{m}{s^{2}}", + "3d8cb36d9a64f3df.png": "h(r)=r^{2}\\cdot loglog\\frac{1}{r}", + "3d95ea163330c5fa.png": "\\overline{S_{n}}=a\\mathbb{I}\\{S_{n}>a\\}", + "3d96200ea60868af.png": "H=\\hat{a}^{\\dagger}\\hat{a}+\\frac{1}{2}", + "3d9ab0899a3a59d4.png": "0=\\sum_{i}f_{i}^{(k)}\\vec{e}_{i}", + "3d9d52beb1c5dbb9.png": "[\\begin{matrix}4&4&7\\\\ 6\\end{matrix}]", + "3da198749ed00367.png": "\\tilde{B}_{2}", + "3da38cd37ec7a9e3.png": "\\hat{D_{B}}", + "3da8a8f6238dd537.png": "\\hat{R}_{I}", + "3daaa099e85dab4d.png": "\\int\\Psi\\Psi^{*}dV=N_{s}", + "3dabcecd349c4abd.png": "X^{2}+X+1", + "3db26404451e4558.png": "\\prod_{i}C_{i}", + "3db5f1649ee7e033.png": "s\\{\\begin{matrix}2\\\\ 7\\end{matrix}\\}", + "3db62ad5f07be9ee.png": "I=\\overline{I}", + "3dba7f689ad78d71.png": "=k\\int_{R}^{\\infty}\\rho dr", + "3dbfdfd9d6e5b783.png": "[\\begin{matrix}0&-1\\\\ 1&0\\end{matrix}]", + "3dc77ca96bb88cf6.png": "J=100(A/A_{w})^{cz}", + "3dcc91aa15cee61d.png": "\\frac{1}{Z_{n}}e^{-ntrV(H)}", + "3dcd78849de1a689.png": "\\int(\\int f(r)dv)dr", + "3dd4e3f6d9cfb428.png": "\\sigma=\\rho K\\frac{\\tilde{F}}{M}", + "3dde6201b13feb16.png": "\\overline{S_{1}}", + "3de4c07ce97f4a19.png": "S=F(\\mu)+L(\\mu)", + "3de4c2438eb63ada.png": "(\\begin{matrix}0\\\\ 2\\\\ 19\\end{matrix})", + "3de6a981f57b79b5.png": "\\{\\begin{matrix}3\\\\ 5\\end{matrix}\\}", + "3df6bfc4e6fd179d.png": "Q=[\\begin{matrix}0&0\\\\ S^{0}&S\\\\ \\end{matrix}]", + "3df8dcd7f571730c.png": "p_{i}|\\phi_{i}\\rangle", + "3dfbfbc43e9bca36.png": "\\hat{K}(n)", + "3e02536867139fc3.png": "\\sum_{j}|c_{ij}|^{2}=1", + "3e02916221e5ada0.png": "(G=1)", + "3e04046b4ebbbeb9.png": "s_{3}^{2l}H_{i}^{\\prime}=H_{i}^{\\prime}", + "3e048d45ccd81e6f.png": "D_{p}^{1}", + "3e05b8c24967299e.png": "\\tilde{\\phi}", + "3e0661c8b60e90af.png": "\\beta((X_{\\beta}^{\\prime})^{\\prime},X_{\\beta}^{\\prime})", + "3e07e78a8f473093.png": "C_{1}C_{2}R_{1}R_{2}=1", + "3e0883d53368e8f4.png": "\\notin\\{0,\\pm1\\}", + "3e0a5d4f2b9ced2e.png": "Slope=-\\frac{\\Delta H}{R}", + "3e113d5d0578a7c3.png": "F_{l}[X]/\\langle X^{p}-1\\rangle", + "3e14e3bbe306b764.png": "\\frac{dB}{dz}", + "3e16c477e47ce71d.png": "\\prod{A_{i}}^{\\prime}", + "3e17d3e798e585c6.png": "p_{i}(e^{t}-1)+1", + "3e272aa0a2bfc9c7.png": "(B_{E}u)(v)", + "3e27a907c5dc4e1c.png": "\\int\\frac{dy}{y}", + "3e27d103b378166d.png": "Ag^{+}+e^{-}\\rightleftharpoons Ag(s)", + "3e2c7017495f1f85.png": "(\\begin{matrix}a\\\\ b\\end{matrix})", + "3e2db6fd6deb0f6d.png": "\\alpha\\le\\zeta_{1}=\\phi_{2}(1)", + "3e2deda78f93825e.png": "\\int_{0}^{1}f(x)dx=1", + "3e2e4266878cb07e.png": "f=\\frac{3\\pi}{4}=135^{\\circ}", + "3e2f4f497e561a18.png": "[\\begin{matrix}A&B\\\\ C&D\\\\ \\end{matrix}]", + "3e3745f815318634.png": "\\hat{C}_{I}", + "3e4184ed15fdb9e3.png": "M_{Q}(\\theta)<\\infty:", + "3e4193152fe7fc5e.png": "D\\underline{u}x", + "3e4850cc22083fef.png": "\\beta=\\frac{\\partial f}{\\partial y}", + "3e4e834d8c2a8fda.png": "\\tau_{a}=\\tau_{s}*\\frac{N_{a}}{N_{s}}", + "3e5813cfe204c81a.png": "\\frac{dy}{dx}", + "3e5b2e0fd505d961.png": "|\\Sigma_{i\\in I}A_{i}|", + "3e61493b803b9048.png": "\\overline{AB}\\cong\\overline{DE}", + "3e66993b214415d1.png": "H_{n}(\\underline{q},\\underline{x})", + "3e67f81af3aa8a10.png": "A[x]A[y]", + "3e68b7eaba563b59.png": "N(1+\\sqrt{5})=6", + "3e6e4a182a59dba3.png": "\\overline{u}", + "3e70d09d095b18d9.png": "\\int_{1}^{x}\\frac{dt}{t}", + "3e7cd5eb679d9800.png": "\\hat{b}_{i}", + "3e8444473eea8878.png": "E_{v}(r)=\\frac{I_{v}}{r^{2}}", + "3e8954367ae253d1.png": "\\int dy\\int f(x,y)dx", + "3e8a3adcd851a498.png": "(\\begin{matrix}8\\\\ i\\end{matrix})", + "3e8bdeb19aa317ee.png": "P", + "3e963b777acd1d81.png": "2r_{-}=\\sqrt{2}(r_{-}+r_{+})", + "3e996e0526e7bace.png": "da=JF^{-T}\\cdot dA", + "3e99c896c04c341f.png": "\\prod_{x}\\frac{x+1}{x}=Cx", + "3e9a5d48a4f33a60.png": "Y^{T}A_{i}Y\\sim\\sigma^{2}\\chi_{r_{i}}^{2}", + "3e9b0b58a9174aaf.png": "\\int f(x)dx", + "3e9e9b5252aa3e96.png": "C_{\\alpha\\dot{\\alpha}}", + "3ea69bf55ddd8c47.png": "V_{i}^{L}||V_{i}^{R}=V_{i}", + "3eab9b1a07f11d46.png": "A={X_{1}}^{2}", + "3eac362b6226ea68.png": "AA=[\\begin{matrix}|00\\rangle&0\\\\ 0&|11\\rangle\\end{matrix}]", + "3eb5b4c681357b95.png": "W_{i}=V,W_{1-i}=\\{\\}", + "3eb954c46c224914.png": "VT^{f/2}=constant", + "3eba0c71009e5849.png": "\\frac{\\partial f}{\\partial\\overline{z}}", + "3ebfc3e27898225a.png": "f_{s}=\\frac{1}{T}>2f", + "3ec106282957f088.png": "\\sum_{i=0}^{n}(-1)^{i}", + "3ec6f7cf661b5050.png": "w\\notin B", + "3ec84b5abe930c47.png": "Q=\\int j_{0}a^{3}d^{3}x", + "3ecb4ee48b9cad61.png": "1-10^{-154}", + "3ecf649fd0f96a03.png": "\\int_{A}P_{A}dA=1", + "3ecf77271787d670.png": "\\pm1\\pm2..\\pm n=0", + "3edc2f782c71e7a6.png": "\\sigma_{n}=\\frac{1}{2}+\\frac{1}{2n}", + "3ee708608271b40d.png": "\\kappa=A_{p}^{-1}(\\overline{R})", + "3ee9baf177f6b712.png": "j=\\beta O_{K}", + "3eed911abc2ccf6d.png": "V_{ind}=-\\frac{d\\phi}{dt}", + "3eee058669305e53.png": "(\\begin{matrix}-1&1\\\\ 0&1\\end{matrix})", + "3ef318236ae57a3a.png": "p^{2}+(1-p)^{2}", + "3ef3cc9ba285cd48.png": "n^{(p_{2})}", + "3eface4c4e732c91.png": "\\int_{-1}^{1}x^{-1}dx", + "3efc07abcda923cf.png": "\\frac{dP}{dw}", + "3f0255c16abfe2e5.png": "S=\\int wdx", + "3f04a43617f9adc1.png": "S_{r^{*}}^{\\prime\\prime}(r^{*})<0", + "3f063fa247a9d2f4.png": "k^{0},k^{1}=k^{0}cos\\theta", + "3f06acd28c405334.png": "\\tilde{T}_{i}:G/G^{\\prime}\\rightarrow H_{i}/H_{i}^{\\prime}", + "3f0822aadc99e3c3.png": "|x|^{2}=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}", + "3f14681b221084bb.png": "\\frac{\\beta:Y\\alpha:X\\\\ Y}{\\beta\\alpha:X}<", + "3f173720ea346ed9.png": "N=(\\begin{matrix}0&1\\\\ 0&1\\end{matrix})", + "3f1f1485a325389d.png": "mv\\frac{dv}{dt}=H-fv-kv^{3}", + "3f1f83afee7c98f6.png": "\\forall\\epsilon>0\\exists\\delta>0", + "3f21e7da5cf3c6d8.png": "P_{0}^{(N)}(\\xi_{1},\\xi_{2},...,\\xi_{N})", + "3f2429c6b6ffb885.png": "u", + "3f254fd41740c3f5.png": "n=n_{0}-\\frac{4n_{0}}{m^{2}}", + "3f27052e32108a39.png": "E[zz^{T}]", + "3f2b96048f4f07e9.png": "\\hat{\\beta}=(\\overline{y/x})", + "3f2d232a9c27d698.png": "(Z_{n},+)", + "3f2e714a010830c7.png": "\\lambda_{\\hat{\\beta}}", + "3f37893fc5153939.png": "(xy)^{n}=x^{n}y^{n}[y,x]^{(\\begin{matrix}n\\\\ 2\\end{matrix})}", + "3f3ddbcc88bd7b27.png": "0^{(\\delta)}=0", + "3f3fb82bb5005961.png": "\\tilde{B}_{3}", + "3f433cd7d7b5269d.png": "V\\otimes\\chi_{i}=\\sum_{j}n_{ij}\\chi_{j}", + "3f447fdfb485c4c8.png": "tan(\\alpha)=\\frac{v}{c}=\\beta", + "3f467fc2d16e7e52.png": "\\hat{q}", + "3f4b08cb283a875b.png": "\\frac{d^{2}y}{du^{2}}+y=g(u)", + "3f51550755a3eb7e.png": "e^{x^{2}-5x-7}-3=0", + "3f516eb1899013d5.png": "\\frac{\\partial L}{\\partial f_{x_{i}}}", + "3f538814bbf8e58b.png": "\\int e^{x}cosxdx", + "3f5394336e3d3a2c.png": "\\frac{\\partial U}{\\partial S}=T", + "3f643810db4a8b02.png": "2\\sqrt{3}", + "3f656920811cbba6.png": "B_{v}=B-\\alpha(v+\\frac{1}{2})", + "3f6aae98638ff8d3.png": "h_{f}\\equiv\\frac{\\delta\\Phi}{\\Phi_{0}}", + "3f6b377438482f5f.png": "(\\begin{matrix}1&2&3&4&5\\\\ 2&3&4&5&1\\end{matrix})", + "3f6e111145e1a948.png": "\\tilde{D}_{3}", + "3f6fed86d458ed37.png": "\\frac{1}{PM}=\\frac{AB}{AP\\times BP}", + "3f766f99dbfb97c6.png": "F=(\\begin{matrix}N&0\\\\ 0&1\\end{matrix})", + "3f77b90315f77ca0.png": "|\\psi\\rangle=\\int_{x}\\psi(x)|x\\rangle", + "3f78d8da194da839.png": "\\frac{f_{r}}{f_{s}}=\\frac{v_{r}\\cdot x}{v_{s}\\cdot x}", + "3f79f8a48b085053.png": "4x^{3}+4y\\frac{dy}{dx}=0", + "3f845e75111b89fa.png": "\\neg p?", + "3f85b48701045b2a.png": "N_{i}=\\frac{g_{i}}{e^{\\alpha+\\beta\\epsilon_{i}}}", + "3f87bdac5e80c93b.png": "\\Theta_{(\\varphi_{\\lambda})}", + "3f88ace877a43258.png": "y^{*}=(k^{*})^{\\alpha}(h^{*})^{\\beta}", + "3f8dde55c4f2c243.png": "D^{-}f(c)", + "3f9296e34ae3ce8f.png": "\\tilde{O}(E^{10/7})", + "3f9b452c4d008c26.png": "H^{n}(R,S;M)", + "3f9c64834a1305a1.png": "\\tilde{B}_{9}", + "3f9cce9707697746.png": "\\int_{S}F\\overline{F}", + "3f9e7f8ef73777cb.png": "\\sqrt{V}", + "3f9ed97683a71f74.png": "v=\\frac{dr}{dt}", + "3fa9d64d739f9cfa.png": "\\alpha\\equiv1(modm_{0})", + "3fae459f6c832621.png": "i=kmodm+1", + "3fba645ea54326ab.png": "8", + "3fbbc7932c3985c7.png": "\\overline{f}=\\hat{f}", + "3fc4eba30d710ffe.png": "\\tilde{x}", + "3fc507581a871ff2.png": "\\int_{L}^{*}", + "3fce7236e714dfcf.png": "\\underline{l}=2", + "3fcfede5d39ab6c8.png": "(\\sqrt{\\frac{2}{5}},\\pm\\sqrt{6},0,\\pm2)", + "3fd6f70447dde70b.png": "-\\overline{v^{\\prime}T^{\\prime}}", + "3fd894adc157c8a1.png": "\\hat{n}_{b}", + "3fd951bf81653683.png": "\\int_{0}^{x}t^{n}dt", + "3fdab8b66afc2211.png": "(\\frac{a}{p})=\\epsilon(\\pi_{a})", + "3fdd98b1ae594763.png": "\\Phi_{0}=h/e-", + "3fde0d70a0b26f16.png": "X\\frac{d}{dX}", + "3fe0145c5748271d.png": "\\prod_{d|n}f(d)", + "3feb23dc216d15c7.png": "Q=xi+yj+zk", + "3fecf4c34e73d033.png": "i\\notin(2+i)", + "3ff4bb331d445185.png": "T", + "3ff73615aad81158.png": "\\omega_{g}(v)=(L_{g^{-1}})_{*}v", + "3ff81aec6f8cc8b0.png": "(R\\oplus R,+,\\times)", + "3ff8e23eb449928b.png": "\\langle\\phi_{k}\\phi_{k^{\\prime}}\\rangle=0", + "3ff98162883e46b8.png": "[\\begin{matrix}17&23\\\\ 11&7\\end{matrix}]", + "3ffb229e33e11a8e.png": "argmax_{W}\\prod_{v\\in V}P(v)", + "3fff9ba3302db553.png": "b", + "4001e3118262764a.png": "\\tilde{X}=\\tilde{Y}", + "4002af8a61d9b588.png": "\\sqrt{n}", + "400a6ad65ba07f11.png": "Z", + "4012367e247a89de.png": "\\overline{X}_{0}", + "40186729e101c916.png": "|\\tau_{cap}(\\omega)|^{2}", + "4018b39f66c19a6e.png": "\\Sigma_{12}\\Sigma_{22}^{-1}(a-\\mu_{2})", + "4020af6d064ddbb7.png": "v_{2}=(\\begin{matrix}a\\\\ 1\\end{matrix})", + "4021c5991429b352.png": "[N_{2}O_{2}]=K_{1}[NO]^{2}", + "40227fb04c18a1aa.png": "d^{2}N(>\\lambda)/dzd\\Omega", + "402310d602b8769f.png": "\\langle x_{i},x_{j}\\rangle^{m}", + "4023709f1cf84141.png": "\\exists!n\\in N(n-2=4)", + "40259ba0587714e1.png": "\\hat{y}", + "4025cf6708c08bff.png": "(\\begin{matrix}n\\\\ 2\\end{matrix})", + "4027cef7ef9bdb48.png": "\\phi(s)=\\prod_{p}\\frac{1}{A_{p}(p^{-s})}", + "402b91f9829b1ac0.png": "(\\begin{matrix}c_{k}\\\\ k\\end{matrix})", + "402dd5e86d877461.png": "\\int_{\\gamma}D\\gamma", + "402ee358156801ab.png": "\\int_{a}^{b}g(x)dx", + "4044a2c0280fe805.png": "I\\subset Z[\\eta]", + "404abea77b87287c.png": "a_{i}-a_{j}=a_{k}-a_{l}", + "404b4f863da3d0be.png": "\\frac{n^{2}}{2h}(1+O(\\frac{1}{n}))", + "404f05af6bae34fc.png": "\\varphi_{m}(x)=E_{-m}(x)", + "405aea6ff94380ae.png": "g^{(n)}(x)=a^{2^{n}-1}x^{2^{n}}", + "4061445617ed39cf.png": "[\\begin{matrix}A&B\\\\ C&D\\\\ \\end{matrix}]", + "4061d97946be0e4d.png": "y_{1i}-y_{0i}=\\beta_{i}", + "406b3c5e91312f67.png": "\\hat{g}_{n}", + "406c61560e9b75d6.png": "\\frac{1}{\\rho(s)}=\\kappa(s)=\\frac{d\\theta}{ds}", + "4073c59eb2f222d0.png": "\\frac{dW}{dt}", + "407965bfc99150ad.png": "(\\begin{matrix}0&1\\\\ 0&0\\end{matrix})", + "407b63619c754844.png": "2x^{7}+x^{2}+1\\ne0", + "40804b8fac813604.png": "y\\notin FV(N)", + "40853556a6982516.png": "\\int_{M}Tr(F\\wedge*F)", + "408ba74140cb75ca.png": "U=(\\begin{matrix}0&1\\\\ 1&0\\end{matrix})", + "4091203431baae6d.png": "[\\begin{matrix}1&0\\\\ 0&1\\end{matrix}]", + "409335794528db9c.png": "D_{j}=\\frac{\\partial}{\\partial x_{j}}", + "409e44d2e9437a49.png": "V_{h^{\\beta}}", + "40a0e76e6e5ae975.png": "\\tilde{C}_{9}", + "40a60774476384c6.png": "(f\\circ i_{j})_{j\\in J}", + "40a7deeccee6007e.png": "F_{grav}=\\frac{GM_{BH}m_{p}}{r^{2}}", + "40a9fed633861e6f.png": "r(t)=\\sqrt{k+(ct)^{2}}", + "40aaa188b660e526.png": "\\{E_{a^{n}}:a^{n}\\in T_{\\delta}^{p^{n}}\\}", + "40ac012952383ecb.png": "(\\begin{matrix}9\\\\ 4\\end{matrix})", + "40b18977ac4ff5af.png": "Z_{\\gamma}^{f}", + "40b56cbb1ac640f5.png": "b^{(t_{j})}", + "40b594bf17ec278c.png": "\\sqrt{1-(\\frac{v}{c})^{2}}", + "40b97dde0c8684e2.png": "y^{2}=b^{2}-\\frac{b^{2}x^{2}}{a^{2}}", + "40bd554ab77d1b5e.png": "\\tilde{\\eta}", + "40c266b8a351d424.png": "\\tilde{g}_{33}", + "40c7d29d2101b2ff.png": "cos^{2}", + "40cb3a88bc773c4e.png": "O(id^{2}+d^{3})", + "40ce2c098823163f.png": "[\\begin{matrix}0&1\\\\ 0&1\\end{matrix}]", + "40d97018e188ee09.png": "e_{k}=\\frac{1}{2}v^{2}", + "40dc80b2a28e6a03.png": "\\frac{a}{a+b}+\\frac{b}{a+b}=1", + "40dfb5e939bc0374.png": "(a^{2}-n|p)", + "40e168d148a193b7.png": "\\frac{\\partial V}{\\partial T}", + "40e232fc3aa12d1d.png": "\\tilde{I}_{1}", + "40e9b66b3022d93a.png": "L:=(P,Z,\\in)", + "40ebfceb6f9b7475.png": "\\sum_{L}L^{2}4^{-2L}e^{-4\\beta L}", + "40ee8cec9b5df0cb.png": "M=\\frac{m}{\\sqrt{1-v^{2}/c^{2}}}", + "40f1cfe1f20ab492.png": "[\\begin{matrix}x\\\\ x^{2}\\end{matrix}]", + "40f20a851beed334.png": "T_{2}=T_{1}e^{\\mu_{s}\\beta}", + "40f374c2347603be.png": "M=[\\begin{matrix}0&1\\\\ -1&0\\end{matrix}]", + "40f7445bea608c6a.png": "\\sqrt{z}", + "40f8e07df4ad450b.png": "\\tilde{\\epsilon}_{ij}", + "40fec7a10dfe9591.png": "r^{(\\delta_{\\rho})}", + "4102c98f53d42153.png": "(\\begin{matrix}m\\\\ 2\\end{matrix})", + "410316cdc78d2fbf.png": "\\int fdg", + "410538d2979615ad.png": "h_{n}=-\\frac{f(x_{n})}{f^{\\prime}(x_{n})}", + "41074b7714c525c2.png": "O(\\sqrt{V}E)", + "4107d37f307dab54.png": "S_{n}=\\frac{S_{n-1}}{3}=\\frac{s}{3^{n}}", + "410969c1c8dd036e.png": "\\frac{dy}{dx}=xy", + "41098756c9b5d04e.png": "F(t)=kt^{a}+f_{0}t", + "410ab24aebc7edff.png": "\\int\\phi dx", + "411290af20fdb935.png": "(\\begin{matrix}n\\\\ c\\end{matrix})", + "4112f5b3c6ce9fd4.png": "[\\begin{matrix}c&-s\\\\ s&c\\end{matrix}]", + "41153de14e4e1495.png": "[n,n+(logn)^{2}]", + "4115c2a8239dd14e.png": "(\\begin{matrix}a&b/2\\\\ b/2&c\\end{matrix})", + "411c685afac1c0fa.png": "1\\le g^{(2)}(0)\\le\\infty", + "4123a3bc3e48798c.png": "\\xi=log(\\sqrt{x^{2}+y^{2}})", + "412640dc60f8e4bb.png": "(\\begin{matrix}n\\\\ k\\end{matrix})k!2^{(\\begin{matrix}n\\\\ 2\\end{matrix})-(\\begin{matrix}k\\\\ 2\\end{matrix})}", + "4126b42463cdc768.png": "\\hat{F}", + "41299a1942389c2e.png": "[\\begin{matrix}3&1\\\\ 0&3\\end{matrix}]", + "413213fddfb90453.png": "\\frac{\\partial v}{\\partial s}", + "41340213c5562ee1.png": "(\\begin{matrix}1&0\\\\ 1&-1\\end{matrix})", + "41349a1d9bfea3fd.png": "\\int dy", + "4134e15dadfb99a3.png": "\\int_{0}^{L}ds", + "4135fb81e4a4e225.png": "R_{i}\\rightarrow R=\\prod R_{i}", + "41389fb0789d088c.png": "\\hat{X}^{n}", + "413dd8cf952e7364.png": "Hom_{Z[G]}(Z,-)", + "413e5dd97db5bd89.png": "[\\begin{matrix}2&2\\end{matrix}]", + "413ffcfada1793b6.png": "\\frac{1}{2}(z+1)", + "41433777321b98b0.png": "\\sum_{n=0}^{\\infty}a_{n}x^{n}\\sim\\frac{1}{1-x}", + "4146db8ff8a3a5c0.png": "\\hat{p}=1", + "4147a2bf3609cbb2.png": "\\frac{5\\pi}{12}(75^{\\circ})", + "4149775f3a979da9.png": "(\\hat{x}\\hat{y})^{2}=\\hat{x}\\hat{y}\\hat{x}\\hat{y}", + "415014aaa9893081.png": "\\sum_{k=0}^{n}(\\begin{matrix}n\\\\ k\\end{matrix})^{2}=(\\begin{matrix}2n\\\\ n\\end{matrix})", + "4150f56c1e03f349.png": "f(r_{1})=3^{2}-2=7", + "41510c9e8cf0e30f.png": "A=(\\begin{matrix}1&1\\\\ 0&1\\end{matrix})", + "4152656fc236a83c.png": "x^{2l-1}+1", + "415985dbba83fb11.png": "(\\begin{matrix}0&1\\\\ -1&0\\\\ \\end{matrix})", + "41601d5493523453.png": "\\tilde{C}_{4}", + "41649869878d70e8.png": "F(s,T)-F(t,T)", + "4167cb14c2dae25d.png": "\\sigma_{k}=\\sqrt{\\lambda}", + "416e027dfe4bcc9e.png": "-\\frac{dN}{dt}=\\lambda N", + "4172722602629278.png": "f_{d}\\approx2v\\frac{f_{t}}{c}", + "417360acd5c9d4b6.png": "V\\rightarrow V+\\Lambda+\\overline{\\Lambda}", + "4174e4f3ae909241.png": "\\zeta<1/\\sqrt{2}", + "4177a7a512adb4db.png": "F[X,Y]/(XY)", + "417ea0ebfe1bf451.png": "0x+0y=4", + "417ffd8bea8687ca.png": "\\frac{\\pi^{12}}{12!}\\approx0.001930", + "418c7d80defbfbac.png": "\\int_{\\gamma}f(z)dz=0", + "418f7c4c104a09a2.png": "d*J=d^{2}*F=0", + "41904ab0dfecf0bb.png": "\\overline{X}_{n}=\\frac{1}{n}\\sum_{k=1}^{n}X_{k}", + "4195e30490e5b394.png": "\\emptyset\\notin P", + "41994c7ede8ede6b.png": "\\langle2x,2y\\rangle=\\langle x,y\\rangle", + "419d60cd5b2c30e1.png": "2^{k-1}+k", + "41a6517a6e0c1cbf.png": "\\int_{0}^{\\infty}f(x)dx", + "41a890c206c7f92a.png": "0\\notin\\mathbb{N}", + "41ad31d373f59764.png": "\\frac{U}{U_{v}}\\approx\\frac{m_{0}}{m^{*}}\\frac{m_{0}c^{2}}{E_{G}}", + "41af426de070f01f.png": "t\\{\\begin{matrix}2\\\\ n\\end{matrix}\\}", + "41b50630d952f24c.png": "\\prod_{x}x=C\\Gamma(x)", + "41b67b906fc4dc89.png": "\\dot{\\partial}_{\\mu}=\\partial_{\\mu}", + "41b7260abd045c0f.png": "(\\begin{matrix}t\\\\ k\\end{matrix})", + "41b8949fba8c7503.png": "(1+x)^{r}\\le e^{rx}", + "41bbdb3f3fde4c1e.png": "(\\alpha+\\frac{1}{3},\\alpha+\\frac{2}{3})", + "41bc6b5b0a245262.png": "\\partial_{t}v=-\\delta_{u}H(u,v)", + "41bf12bfa6a7cca7.png": "J", + "41bfb7a475604899.png": "\\overline{\\psi}=\\sum_{i}\\psi_{i}b^{i}", + "41c6736570400100.png": "d_{K}^{-p/2}", + "41cb57732a5ee745.png": "M^{2}=\\frac{1}{b}\\frac{H}{M}-\\frac{a}{b}\\epsilon", + "41cf38c60c14ccbc.png": "\\hat{w}", + "41cf9bd05b6c4525.png": "\\tilde{P}(q,\\omega)", + "41d5cbb42f8d20a7.png": "\\underline{m}=\\{1,2,...,m\\}", + "41dc135c47c94069.png": "(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "41e21c8e4253a3fc.png": "(\\begin{matrix}n-1\\\\ t-1\\end{matrix})=r(\\begin{matrix}k-1\\\\ t-1\\end{matrix})", + "41e43b5a15425027.png": "g^{c_{i}y_{i}}", + "41e581458d371d0c.png": "4M\\Delta=\\Delta_{c}M", + "41e624b4643efbd8.png": "bk_{B}T-2a", + "41eaa78b8da5c42f.png": "\\tilde{\\psi}", + "41f2ce4fe6897a73.png": "Q_{i}[x_{\\alpha}^{j}(t)]=t\\delta_{i}^{j}", + "41f9cf6180652c79.png": "(\\begin{matrix}6\\\\ 5\\end{matrix})", + "41ff23b65a5ac7bf.png": "\\sqrt{A}", + "4204d53aa12b0dfa.png": "a^{i}b^{j}(ba)^{k}", + "4204eed1427d6685.png": "[\\begin{matrix}1&2\\\\ 1&1\\end{matrix}]", + "4207aa91dc38a54c.png": "\\tilde{W}_{t}=W_{t}-[W,X]_{t}", + "420818aa33a8ab61.png": "k\\ge exp(c\\sqrt{logd})", + "420e2059914c592e.png": "U_{1}=\\prod_{P|p}U_{1,P}", + "420f10103c2f0683.png": "\\Delta_{r}G>0", + "4210c629e89132f6.png": "\\int_{a}^{b}f(x)dv(x)", + "42172803cfb3a2eb.png": "\\frac{dP}{dx}", + "4217cf1988130911.png": "T^{*}=\\frac{(T-T_{o})}{(T_{s}-T_{o})}", + "421861630f43bb14.png": "L_{P}^{\\sigma}=L_{P}-aM", + "421e46b55502cee6.png": "n^{\\underline{n}}=n(n-1)(n-2)\\cdot\\cdot\\cdot1", + "421ead23cf06c1ec.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "422099720f841957.png": "\\frac{\\partial f}{\\partial n}", + "4220b7afbe27ce16.png": "-\\sqrt{x}", + "422bb0de7db8770c.png": "\\frac{dV_{-}}{dt}=0", + "42385e47548637e9.png": "V_{in}\\approx\\frac{I}{j\\omega C}=V_{C}", + "423c426a02fad6b8.png": "R:L_{d}^{p}\\rightarrow F_{M}", + "42401d5306e44053.png": "\\hat{\\beta}\\pm2.5se_{\\beta}", + "42429142c2893fca.png": "|1,2,0,0,0,...\\rangle", + "42435ea609e4ca26.png": "Res(f^{\\prime}/f)=m", + "4243ba3c0eba73e5.png": "K=k^{2}B^{2}/\\mu_{0}\\rho:", + "424520c89f5f6681.png": "m_{\\tilde{t}}", + "424e6dfd2f707cf6.png": "y_{1i}-y_{0i}=\\beta_{i}", + "424e9094cda6578f.png": "=\\frac{2p_{1}q_{1}+2p_{2}q_{2}}{2}", + "4256edfab19c3dc8.png": "Ax=f-By=f^{\\prime}", + "4258ab2e0f17eaad.png": "\\sum_{j\\in J}r_{ij}x_{j}=m_{i}", + "425bbd70c2491037.png": "\\overline{Q}=0", + "425d12fa086462f0.png": "q=-K\\frac{\\partial h}{\\partial z}", + "42603dcfe4e80cbb.png": "S\\subseteq[n],|S|\\le d,j\\notin S", + "4267584e4a7c649e.png": "A_{i}^{\\prime}\\in A^{\\prime}", + "426e685c152f30df.png": "||P_{n}-P||_{C}=1", + "4270e6c9e05299dc.png": "\\int p(x)f(x)dx=-H", + "4272f96e2666883c.png": "Y_{l|m|}^{sgn(m)}", + "427e69cfdbd01762.png": "\\hat{2}", + "428a9c04bee9a50c.png": "\\sum D^{2}=ND_{o}", + "42919a6ea2ab90ba.png": "[\\hat{H},\\hat{T}(x)]=0", + "4293fa5929457cc4.png": "c_{n}=\\prod_{i=1}^{n}p_{i}", + "42951546b579af38.png": "A\\Rightarrow_{amb}^{*}B", + "42959ea3a5aa5aa9.png": "lim_{n\\rightarrow\\frac{1}{4}}\\frac{1}{\\frac{1}{n}!}", + "4297e6edf7e58bea.png": "\\int dV|\\Psi|^{2}=N", + "4299c98eb4cd9cfa.png": "(\\begin{matrix}n\\\\ c\\end{matrix})", + "42a11f80131eb31b.png": "(\\begin{matrix}1&1\\\\ 0&1\\\\ \\end{matrix})", + "42accee0d4ce2b98.png": "\\Phi_{ij}=2\\phi_{i}\\overline{\\phi_{j}}", + "42af306c5ad7ad4e.png": "\\tilde{z}", + "42b23bd6aa518f0b.png": "T\\ne\\overline{U}", + "42b5497647befe08.png": "\\sqrt{R}", + "42be75642642593a.png": "\\frac{dP}{d\\tau}", + "42bf487a4e092b59.png": "p_{i}((x_{j})_{j\\in N})=x_{i}", + "42bf5c5b84351080.png": "\\frac{\\partial V}{\\partial t}", + "42c3ed50c97f2af7.png": "A=(\\begin{matrix}2&0\\\\ 0&1\\end{matrix})", + "42c626636010ac76.png": "\\varphi=\\frac{d\\varphi}{dz}=0", + "42c6c3b8e5d70262.png": "]0,1[^{3}", + "42c6d716ad374f1f.png": "\\int_{-\\infty}^{\\infty}d\\epsilon_{x}d\\epsilon_{y}d\\epsilon_{z}", + "42cff1fae88c936c.png": "f=\\frac{x}{1-x-x^{2}}", + "42db001f5b99e258.png": "g^{(2)}(r_{1},r_{2})", + "42dd94f28f371a4d.png": "m_{E}=-A-2B", + "42e1703806b05120.png": "ax^{2}+bx+c", + "42fa5d7c0b4d95a7.png": "\\oint_{C}\\frac{e^{z}}{z^{5}}dz", + "42fcd6fc4c7520ea.png": "p_{\\lambda}^{\\epsilon}", + "42fe8157e63f80b3.png": "a_{n}\\rightarrow\\sqrt{S}", + "430118d3589c6fbe.png": "\\frac{dy_{1}}{dt}=-Ay_{1}", + "4301ee99a26411a0.png": "\\overline{16}_{H}", + "43072df1e125e669.png": "\\psi_{\\phi}^{t}", + "43147fce69b16e27.png": "x\\notin P", + "43226ee071c15085.png": "e(k)=\\hat{x}(k)-x(k)", + "432c1e9e887b6a14.png": "g(x)=\\int f(x,y)dy", + "432dc0275a540348.png": "\\partial_{g}(U|\\Psi_{0}\\rangle)", + "4343e594b0a90e96.png": "\\frac{d}{dx}7", + "43450b4239a11881.png": "(\\begin{matrix}mn\\\\ k\\end{matrix})=\\frac{(mn)!}{k!(mn-k)!}", + "43491c9f80d63e57.png": "\\int rcos\\theta dm", + "434b0cb24e48a5e1.png": "Nu=\\frac{1}{2}u\\frac{d^{2}}{dx^{2}}", + "434b5df840de8868.png": "S_{xx}(-\\omega)=S_{xx}(\\omega)", + "434f6f1de5a0ebe8.png": "(\\begin{matrix}-1\\\\ 0\\end{matrix})", + "4352a4bdc7e83c77.png": "u=\\frac{c(x,y)}{n^{2}-n}", + "43628b33018071c9.png": "(\\begin{matrix}9\\\\ 6\\end{matrix})", + "43695337e3dcabce.png": "\\sqrt{-h}", + "43706c278a2201fa.png": "X^{(0)}=\\frac{1}{\\sqrt{p}}X^{(m)}", + "4375858d0758d650.png": "M_{2}=M_{1}+C+I", + "4377ac62b211aca8.png": "E_{c}=\\frac{V_{m}}{E_{m}}+\\frac{V_{f}}{E_{f}}", + "437fc7cc6448fe38.png": "[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "43859096b82bb6bd.png": "F=S\\int udt", + "4386a12ddf4b248d.png": "t=\\frac{\\overline{x}-\\mu_{0}}{s/\\sqrt{n}}", + "4389049138afab6d.png": "F^{\\prime}(x)=\\int_{0}^{x}f(t)dt", + "438a451244e1d712.png": "b(t)=b1\\times e^{\\frac{-t}{\\tau}}", + "438e520a84a34121.png": "C=\\frac{def}{d^{2}-c^{2}}", + "4398d3bbaba954fa.png": "N_{n}\\sim\\frac{q^{n}}{n}", + "439cd173b20755c4.png": "\\tilde{G}_{2}", + "439e8442c50e4382.png": "z=a_{x}x+a_{y}y+d", + "43a330fd3bf1ff93.png": "-\\sqrt{\\frac{1}{60}}", + "43adbeb5fe285f76.png": "\\tilde{B}_{3}", + "43b020eb0eba2a86.png": "\\overline{d}(A)", + "43b0dd355be70f6c.png": "a\\sqrt{2}", + "43b3b24ef3bc026f.png": "\\int vdu", + "43b85e3a51fb570a.png": "\\int_{p}fdx", + "43bb86078d49ed6a.png": "\\int\\sqrt{x^{2}+a^{2}}dx", + "43bed366a3e5b53e.png": "\\sqrt{x}", + "43bf153e9bfd144e.png": "value=\\lambda v.(\\lambda h.hv)", + "43c0a22021550083.png": "A=\\int_{0}^{1}dAds", + "43c0ac35e841a96f.png": "O(n^{4k-3})", + "43c23fa3f4be1a33.png": "V_{R_{2}}=R_{2}\\cdot I", + "43ca3b3f1852724c.png": "L=10\\cdot0.5=5", + "43ca6b73a90a4294.png": "\\tilde{S}_{t}", + "43d33f791f4bc398.png": "-\\pi^{-\\pi}", + "43df74830bde6e1d.png": "\\alpha\\in\\tilde{P}_{i}", + "43e0a6102267f361.png": "f_{xx}=-\\frac{3}{8}<0", + "43e16f27ca6e0c8b.png": "\\pi:Z_{\\underline{w}}\\rightarrow X_{w}", + "43e2c4dedc1d307f.png": "{K^{L}}^{f}", + "43e34a7083efb0c9.png": "\\frac{dx}{dy}=-\\frac{\\beta}{\\alpha}", + "43e37a686c6d0909.png": "2^{1/12}=\\sqrt[12]{2}", + "43e5bbd750c4a1ba.png": "\\frac{1}{T}=\\frac{dS}{dE}", + "43e67559eeb22982.png": "\\tilde{W}", + "43ed20f9e748fa3b.png": "(1|1)", + "43f4d7c7e872ec6d.png": "|T_{n}|=2^{n}", + "43f618fb4ea95340.png": "|x+p|=\\sqrt{(x-p)^{2}+y^{2}}", + "43f83ec35b4ca83c.png": "\\phi_{x}(m_{x}|\\Theta)", + "43fa8c5c02b93f4f.png": "|x-\\sum_{n=0}^{N}x_{n}|\\rightarrow0", + "44012dcb46d56724.png": "2\\pi\\sqrt{a^{3}/GM}", + "44014df1832ef49d.png": "d=a=\\frac{KM}{r^{2}}", + "4404399ee2cf2938.png": "F^{\\bullet}\\Omega_{Y}^{p}(logD)", + "4405e12f861475a4.png": "(L^{-1})^{-1}=L", + "44063ce44dc3f108.png": "\\prod(1-d_{i})", + "440765a95882719e.png": "\\alpha_{k}=\\gamma/||g^{(k)}||_{2}", + "440a246ce9aa2b4f.png": "q_{i}=2p_{i}(1-p_{i})", + "440b66efeced23bf.png": "f_{i}(x^{1})\\le f_{i}(x^{2})", + "4418fd6605fd546c.png": "(\\begin{matrix}n\\\\ 3\\end{matrix})", + "4423417bef299d63.png": "[\\begin{matrix}3/2&0\\\\ 0&3/2\\end{matrix}]", + "44271569c5682bff.png": "b\\underline{)a}", + "442a3a3327e869ba.png": "F=Q(\\zeta_{p}^{+})", + "442f982b2c6a89ff.png": "C(X,R)", + "44302367929d4bae.png": "R_{k,P(k)}=S_{k}", + "443235007f48c903.png": "\\frac{\\sqrt{3}}{4}a^{\\prime2}", + "4432accdf99dbca9.png": "L^{-1}=\\int_{0}^{t}()", + "44386b11ff2f8dcb.png": "\\hat{e}_{j}", + "4438fdde4043abd4.png": "\\frac{1}{S}=-\\frac{2Gm}{c^{2}}", + "4439b4e9144a7e44.png": "\\frac{\\partial u}{\\partial x}", + "443e87348403667d.png": "\\tilde{m}", + "4443c229f4e69a63.png": "M,\\hat{d}", + "4447296c47e3fa98.png": "arg(L(j\\omega))=\\frac{\\alpha\\pi}{2}", + "444c1e6377da6511.png": "A=n\\sqrt{\\frac{m}{2\\pi kT}}", + "444c3e1b26c6743b.png": "U", + "4451ca20e6b0f7a3.png": "\\Pi_{i=1}^{n}(X_{i}+1)", + "4457afea85267ac4.png": "\\tilde{A}_{1}\\tilde{G}_{2}", + "445be7c16a8cf233.png": "E[Y]=g(\\mu)", + "446435639f86ac96.png": "\\frac{d}{da}", + "4468bb61462a21d8.png": "\\mathbb{Q}:X\\notin\\mathbb{N}", + "44696ddaa67a9f78.png": "f(t)=k/\\sqrt{t}", + "446a75537af2046c.png": "\\tilde{H}(q,I)", + "446da0b1a6548fc5.png": "X", + "446e6abca668210e.png": "2(\\begin{matrix}n\\\\ j\\end{matrix})", + "446f59d9849e2fd1.png": "\\Omega_{\\nu}^{\\mu}=d\\omega_{\\nu}^{\\mu}+\\omega_{\\xi}^{\\eta}", + "447a696f4476f1c2.png": "f_{0}=\\frac{1}{2\\pi\\sqrt{LC}}", + "447c2b93ef2a1e2e.png": "P(A_{1})\\le P(A_{1})", + "447c8f1021568b93.png": "V_{w1}+U", + "44815bf67c1ac6f4.png": "(\\begin{matrix}n+2\\\\ 2\\end{matrix})", + "44844f4ba2b1711d.png": "\\int_{0}^{t}f(u)du", + "448e6f645c190a7b.png": "\\prod_{i}A_{i}", + "44919687920adb73.png": "a=\\int\\frac{da}{dt}dt", + "4492ceffa25381ce.png": "\\Pi_{i}=\\cup_{o\\in S_{i}}H_{o}", + "4493cfdd72b4057e.png": "[\\begin{matrix}x\\\\ y\\end{matrix}]", + "4494d2202e35f913.png": "cos^{2}\\theta=\\frac{1+cos2\\theta}{2}", + "44a21dad35e76c61.png": "\\int f(x,y)dx", + "44a303589c2805e0.png": "X=R,G,orB", + "44a51bd69afc13fa.png": "S_{r^{*}}^{\\prime\\prime}(r^{*})<0", + "44a7e72476cd5fae.png": "|\\sum_{i=1}^{k}x_{i\\cdot d}|>C", + "44a91d42d3256359.png": "\\tilde{E}_{6},\\tilde{E}_{7},\\tilde{E}_{8}", + "44adeb3abf263393.png": "(Nkr/Tkn)*100", + "44af634a5f3e942c.png": "\\tilde{A}_{3}", + "44bb4c751ce56a00.png": "\\int_{a}^{b}f(x)dg(x)", + "44bcf793961bf7d7.png": "{i^{y}}^{2}", + "44cd69696513247f.png": "d\\cdot(k-k^{\\prime})=2\\pi m", + "44d288065fd0fe04.png": "m^{*}(B)=inf_{S\\supset B}m(S)", + "44d6bc2d99939bd1.png": "\\hat{t},\\hat{\\omega}", + "44d973774ead3319.png": "\\overline{K}_{n}", + "44de9c677f137b19.png": "p_{n}\\#=\\prod_{k=1}^{n}p_{k}", + "44e41602a2bed237.png": "F(x)=\\int_{x}^{0}f(y)dy", + "44e55a4c9dfe7aa4.png": "(1-2t(n-1))", + "44e6c9d3b9220c00.png": "\\overline{S}_{p}", + "44e7e32cc7e4d715.png": "(\\begin{matrix}9\\\\ 4\\end{matrix})", + "44e901eeb1bcc1fb.png": "a_{n}\\notin O(2-\\epsilon)^{n}", + "44ec4b102c1eeec0.png": "\\mu=\\frac{1-e^{-r}}{r}", + "44ef905221d8b9cd.png": "\\hat{f}(k,y)=C(k)F(k,y)", + "44efb63dee42b866.png": "K=\\frac{V}{A_{p}L}", + "44f1a660c6a9d52b.png": "\\int_{now}^{\\infty}\\frac{cdt}{a(t)}", + "44f1d06a8e94f786.png": "\\frac{4\\pi}{3}(nx)^{2}\\beta_{2}R_{S}^{3}=S_{*}", + "44f24b9b93796daf.png": "\\rho(u)=\\frac{1}{\\sqrt{1-\\frac{u^{4}}{r^{4}}}}", + "44f5ec4955b3a68d.png": "a^{\\prime}=\\frac{dv^{\\prime}}{dt}=a", + "44f9e62e574de4e9.png": "H=\\int\\rho hdV", + "44fa5480c09dfaf9.png": "G_{r}=G_{r}^{+}+G_{r}^{-}", + "44fcf5069478dea9.png": "x^{p/q}=\\sqrt[q]{x^{p}}", + "44fe2ed6524c0d63.png": "\\overline{R_{n}}=\\frac{1}{N}\\sum_{i=1}^{N}|z_{i}^{n}|", + "4501744c7747f1fd.png": "(n+1)p-1\\notin\\mathbb{Z}", + "45073b51cb133553.png": "\\int fdx", + "450806df4a8e8bcd.png": "\\hat{y}\\in\\{-1,1\\}", + "4513b44b1c81d4d3.png": "F(x+b)=\\int f(x+b)dx", + "45156356dcc61eee.png": "C=p_{t}+C^{\\prime}(x,p)", + "4515fbaa6f3b6fd7.png": "|0|<|1|+|-2|", + "451ae25bbd0beb7b.png": "a(t)=\\frac{d}{dt}v(t)", + "45212ce13aa5892a.png": "f(\\hat{Y})", + "4522538456e0ff7f.png": "\\frac{dV}{dt}=Q_{0}", + "452600a612b78d2f.png": "f^{\\prime}(z)=\\frac{-e^{\\frac{1}{z}}}{z^{2}}", + "45264e19d16ff431.png": "|0\\rangle=(\\begin{matrix}1\\\\ 0\\end{matrix})", + "452e161869feac05.png": "f^{\\prime}=f-By^{\\prime}", + "453c292500d7ea07.png": "E=-Blv", + "45487ef6dfdd61e1.png": "(\\begin{matrix}I&0\\\\ 0&F\\end{matrix})", + "4548eb2d2c24c452.png": "A_{t}+F_{t}=0", + "4557d99abdc56ce2.png": "X", + "45593cd02bc153d2.png": "\\int_{0}^{t}e^{B_{s}}dB_{s}", + "455a586fbbfe21f6.png": "\\sqrt{i}=\\pm(1+i)/\\sqrt{2}", + "455cf6c469259e80.png": "\\overline{X}_{n}=(X_{n1},...,X_{nk})", + "456008487adf77e7.png": "tr\\{\\begin{matrix}5\\\\ 3\\end{matrix}\\}", + "4562f0c33c9b5565.png": "\\eta_{8}=\\frac{u\\overline{u}+d\\overline{d}-2s\\overline{s}}{\\sqrt{6}}", + "4562fa89b242a8e7.png": "\\tilde{W}_{t}=W_{t}-[W,X]_{t}", + "45653078f9c9a409.png": "n=(\\begin{matrix}2k-1\\\\ k\\end{matrix})", + "456636fca291f494.png": "\\int\\frac{xdx}{r}=r", + "4569563a0a9d46f4.png": "x\\in[a,b]\\cap N_{\\delta}(c)", + "456a8592df54e5d3.png": "\\frac{1}{2}r^{2}(\\theta)d\\theta", + "4576f40181b77f8b.png": "\\phi_{h}=H=\\langle h|", + "457d4e282e31ec6d.png": "\\int_{-1}^{1}x^{-1}dx", + "457fd21602f6fa56.png": "\\frac{dF}{dx}+2xF=1", + "458241d715fb5f84.png": "A(t-r,\\theta,\\phi)/r", + "458353390ab9d9da.png": "A=\\sum x_{ij}", + "4584fde702a23ce8.png": "u:=\\int_{a}^{b}v(t)dt", + "4586698776f97449.png": "(\\begin{matrix}n+2\\\\ 2\\end{matrix})", + "45907868561ce650.png": "1\\le\\frac{m}{d}\\le\\sqrt{2}", + "459092f9c673a801.png": "w_{-}=\\frac{c}{n}-v", + "45931e8eff2c1e54.png": "A_{\\mu}\\rightarrow A_{\\mu}+\\partial_{\\mu}\\phi(x)", + "45953b81d0d2b0f3.png": "-\\leftarrow\\rightarrow-", + "4595dd4c3597995d.png": "\\pi_{2}(SO(3)/SO(2))=Z", + "4597ba179dd30f93.png": "(\\begin{matrix}n\\\\ d\\end{matrix})", + "459ae543b4d54f0e.png": "(1|1)", + "459ef5fa078a2b61.png": "\\alpha_{12}=\\frac{1}{2}(\\alpha_{11}+\\alpha_{22})", + "459f5abba897d621.png": "P=1,2,3,...,n", + "45a4b7eb3673ccdf.png": "dy/dx=e^{-3x}/y^{3}", + "45abd4d709561a0b.png": "\\hat{z}", + "45abf1f06c32382f.png": "\\tilde{M}=M//G", + "45bc10d46f55d35e.png": "\\theta_{3}=-22.5^{\\circ}", + "45bdd2b8f43c245d.png": "I=\\frac{|E|^{2}}{2\\eta}", + "45c44868d2ae09fe.png": "||u-f||_{p}^{p}", + "45c6fe8c8af3d1df.png": "\\hat{f}:\\hat{X}\\rightarrow\\hat{S}", + "45c9d1521910b8d9.png": "k^{\\theta_{\\eta}}", + "45d0667bcde3e896.png": "O(N^{K+1}KT)", + "45d3f171fe323aae.png": "P(N)\\sim1/N^{1+\\nu}", + "45da4cc761760b56.png": "x(\\underline{n})", + "45db9654e3cd3266.png": "(\\begin{matrix}1\\\\ 0\\\\ -1\\\\ 0\\end{matrix})", + "45df02a61d7a05c7.png": "E=\\frac{q}{q_{max}}", + "45e0a245a7185970.png": "\\frac{dv}{dt}=Mv", + "45e3717a1e5515d2.png": "E=Q(\\lambda)", + "45eb02af8ea2be32.png": "v_{\\overline{x}}=v_{\\overline{x}}^{\\prime}", + "45eb40cb8fbd2b0c.png": "K=K_{0}+K_{0}^{\\prime}P(4)", + "45f2bdaff25c8649.png": "\\overline{O}=O", + "45f99d65cbe14a6c.png": "(\\begin{matrix}5\\\\ 5\\end{matrix})", + "45fb3aa8c6097337.png": "\\frac{\\partial i_{l}}{\\partial x}=-i_{m}", + "46054d1cdfe6921a.png": "f(r_{1})=3^{2}-2=7", + "4608254cf41cebe3.png": "(\\begin{matrix}14\\\\ 5\\end{matrix})=2002", + "460a219f773aab75.png": "\\frac{\\partial V}{\\partial Y}=\\lambda", + "460c8b387486964b.png": "v=\\frac{1}{m}(p-\\frac{e}{c}A)", + "460cbafe6f9d27f0.png": "\\frac{1}{\\frac{1}{88}-\\frac{1}{365.24}}\\approx116", + "460eeebba43e15a3.png": "\\overline{OP_{i}}", + "461837717190135f.png": "\\hat{A}_{i}", + "46195eb1dfde301a.png": "I_{o_{lim}}=\\frac{V_{i}-V_{o}}{2L}DT", + "4628133960ca1d34.png": "S=-mc^{2}\\int_{C}d\\tau", + "462b3ccb33f598a2.png": "\\tilde{k}", + "46333cda01bfd160.png": "\\int_{G}fd\\mu", + "46372847470a74bb.png": "F_{A}^{*}\\subseteq F^{+}", + "4645e63719d21c23.png": "n", + "46472d1ce25f80e6.png": "\\frac{dC}{dt}", + "464fd35eecebbf50.png": "g(x)", + "465e33fa4e9da0e2.png": "\\pm EI\\frac{d^{2}w}{dx^{2}}=M", + "466b11bec6d766d5.png": "(\\begin{matrix}N+I-1\\\\ I-1\\end{matrix})", + "466fb3e73eab86bd.png": "(\\begin{matrix}m\\\\ r\\end{matrix})_{q}", + "46702aae60bbc115.png": "f(\\frac{1}{n},\\frac{1}{n})", + "46709c0f28ef9bf6.png": "\\int_{x}^{1}f^{\\prime}(t)dt", + "46730726e57dc1d5.png": "\\underline{d}(X)=\\overline{d}(X)", + "4674c0236dc19b26.png": "P=|vw|^{2}", + "4675469d0ebe3d81.png": "\\prod_{i=0}^{n}Y_{i}", + "4678a924f7efeed7.png": "J(u)=\\frac{mk}{L^{2}}u^{1-\\beta^{2}}", + "467edd3ae5a7dc8f.png": "\\frac{\\zeta^{4}(s)}{\\zeta(2s)}=\\sum_{n=1}^{\\infty}\\frac{d(n)^{2}}{n^{s}}", + "4689f10237201748.png": "g=(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "468d93881d8f5678.png": "(\\begin{matrix}6\\\\ 3\\end{matrix})", + "4693919257333f55.png": "\\sqrt{p}", + "469fcdd16997a9ae.png": "s=(a+b+c)/2", + "46a361b1f3a3e7f5.png": "x^{d}-1=\\prod_{m|d}\\Phi_{m}(x)", + "46b014d33aef2361.png": "\\frac{dA}{dt}", + "46b21178b6b8a58d.png": "\\frac{dy}{dx}", + "46b7968aa77b00db.png": "P\\approx e^{-\\frac{50}{\\sqrt{\\pi N}}}", + "46b8e441e1225bcb.png": "\\psi=(\\begin{matrix}u^{1}\\\\ u^{2}\\end{matrix})", + "46c17d0496064320.png": "x\\notin x", + "46c3ffbcc60800d9.png": "argmax_{x\\in[x^{\\prime\\prime},x^{\\prime}]}f(x;s)", + "46c4630538a1a0c0.png": "\\int f(x)dx=F(x)", + "46c4b522c38879ac.png": "b=y1-m.x1", + "46c939b4974c4fb5.png": "\\frac{d^{2}y}{dt^{2}}", + "46c9d6a6a4c4150a.png": "f_{s}\\sim\\int f_{s+1}", + "46ca3e23f6970e15.png": "\\sqrt{S}", + "46cefbc6152d37e9.png": "[\\begin{matrix}2&2&4\\\\ 3&5\\\\ 6&6\\end{matrix}]", + "46d044a97abebaf3.png": "\\tilde{e}_{i}L\\subset L", + "46d1d27f16b2597a.png": "\\tilde{V}", + "46d241f3da6e5456.png": "\\frac{\\partial^{2}U}{\\partial g^{2}}<0", + "46d40a0e0f11f5f6.png": "\\hat{a}_{j}", + "46d6b178fd8acf8f.png": "i=C\\frac{du}{dt}", + "46d7137849040849.png": "c_{k-1,0}=0", + "46d95712b9ea7b26.png": "\\frac{du}{ds}=0", + "46e0b58219434924.png": "Pr(n)\\propto1/n^{2}", + "46e137f939fdb444.png": "\\tilde{d}>1", + "46e6b2dbd666c0bf.png": "G\\in G(V,E,F)", + "46e7935c461f98eb.png": "\\int_{0}^{x}(cos(Nt)-1)dt", + "46ec995ecc47aaa2.png": "\\frac{2\\omega_{i}}{d}", + "46f4b29c66302ee5.png": "\\frac{F}{\\epsilon^{D}}\\cdot\\epsilon", + "46fcce2c2d8d3591.png": "\\omega=\\sum_{i}d\\xi_{i}\\wedge dx_{i}", + "47015fecf23017b2.png": "\\frac{\\partial}{\\partial Y}", + "471208d3cd173740.png": "\\prod_{i=0}^{\\infty}a_{i}", + "47165656ec1c5163.png": "p<\\frac{(1-\\epsilon)lnn}{n}", + "471abdaa60db664d.png": "(Tx_{n})_{n\\in N}", + "471db1cf72331e6b.png": "\\tilde{c}(\\Pi)", + "471ea01f0f6d36ce.png": "(A-B)\\sqrt{g}=1.", + "47212873324cfb2a.png": "\\hat{f}(k)", + "47294f0762dcad45.png": "\\prod_{i=1}^{n}f(x_{i})", + "472e2e49076fc7d1.png": "\\sqrt{3}a", + "473140ee6b6f4d31.png": "M-\\overline{V}", + "4739999ee317be7d.png": "E(X)=\\int_{\\Omega}XdP", + "47499c99345db780.png": "-i\\hbar\\frac{\\partial Q}{\\partial t}(t)=[H,Q]", + "474c6da5d9c66f48.png": "X,T=AX", + "474df06b7092eda1.png": "f=f_{0}(1+\\frac{v}{c})", + "47545f8ed09d54e4.png": "X(f)=L_{X}f", + "4754a3b98fdd758e.png": "l_{OB}\\cdot l_{OD}=k^{2}", + "4755d44e3aa0c786.png": "D_{\\gamma}^{t}", + "47572c95155faa85.png": "\\underline{x}(t)", + "475cdf992c29572b.png": "2(x^{2}+y^{2})=s^{2}", + "47613de5bf7c9b83.png": "\\int_{t-r}^{t}E(t^{\\prime})dt", + "476477b8b349df8e.png": "\\sqrt{x^{2}-1}\\ne x-\\sqrt{1}", + "4765d7f1bf5901ad.png": "\\int_{M}A\\wedge dA", + "476bc7747af9c1fa.png": "(1-m_{k})", + "4778003c34abf634.png": "2^{\\frac{1}{2}}=\\sqrt{2}", + "4780ec63584a2aec.png": "(1-\\frac{|n|}{N})1_{-N\\le n\\le N}", + "47816f1446b37029.png": "c=sup_{i\\in[|1,n|]}-\\frac{y_{i}}{p_{i}}", + "4792a06f091b0fa3.png": "x_{i}\\notin D", + "4797d34dd023bbda.png": "\\langle\\overline{\\psi}\\gamma_{0}\\psi\\rangle", + "4798a1aae0351ab8.png": "\\sum c(S_{i})\\cdot x_{i}\\le B", + "479a8ee3dbf42070.png": "B_{\\tilde{\\nu}}", + "479d961f84ee9393.png": "\\chi_{\\omega}^{\\phi}", + "479df15f0e9ca2ce.png": "C_{E_{2}}^{J}=-\\epsilon_{1}^{1}\\epsilon_{2}^{3}/D", + "479e097307e7a024.png": "P_{A}V=n_{A}RT", + "47a0c202eaed64d8.png": "\\int\\frac{1}{u}du", + "47aa27ce320bdc62.png": "(\\begin{matrix}n-1\\\\ n-x\\end{matrix})", + "47b70d83fd6b0ce2.png": "V^{C}=V\\otimes_{R}C", + "47b79f2efdaf3acd.png": "\\{\\begin{matrix}4\\\\ 3\\end{matrix}\\}", + "47ba1f0029217a07.png": "C/S", + "47ba68f8951605d3.png": "p\\in Z(g^{*})", + "47ba88b22952b904.png": "\\frac{v_{m}}{v_{r}}=\\frac{p_{b}}{p_{b}-p_{r}}", + "47bd14bc709dd3e6.png": "A^{2}S^{2}|F(q)|^{2}", + "47bdc0fcc17a1a87.png": "\\sqrt{s(s-a)(s-b)(s-c)}", + "47c08543063746b2.png": "[\\begin{matrix}1&R\\\\ 0&1\\end{matrix}]", + "47c1f9fadfaff491.png": "\\int_{a}^{b}(f(x))^{2}", + "47c2ca596e5c2c5d.png": "\\tilde{\\phi}\\circ\\omega_{G}=\\omega_{H}\\circ\\phi", + "47c351e1c7703ec1.png": "\\frac{n}{2\\pi}sin\\frac{2\\pi}{n}", + "47c6ed398b82cdaa.png": "3t+9s^{2}+3y^{3}", + "47c76ce91bcad1bf.png": "0\\frac{d^{2}}{3}", + "48bdd47c2169488c.png": "1(u\\Delta^{*})=u_{0}", + "48c7a2f1e1362d71.png": "\\tilde{O}(n)", + "48d0a7fdc1749e7c.png": "O_{X,x}\\otimes\\kappa(f(x))", + "48d315741a2f07fc.png": "\\int\\frac{1}{1+e^{x}}dx", + "48d6599579324bb3.png": "H_{k}\\equiv\\frac{2K_{u}V}{\\mu}", + "48d6898c2fbcdb3d.png": "(\\begin{matrix}6\\\\ 3\\end{matrix})", + "48d820d1e93f02bb.png": "p_{c}=\\frac{a}{27{b^{\\prime}}^{2}}", + "48d9756d44e5572b.png": "10\\%=0.1", + "48de9bfde5ea8ae0.png": "\\hat{x}^{o}", + "48e7ddfb29adc38e.png": "[\\begin{matrix}2&0\\\\ 0&1\\end{matrix}]", + "48eaf4b429e6bc42.png": "dz", + "48eebf3ff17383ce.png": "A_{\\theta}^{\\alpha}", + "48f0284d09349a23.png": "\\hat{f}(x)", + "48f800786e84881b.png": "\\frac{d^{2}x^{i}}{dt^{2}}=-\\Phi_{,i}", + "48f9af9899840bec.png": "T:\\Omega_{c}^{m}(M)\\rightarrow R", + "48fedd727e3dd686.png": "deg(a)\\le\\lfloor t/2\\rfloor", + "4903a288547bd047.png": "r(t)=\\sqrt{k+(ct)^{2}}", + "49046cd5db868686.png": "A=[\\begin{matrix}a&b\\\\ c&d\\end{matrix}]", + "49063d606c29b4c6.png": "\\hat{3}", + "49076f3dff15073f.png": "P^{2}\\psi=e^{i\\phi}\\psi", + "490a395b78eee6c2.png": "(\\begin{matrix}5\\\\ 5\\end{matrix})", + "4915e64b4dc77efb.png": "O_{i,j}=E_{i,j}\\forall i,j", + "4916a69435daa971.png": "\\int_{0}^{t}p^{\\prime}(s)p(t-s)ds", + "4917fcadca1e591a.png": "\\tilde{w}_{i}", + "49184f0c6253fe67.png": "\\hat{A}_{n,\\alpha}^{\\dagger}", + "491a9d34e4e25aa6.png": "A=\\frac{M}{\\rho}\\frac{n^{2}-1}{n^{2}+2}", + "4925dd382025e4f4.png": "y=\\int f(x)dx", + "4928a7143c477306.png": "\\chi(F(n))=P(n)", + "493254a4f2ffb9eb.png": "\\hat{Y}_{2}", + "4933442d2bfe78f4.png": "\\frac{d}{dt}(E_{kinetic})=0", + "493427301557dffb.png": "(\\begin{matrix}a\\\\ a+1\\end{matrix})=0", + "4934808e5e92ad70.png": "\\tilde{Z}", + "4935bc87a665e42b.png": "lim_{y\\rightarrow0}g^{\\prime}(y)=-\\infty", + "4940535b470dcbc1.png": "\\frac{1}{\\rho}=\\frac{d^{2}w}{dx^{2}}", + "4944b9f3f8176f03.png": "(\\begin{matrix}n/2\\\\ n/4\\end{matrix})^{2}=\\Theta(\\frac{1}{n}2^{n})", + "4947bd8efee21f12.png": "[\\Omega]=\\dot{A}A^{T}", + "494b13f9a2cd1fc4.png": "\\int_{\\partial\\Omega}", + "494e3516ec4359a6.png": "u(t)", + "494e5d40a46d1425.png": "\\sqrt{x}/lnx", + "494ff1534f010a00.png": "\\overline{ab}\\approx dx+\\frac{\\partial u_{x}}{\\partial x}dx", + "4950258aba818231.png": "\\frac{1}{T}=\\frac{dS}{dE}", + "49559da3c8a339a4.png": "C(\\varphi_{i})\\subsetneq C(\\varphi_{f(i)})", + "4956f72c224bac89.png": "A=(\\begin{matrix}1&-2\\\\ 1&-1\\end{matrix})", + "4959dd9c57d20dfc.png": "\\frac{\\partial I}{\\partial t}", + "496bb49c28cb0b4a.png": "\\hat{\\zeta}_{0}(\\omega)", + "4970c69128b9ce7a.png": "y^{\\prime}=y+\\sum_{i=1}^{k}z_{i}", + "4972676c3484952a.png": "u=\\frac{c(x,y)}{n^{2}-n}", + "4973c9423d584180.png": "|x|\\le1,|y|\\le1", + "497863027012c9e3.png": "\\lambda(s)=f_{s}^{\\prime}(0)", + "497af331384b2c60.png": "\\frac{\\partial L}{\\partial f}", + "497d4e599920cb9a.png": "\\tilde{C}_{7}", + "4980d96106afaa5a.png": "Slope=-\\frac{\\Delta H}{R}", + "4983091555950de6.png": "e^{it^{T}\\mu-\\sqrt{t^{T}\\Sigma t}}", + "4985919cb3eb5f55.png": "R[t]\\rightarrow S,f\\mapsto\\overline{f}", + "4985fb0ab28378e4.png": "\\pi\\tilde{f}=f", + "49872cb6bd853753.png": "P^{\\infty}(R)=R^{\\infty}/R^{*}", + "498c8ab6ff9edb81.png": "\\sqrt{R}", + "498c8c65a54d3442.png": "\\phi,\\tilde{\\phi}", + "499034e12327210c.png": "p=\\gamma_{(u)}m_{0}u", + "4990ca9cdca757c5.png": "x_{0}\\in M(t_{0})", + "49aa626288ed867f.png": "\\frac{\\partial y}{\\partial x_{1}}dx_{1}", + "49ab0180d6d2708b.png": "1-\\frac{N_{0}}{N}", + "49b254e13824aaeb.png": "\\hat{d}", + "49b9d9f690b44a22.png": "\\overline{lim}(loga_{n})/2^{n}<+\\infty", + "49be42c4b8db82dd.png": "(\\begin{matrix}2&-4\\\\ -1&2\\end{matrix})", + "49be8750475aa051.png": "\\tilde{h_{1}}\\leftarrow u_{1}^{z_{1}}remP", + "49c16b0f78313134.png": "\\overline{x}", + "49c2ddafb04ce336.png": "\\vec{w}\\cdot\\vec{x}_{i}-b\\le-1", + "49c6b8f667fb9955.png": "\\frac{2e}{h}U_{DC}", + "49c9a9bb81dd52f0.png": "\\int u(x,t)d\\mu", + "49cb9eb16336f3bd.png": "(\\begin{matrix}-1&-1\\\\ 1&0\\end{matrix})", + "49d0e3ef969ee476.png": "(\\frac{a}{a^{2}+b^{2}},\\frac{b}{a^{2}+b^{2}})", + "49d947f5188677d9.png": "u(x)=\\tilde{u}(x)^{\\frac{1}{\\lambda}}", + "49ddbe367bcc6efa.png": "\\bigcup_{i}F_{i}(\\lambda)=I(\\lambda)", + "49ddd63772f9b0a7.png": "Cv=\\overline{w}", + "49de4f2bbc7ac1ae.png": "{\\lambda_{a}^{b}}^{\\prime}", + "49e3d998fc0af9f0.png": "L^{-1}=\\int_{0}^{t}()", + "49e6047b96c21041.png": "C_{X\\tilde{Y}}", + "49ea7b40a076c677.png": "F(n):=n!", + "49eb3d9cdf43656d.png": "T^{2}\\sim qF_{p,\\nu}", + "49ecb113c9d1d77c.png": "g(f_{i})_{i\\in m}=g", + "49ecefe8b055c8cb.png": "-\\sqrt{\\frac{1}{60}}", + "49effd512e9d2ed9.png": "V=\\frac{16\\pi h-\\pi h^{3}}{3}", + "49f15e3101cedecd.png": "\\vec{b}=(b_{0},...,b_{L-1})", + "49f55f97e54726d5.png": "(\\begin{matrix}12\\\\ 4\\end{matrix})", + "49f8774a99a0e7b7.png": "A=B=P(N)", + "49f9b186d7a9875f.png": "(S,V,\\{N_{j}\\})", + "49ff7b339d1b78c5.png": "PV=\\frac{1-e^{(-rt)}}{r}", + "4a0078684b9fe6a7.png": "x\\dot{=}0\\rightarrow x\\dot{=}0", + "4a0248308aa7b590.png": "\\sqrt{2p}", + "4a0a0e150c685fbf.png": "\\prod C", + "4a19b218ec8e4085.png": "a=[\\begin{matrix}2\\\\ 0\\\\ -1\\\\ 1\\end{matrix}]", + "4a1d2492f672e165.png": "(\\begin{matrix}7\\\\ 5\\end{matrix})", + "4a21f5ce966ba752.png": "e^{t/2}\\prod_{i=1}^{\\infty}cosh(\\frac{t}{3^{i}})", + "4a227728dfc09c8a.png": "|\\overline{BL}|=\\frac{\\pi}{2}r", + "4a2600ae6d7a08cb.png": "E\\cap\\overline{E}=\\Delta\\otimes C", + "4a26176d89be6201.png": "(\\begin{matrix}I_{p}&0\\\\ 0&-I_{q}\\end{matrix})", + "4a263d28eea2026d.png": "x^{d}-1=\\prod_{m|d}\\Phi_{m}(x)", + "4a2a6ec99511b95c.png": "(n+1)p-1\\notin\\mathbb{Z}", + "4a2ea86b627efff2.png": "(C,\\partial_{\\bullet}^{\\prime\\prime})", + "4a337599a88afac2.png": "\\int V(t)I(t)dt", + "4a457bceab0692cc.png": "f(x)=x^{2},(x>0)", + "4a462099b543c87d.png": "C_{2}=\\{U^{3}=-I\\}", + "4a466726d728b491.png": "2\\pi Ib|db|=I\\frac{d\\sigma}{d\\Omega}d\\Omega", + "4a49096efc3efc61.png": "A=\\frac{\\sqrt{3}}{4}a^{2}", + "4a4a14f5c9f33bba.png": "\\frac{\\partial F}{\\partial y}=J", + "4a4a6ebe482e6f75.png": "f(t)G(t)+g(t)F(t)", + "4a4e0ce6eb05b884.png": "(\\begin{matrix}2m-2\\\\ m-1\\end{matrix})", + "4a4fa98ceb1d635a.png": "|B^{\\prime}|\\le w(X)", + "4a4fe42ad4626810.png": "\\frac{1}{10}x^{5}+\\frac{1}{2}x", + "4a598562953ae2f2.png": "\\frac{dx}{dt}(t)", + "4a5b8e1502c14e1f.png": "\\hat{y}_{t}", + "4a5b93dc49c084d3.png": "(\\begin{matrix}I&M\\\\ 0&I\\end{matrix})", + "4a6b6ef1c2216244.png": "t\\sqrt{m}", + "4a7146c314b9ce28.png": "\\tilde{A}_{n}", + "4a82baea781cb002.png": "\\underline{X}:U\\rightarrow\\mathbb{R}^{n}", + "4a8a64ac5dd5dad0.png": "f(t)=L^{-1}\\{F(s)\\}", + "4a8d9325e8018ad3.png": "H=\\int\\rho hdV", + "4a93bdcbcc661c72.png": "t\\leftarrow\\lceil1+|V|/\\sqrt{2}\\rceil", + "4a93ce09ce1ccf91.png": "\\hat{H}\\Psi=0", + "4a95a63fc4127cb2.png": "\\tilde{e}", + "4a9be50a44f9c7f9.png": "\\int x^{k}d\\mu(x)=m_{k}", + "4a9dc5b148ab777c.png": "\\frac{7}{9}\\le\\frac{A_{1}}{A_{2}}\\le\\frac{9}{7}", + "4aa0c80ba2a05aff.png": "S_{Fermigas}\\approx\\frac{\\pi^{2}k}{-3e}T/T_{F}", + "4aa27e54e0211195.png": "\\frac{dt}{dU}=0", + "4aac360bf304d86b.png": "W^{\\perp}=span(e_{3})", + "4aac5e5fcc9e281b.png": "\\frac{3^{11}-1}{3-1}=88573", + "4aaced3f0d2761ae.png": "Z=\\frac{\\partial}{\\partial z}", + "4aafb16900c7ecbc.png": "\\hat{n}", + "4ab673f48694f3fc.png": "0-(x-y)=y-x", + "4ab8039f316a433b.png": "\\frac{\\partial\\Pi}{\\partial x_{j}}", + "4ac0e42496746a8c.png": "f(x)=x+\\sqrt{|x|}", + "4ac445bffef4cc0e.png": "(\\begin{matrix}6\\\\ 3\\end{matrix})=20", + "4ac531438116d423.png": "\\hat{I}_{S},\\hat{I}_{B}", + "4aca09a880db9451.png": "K=-(n.T)", + "4acbc700ce0a2863.png": "\\nabla T=e_{i}\\otimes\\frac{\\partial T}{\\partial x_{i}}", + "4acc0127aeea464e.png": "\\phi(t,q^{I},Q^{II}(t))=0", + "4acc4815c176ed43.png": "(X_{b}^{*},Y_{b}^{*};Z)", + "4acf35c7114072fe.png": "\\{\\begin{matrix}3\\\\ 5/2\\end{matrix}\\}", + "4ad1bc8adb27e5a5.png": "cosx=1-\\frac{x^{2}}{2}", + "4ae3b19df319e995.png": "\\frac{dx}{dt}=c", + "4ae445927fd82a2a.png": "\\frac{\\partial L}{\\partial f}", + "4af1f122ea32e5d7.png": "2(\\sqrt{2}-1)\\approx0.828", + "4afc054f9d2d3ef4.png": "\\gamma(t)=e^{it}t\\in[0,2\\pi]", + "4b017725e4b275aa.png": "AC^{0}", + "4b02b80f17f4f82b.png": "V(x)=-\\int w(x)dx", + "4b05806abc9e49f3.png": "\\frac{P_{2}}{P}-(\\frac{P_{1}}{P_{0}})^{2}", + "4b09fe83d9b33bf3.png": "\\frac{d}{dx}(x!)", + "4b0b43d3920b24ae.png": "\\underline{S}_{\\lambda}", + "4b0e314c322c2dee.png": "\\int_{A}f=\\int_{[-a,a]^{n}}\\tilde{f}", + "4b19ef997f0f5e42.png": "R_{j}=\\frac{1}{2\\sigma_{j}^{2}}I_{d\\times d}", + "4b215244e8b93ba7.png": "\\frac{dt}{dr}=2r", + "4b2a0e6f5ef56e90.png": "(\\begin{matrix}7\\\\ 3\\end{matrix})=35", + "4b2d820256ef1b89.png": "C=(\\begin{matrix}1&0\\\\ 0&-1\\end{matrix})", + "4b313e97caa513e0.png": "\\tilde{A}_{7}", + "4b3397d481112222.png": "S=\\int Ldt", + "4b33b3ddb7a4d33b.png": "\\tilde{\\delta}", + "4b33d59cc4b8106b.png": "\\sigma(\\tilde{\\nu})", + "4b3c4eaa7f448486.png": "y=\\frac{1}{2}laea_{y}(\\frac{\\lambda}{2},\\varphi)", + "4b407c466d7193ce.png": "X=(X(t),t\\ge0)", + "4b408319b3ea50f7.png": "(\\begin{matrix}[n]\\\\ 1\\end{matrix})", + "4b423415f6a0f154.png": "T_{o}(p_{i,j})=p_{i,j}+t_{o}", + "4b4430cfd9f113b6.png": "(t_{1}...t_{n})", + "4b4a5372df67bd45.png": "dS=\\frac{dQ}{T}", + "4b4ab34c017ad8b7.png": "\\overline{A_{t}}", + "4b4ef0a643800a35.png": "(p>\\frac{lnN}{N})", + "4b508f4ba3972a20.png": "e^{W(z)}=z/W(z)", + "4b5e3e7dfd23103d.png": "(\\begin{matrix}n\\\\ n\\end{matrix})", + "4b6187e0284ef99f.png": "\\{\\begin{matrix}5\\\\ 5\\end{matrix}\\}", + "4b69448be97f1134.png": "(\\begin{matrix}12\\\\ 5\\end{matrix})", + "4b6f3be0a0a38dd6.png": "\\psi_{1}({\\Omega_{2}}^{\\Omega_{2}})", + "4b70af10a8ae773a.png": "\\int_{\\gamma}dz=0", + "4b70cd1f0291cb5c.png": "\\sqrt{-x}", + "4b74eb13f67bcb98.png": "\\hat{H}=\\hat{H}(\\hat{P})", + "4b75c2af916920c1.png": "F[y]=\\prod y", + "4b79435cb4ff5fc1.png": "x=I_{\\frac{1}{2}}^{[-1]}(\\alpha,\\beta)", + "4b7a7c4b3eb9d77a.png": "\\frac{-1}{2}=\\frac{1}{-2}", + "4b7ad75745032570.png": "\\vec{J}=\\frac{\\vec{E}}{\\rho}", + "4b7c9e3037966e60.png": "\\frac{d^{2}y}{dx^{2}}", + "4b808f82990888f7.png": "\\tilde{E}_{6}", + "4b81ff98c4ce312b.png": "\\Psi:H(n)\\rightarrow u(n)^{*}", + "4b83b38922ce06c6.png": "T^{\\prime}\\approx\\frac{1}{\\Delta f}", + "4b861661268c26a8.png": "(\\begin{matrix}5\\\\ 5\\end{matrix})", + "4b868c45d5fc1f44.png": "A\\overline{B}", + "4b88ce1ced60ac5f.png": "2\\int_{0}^{L}pdq=nh", + "4b8ab8639cde365d.png": "{\\lambda_{a}^{b}}^{\\prime}", + "4b8bc8e28f1b137c.png": "J_{-}|\\psi\\rangle", + "4b8eaafaa8ef22d3.png": "E\\{e^{2}(n_{1},n_{2})\\}", + "4b92cfd91af80f61.png": "\\tilde{b}_{ij}", + "4b98c317762ae152.png": "\\delta=\\hat{h}(n)-h(n)", + "4b9ad6677e3a7a7b.png": "Q(x,y)=y-4x^{2}", + "4b9dff3d1add27ca.png": "L=\\int_{S_{o}}^{S}nds", + "4b9e6dc09cb7b5e4.png": "\\frac{\\partial p}{\\partial z}=0", + "4ba0ad7ab9c309d8.png": "\\frac{\\partial n}{\\partial\\mu}=\\frac{3}{2}\\frac{n}{E_{f}}", + "4ba44a0ef5a30bb3.png": "\\{(x_{n},f(x_{n}))\\}", + "4ba754c2ef92616b.png": "\\mathbb{Q}", + "4baa3a5dfd011f02.png": "T_{2}=T_{1}e^{\\mu_{s}\\beta}", + "4baac95656ab0720.png": "\\int_{a}^{b}f(x)dx", + "4bab6f1e375b034e.png": "M_{f}=(\\begin{matrix}3&1\\\\ 2&0\\end{matrix})", + "4bada45bcc6a0498.png": "L=\\mu\\dot{r}d", + "4bb2e217ed30559a.png": "\\tau=\\frac{N}{2}\\frac{8.69}{D}", + "4bb813f0b756ce93.png": "2(\\begin{matrix}n\\\\ j\\end{matrix})", + "4bbbce91c65ca675.png": "\\partial^{2}f/\\partial x^{2}", + "4bc1a239c54e4931.png": "\\hat{e}(s_{0})", + "4bc5360ec259f7bf.png": "\\int_{0}^{L}ds", + "4bd2065b68339a55.png": "PF\\approx1-2\\pi\\Delta t/T", + "4bd322a24877ac4e.png": "C_{\\tilde{Y}}", + "4bd761d4c26d3eb0.png": "\\tilde{V}_{0}", + "4bda778cf1c41810.png": "\\sum_{j=0}^{n}(\\begin{matrix}n\\\\ j\\end{matrix})(-1)^{j}(n-j)^{k}", + "4bdc05a31d0da6b7.png": "\\sqrt{10}(4\\rho^{4}-3\\rho^{2})sin2\\theta", + "4bde54a075bab1e4.png": "1+\\sqrt{2(2+\\sqrt{2})}", + "4be08900f327f15d.png": "(A\\times B)^{\\sigma}", + "4be25091f323d1ea.png": "\\hat{Y}_{j}", + "4be41b466b9a0784.png": "(\\begin{matrix}n\\\\ 3\\end{matrix})-\\lfloor\\frac{n}{2}X\\rfloor", + "4bed806b79af0fb1.png": "\\prod_{i\\in I}S_{i}", + "4bf429d494fa42b2.png": "r^{r^{r^{\\cdot^{\\cdot^{\\cdot}}}}}", + "4bf7c38f63583a7f.png": "A=C^{\\infty}(M)", + "4bf7d83e9216aca4.png": "\\sigma^{-1}(m-m^{\\prime})", + "4bfa7d8afdc4bf20.png": "u_{2}=[\\begin{matrix}1\\\\ -1\\end{matrix}]", + "4bfb169e77b4624d.png": "\\tilde{C}_{6}", + "4bfc499322251c51.png": "[\\begin{matrix}4&7\\\\ 3&5\\end{matrix}]", + "4c0069839e28cf48.png": "x\\leftarrow\\frac{a+bx}{1+x}", + "4c07f9b20d846868.png": "Q=\\int j_{0}a^{3}d^{3}x", + "4c0849beab2f0236.png": "\\tilde{C_{n}^{m}}=-\\frac{C_{n}^{m}}{\\mu R^{n}}", + "4c0a7e70ee2f0f5e.png": "\\varphi_{ij}=\\phi_{j}\\phi_{i}^{-1}", + "4c10c01f2729807b.png": "P=P_{0}+\\int vdt", + "4c11b87ce94e7867.png": "p_{j}(x)\\approx f_{j}(x)g_{j}(x)", + "4c1eb741a1f8ea29.png": "R_{x}=(R_{2}/R_{1})\\cdot R_{3}", + "4c22b14ec6c12a59.png": "\\tilde{D}_{9}", + "4c2383b9b5a9332c.png": "\\theta^{\\omega_{8}}", + "4c3766276dabf392.png": "[t_{i-1},t_{i}]", + "4c376da4dd017cc3.png": "U_{-1}(x)=0", + "4c41b4782e87628d.png": "aR", + "4c46528ecfeaec7a.png": "T(G_{0}^{3}(0,0))", + "4c48a55a15f32b18.png": "\\langle\\psi^{\\prime}|=\\langle\\psi|\\hat{U}^{\\dagger}", + "4c48b65274e5349b.png": "(\\lambda F.M)N", + "4c4c0da7cf3c4495.png": "u_{1}=[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "4c4ef815e00f4c99.png": "\\lambda_{n}(x)=\\sum_{j=0}^{n}|l_{j}(x)|", + "4c60b248dcfb5009.png": "S\\equiv\\frac{\\overline{D}}{\\sigma_{D}}", + "4c66d7dc5820d78a.png": "\\nabla_{i}\\nabla_{j}\\varphi=\\nabla_{j}\\nabla_{i}\\varphi", + "4c69e0e38ed50135.png": "(\\begin{matrix}n\\\\ 0\\end{matrix})", + "4c6df4f62ff757ce.png": "4^{2}+4\\cdot1+1^{2}=21", + "4c71a8a3919ae49e.png": "\\int d^{4}p/(2\\pi)^{4}", + "4c7317a2aa06a7ea.png": "cos\\nu=\\frac{d_{1}-d_{2}}{2a}", + "4c78323812250484.png": "|\\overline{VT}|", + "4c78e5768b9395ca.png": "(x-2)(x-1)^{3}x", + "4c7bdb5ac6e86932.png": "\\hat{P}^{2}", + "4c84f1d2d53066e6.png": "T(\\theta)=\\frac{M(\\theta)-C_{1}}{C_{2}}", + "4c91ca1026abc210.png": "\\hat{y}-y", + "4c94b84b92d7fc6c.png": "E=\\sum_{n=-\\infty}^{\\infty}e[n]^{2}", + "4c96c7887545eac9.png": "(\\begin{matrix}e&f\\\\ 0&g\\end{matrix})", + "4c9e59d29a49ba53.png": "v_{y}\\sqrt{v_{x}^{2}+v_{y}^{2}}", + "4c9eaf0d0858957f.png": "(\\begin{matrix}a&z\\\\ \\overline{z}&c\\end{matrix})", + "4ca18371058bc441.png": "u_{g}=\\frac{1}{f}\\hat{z}\\times\\nabla\\phi", + "4ca37859e2eddf39.png": "\\hat{L}^{2}", + "4ca722bc9274dccd.png": "\\int_{a}^{b}f(x)dx", + "4ca823857a045084.png": "u=\\frac{x-b}{c\\sqrt{2}}", + "4caa2ad519db1e49.png": "D_{x}(r)=1-e^{-\\lambda\\pi r^{2}}", + "4cb77d2c09e40e94.png": "\\int_{a}^{b}f(x)d_{h}x", + "4cbfa57422c27702.png": "I_{C}=\\sum_{i}m_{i}\\Delta r_{i}^{2}", + "4cc3048401038cd1.png": "g_{kl}=2\\chi\\Delta n\\overline{n}", + "4cc39259cdaa8b76.png": "L=n_{l}-n_{\\overline{l}}", + "4cc49e52b80b5c51.png": "[\\begin{matrix}a\\\\ b\\\\ d\\end{matrix}]", + "4cc4d2421bdd6900.png": "\\hat{D}(\\alpha)|0\\rangle=|\\alpha\\rangle", + "4ccc6cbbb3aa4c01.png": "Hom_{S}(S,-)=-", + "4ccde16fe0f0fb24.png": "\\int_{1}^{3}(27-x^{3})dx", + "4ccded158c752afc.png": "\\underline{P}(Cl_{1}^{\\le})=\\{x_{1},x_{5}\\}", + "4cd2cc72f3ee29f4.png": "\\int_{-r}^{r}|y-s|dx", + "4cd56fe6f11aebc2.png": "\\phi_{e}\\notin F", + "4cda1135dda32bb9.png": "(q^{-1}+q^{-3}-q^{-4})^{2}", + "4ce07d02a46cd5fb.png": "[\\begin{matrix}S/I&S/I\\\\ 0&S\\end{matrix}]", + "4ce5198eabe8526a.png": "\\frac{dx}{dt}(t)", + "4ce85c91d77c44fa.png": "D=\\{x^{2}+y^{2}\\le4\\}", + "4ce877d83c0b82ff.png": "\\hat{Y}_{j}", + "4ce9f4d986e82256.png": "(\\begin{matrix}n\\\\ 4\\end{matrix})", + "4ceaeff71d6c33c0.png": "d=\\sqrt{a^{2}+b^{2}+c^{2}}", + "4cec08a24b8e817d.png": "(\\begin{matrix}4\\\\ 2\\end{matrix})=6", + "4cf13c84c6ae50ba.png": "A=C^{\\infty}(M)", + "4cf2789c83054e38.png": "\\tilde{a}", + "4cfd26e599f7f86a.png": "k\\notin S", + "4d01bc39b1fb4863.png": "0\\le f(\\vec{R})\\le1", + "4d035dab81dfd793.png": "s_{n}^{2}=\\frac{Q_{n}}{n-1}", + "4d0e1357305f884d.png": "\\tilde{\\epsilon}_{ij}", + "4d1049a35b2a2031.png": "AB", + "4d1065b1b7dab141.png": "\\frac{1}{2}\\sqrt{r-r^{2}}", + "4d182acb30122219.png": "\\int_{0}^{\\infty}f(x)dx", + "4d1e7563db9edf31.png": "(\\overline{A}\\vee\\overline{C})\\wedge(A\\vee C)", + "4d2422e3f1ddb341.png": "\\frac{\\partial p}{\\partial t}=0", + "4d24d96a2a9e11e6.png": "A=[\\begin{matrix}a&b\\\\ c&d\\end{matrix}]", + "4d2ac5f33dc8a73d.png": "\\frac{\\partial q^{i}}{\\partial x_{j}}", + "4d2e45f2b18761f8.png": "\\int_{0}^{T}dy_{2}dt", + "4d2fd7877d4e99fa.png": "a_{n}\\rightarrow\\sqrt{S}", + "4d309c4d64c009d8.png": "\\forall x,y(xRy\\rightarrow yRx)", + "4d349ac5f3cf6a2b.png": "|2\\rangle=(\\begin{matrix}0\\\\ 1\\end{matrix})", + "4d3c141fa5a01edc.png": "b^{(k_{4})}", + "4d40626cf5912ffb.png": "MG", + "4d419e571c97f4f0.png": "(\\begin{matrix}n\\\\ 2\\end{matrix})p", + "4d48081bd1ce8e15.png": "R_{0}\\sqrt{1-\\omega^{2}R_{0}^{2}}", + "4d4937890efa6b42.png": "f(\\langle x_{0},1\\rangle)", + "4d51bcd3079cc62b.png": "\\frac{x^{\\prime2}}{25}+\\frac{y^{\\prime2}}{9}=1", + "4d53bd827cdb2e6c.png": "A=4\\pi{R_{p}}^{2}", + "4d551ff12d1b0a29.png": "(\\int f)^{3}", + "4d56cb083e322b2b.png": "\\frac{du}{dx}=6", + "4d57ba80f1a40cac.png": "-\\sqrt{x}", + "4d5d2f5d2aab20a7.png": "y_{C}=-h_{2}/tan\\varphi", + "4d61672623b44995.png": "(U_{\\alpha})_{\\alpha\\in A_{n}}", + "4d62a9c9494efeef.png": "=(\\frac{95-5}{2})", + "4d663c4de2cb4387.png": "\\frac{dy}{ds}=1", + "4d6bf7ec1aa4afe0.png": "p=\\frac{mv}{\\sqrt{1-(v^{2}/c^{2})}}", + "4d74852d6cfe7e0e.png": "F[X,Y]/(XY)", + "4d7508cf760c280d.png": "P_{2n}+P_{2n+1}", + "4d7630dd42b74d5b.png": "\\tilde{f}(s)=\\frac{a_{N}}{s-N}+\\cdot\\cdot\\cdot", + "4d7828482fd738bc.png": "\\sqrt{X}", + "4d7b5a8ee32ddf9a.png": "K^{ab}[q]", + "4d7d3d38bb1a0243.png": "\\int f(t)dt=0", + "4d8cef500be37e19.png": "m-2r<-1", + "4d8e80cd396529c6.png": "B(z)=1+zB(z)^{2}", + "4d8e9bdb1368cd20.png": "\\mathbb{U}", + "4d903d220834fdb6.png": "F^{u_{u}}", + "4d957af2acd279ea.png": "\\tilde{u}(x)", + "4d9926bba18e17b4.png": "U^{[p]}(L)=U(L)/I", + "4d9941d5e081b7ac.png": "\\{\\begin{matrix}3\\\\ 3\\end{matrix}\\}", + "4d9d6dce5b280e06.png": "2^{5}3^{4}", + "4d9dae621c6b90c0.png": "\\Delta_{2}f_{\\lambda}=(\\lambda^{2}+\\frac{1}{4})f_{\\lambda}", + "4da1206f2c58bbca.png": "\\frac{d^{2}u}{dx^{2}}-u=0", + "4da21879843d4d09.png": "\\hat{I}_{3}", + "4da834ad6195e724.png": "p_{i}=\\frac{\\partial u}{\\partial x_{i}}", + "4dac02a4248d6f42.png": "\\underline{m}=\\{1,2,...,m\\}", + "4daec9c818b93ed5.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=\\frac{n^{\\underline{k}}}{k!}", + "4dbaa46530ef6032.png": "f_{t}(\\zeta(t))=\\gamma(t)", + "4dbe3b2470a429b2.png": "|P|=9", + "4dc1be1b5eb380f1.png": "l", + "4dcecc97b47d0887.png": "F=Mg=\\dot{m}\\Delta v", + "4dd35f68389a7743.png": "\\int_{0}^{h}exp(x^{2})dx", + "4dd73e8f38421747.png": "\\overline{S}=V", + "4dde5f78eb4dad0b.png": "k>2d_{A}", + "4ddff510fe7cf77a.png": "\\frac{dS_{t}}{S_{t}}", + "4de02d9c51b6250b.png": "|-\\rangle", + "4de092eca5b1d565.png": "f^{*}(x)=e^{\\frac{xf^{\\prime}(x)}{f(x)}}", + "4de3502a8401491f.png": "(\\begin{matrix}0&-1\\\\ 1&1\\end{matrix})", + "4de464feb66bc27d.png": "\\lambda(r,\\theta)=e^{-r^{2}}", + "4de6910dd586b0c3.png": "\\hat{\\beta}=(\\overline{y/x})", + "4df1086f07c830f2.png": "A=\\frac{\\sqrt{3}}{4}a^{2}", + "4df161d84798dd31.png": "(\\begin{matrix}A&B\\\\ C&D\\end{matrix})", + "4df2d702cd516d78.png": "\\Delta f=\\frac{\\partial^{2}f}{\\partial x^{2}}+\\frac{\\partial^{2}f}{\\partial y^{2}}", + "4df566bde8d9081f.png": "f(x)=\\prod_{i=1}^{n}x_{i}", + "4dfd5361e66d520b.png": "G*\\underline{A}", + "4e0515264cb80aec.png": "\\gamma(-1,i)=1", + "4e074d2664c1592b.png": "\\overline{v_{i}}", + "4e0b94d0d49d9620.png": "f(\\underline{x},t)", + "4e16632472c9f1a1.png": "(\\begin{matrix}2&-2\\\\ -2&2\\end{matrix})", + "4e2a3ac8bf66c77e.png": "R", + "4e2e8831d7678ce4.png": "a", + "4e31e6810277c8b6.png": "(1,2,3)\\ne(3,2,1)", + "4e45757a47c2aa80.png": "E=\\sum_{i=1}^{n}\\dot{q}_{i}\\frac{\\partial L}{\\partial\\dot{q}_{i}}-L", + "4e4d817929e4576c.png": "(x_{1},y_{1})=k\\times G", + "4e56c3f31b62b46e.png": "\\frac{dx}{dt}=\\dot{x}", + "4e5bfb80a25b9308.png": "\\overline{X_{v}}", + "4e5cd70d0eebd9c0.png": "AC", + "4e5eda678e39c55a.png": "\\epsilon(\\omega)=\\epsilon_{0}+\\frac{i\\sigma(\\omega)}{\\omega}", + "4e6205f3afc92f6c.png": "\\frac{dN}{dt}", + "4e659cb51158de7a.png": "[\\begin{matrix}x\\\\ x^{2}\\end{matrix}]", + "4e6a1f7108708dca.png": "|t|^{2}=t\\overline{t}", + "4e74be9176d9215e.png": "\\sqrt{64}", + "4e76056cfda04694.png": "\\frac{\\partial\\sigma}{\\partial K}", + "4e77302fdb367cff.png": "(\\begin{matrix}13\\\\ 4\\end{matrix})", + "4e7de3d779d1b326.png": "\\Xi_{(\\alpha_{\\sigma})}", + "4e805f59711166fb.png": "\\sqrt{\\beta}", + "4e87d4711f46cd0c.png": "-\\vec{\\omega}\\times\\vec{R}", + "4e8c181cb798be37.png": "[\\begin{matrix}17&23\\\\ 11&7\\end{matrix}]", + "4e935fe62980c700.png": "E=mc^{2}+\\frac{p^{2}}{2m}", + "4e965b8227cc38bb.png": "w_{2}l^{*}>D_{1}", + "4ea096771d7b18e1.png": "k>10\\sqrt{n}", + "4eaa76b346545beb.png": "(ab)=a_{1}b_{2}-a_{2}b_{1}", + "4eaa8c1df95d6ba9.png": "E_{n}=\\frac{2\\hbar^{2}v_{n}^{2}}{mL^{2}}", + "4eb56f637752f3e6.png": "\\sqrt{A}", + "4eb99901e794b1af.png": "K=-(n.T)", + "4ebb171c217ac98a.png": "\\int_{a}^{b}g(x)dx", + "4ec03540e1c5ac83.png": "\\frac{dt}{ds}=1", + "4ec57eff8d0bc31b.png": "N(a)=|N_{L/Q}(a)|", + "4ec97198382a25d2.png": "\\overline{A}D", + "4ed049fd4af5069c.png": "\\prod_{i=2}^{2002}1", + "4ed3877da8d13233.png": "d[x,x^{*}]", + "4ed5d692892f1055.png": "(M_{i}\\otimes I)", + "4edd80e3b9db8a31.png": "\\lambda^{-1}R_{x}^{-1}(n-1)", + "4edf31b90c46537a.png": "\\int_{-N}^{N}f(x)dx", + "4ee00e1d207511a9.png": "\\omega_{a}=\\frac{me^{4}}{(4\\pi\\epsilon_{0})^{2}\\hbar^{3}}", + "4ee226b6ed83094b.png": "W^{24}=F_{4}/Spin(8)", + "4eed0f7510d72cd0.png": "(c:a:a):4_{2}\\odot\\tilde{ac}", + "4eed59994a7703f4.png": "m(A)=\\int_{A}Xdn", + "4ef4184ddc0b4d46.png": "\\overline{N}(f)", + "4ef478fc6528c48b.png": "\\phi,\\tilde{\\phi}", + "4f008c88458370f9.png": "\\sqrt{10}(4\\rho^{4}-3\\rho^{2})sin2\\theta", + "4f12c38bf607778b.png": "(d\\varphi_{x})_{a}^{b}=\\frac{\\partial\\hat{\\varphi}^{b}}{\\partial u^{a}}", + "4f19062c2dff3e45.png": "x_{C}\\notin U_{a}", + "4f1be5e9f33c3432.png": "E=\\hbar\\omega-E_{k_{f}}-\\phi", + "4f238f52c9e27511.png": "R", + "4f2802bf1fc23731.png": "L", + "4f2fa56f32d3d6ce.png": "A=\\frac{\\sqrt{3}}{4}a^{2}", + "4f30019fad0b7f5a.png": "-15X^{4}+3X^{2}-9", + "4f306f35c155ee0a.png": "l=\\int_{a}^{b}|\\gamma^{\\prime}(t)|dt", + "4f33152b7f2420cb.png": "-qln(q)-pln(p)", + "4f357e5bc5b2a934.png": "C_{e}=C_{X}-C_{\\hat{X}}", + "4f35ef082202c5cd.png": "M=[\\begin{matrix}a&b-a\\\\ 0&b\\end{matrix}]", + "4f3956ce9bc257f2.png": "(\\begin{matrix}i\\\\ j\\end{matrix})", + "4f3aeb8bf41be9af.png": "\\frac{\\partial}{\\partial y_{1}}=X", + "4f491c038aebc1e4.png": "\\frac{d^{2}y}{d^{2}t}", + "4f49d13f883c20f7.png": "A=\\frac{1}{2}r^{2}\\theta", + "4f4d6664b23d6488.png": "dn(M,z)/dM", + "4f51a2b4d483e81f.png": "D(\\hat{X})", + "4f53ee94d2eb523c.png": "L_{QA}=\\frac{4\\pi R_{H}}{\\omega_{B}}", + "4f57b1446fc6fb26.png": "\\sigma_{f}=\\sqrt{n}a\\sigma", + "4f60fe07b71c384f.png": "G(t;\\mu_{1},\\mu_{2})", + "4f61341f4e55482b.png": "\\{F(x):x\\in A\\}", + "4f62750dfb946d56.png": "(\\begin{matrix}\\alpha\\\\ k\\end{matrix})", + "4f62f8cc327f2e8a.png": "h=R(1+\\frac{3\\sqrt{2}}{4})", + "4f67491678ff12f4.png": "\\hat{v}^{*}", + "4f72abceac2395a4.png": "B=\\frac{\\sqrt{m-1}}{Q}", + "4f88d73d126aedd7.png": "\\frac{T^{2}}{C_{V}}", + "4f8930ec51d29774.png": "\\sqrt[5]{100}\\approx2.512", + "4f8ee9abee682754.png": "\\pi(R^{2}-r^{2})", + "4f91b4474259c92e.png": "\\phi\\notin Y", + "4f925192cd6736ff.png": "E(f_{t}^{z})-E(f_{\\rho})", + "4f92b8532832773f.png": "\\alpha=\\sqrt{\\beta^{2}-1}", + "4f96f98aedf01fee.png": "S=-\\frac{\\partial F}{\\partial T}", + "4f9bf7b3bdc53b6c.png": "k=(1/\\lambda)\\hat{e}_{\\angle}", + "4f9f5ba3de5374b8.png": "\\pm[\\begin{matrix}1&1\\\\ 1&-1\\end{matrix}]", + "4fb0eebe48bea40e.png": "\\underline{\\varphi}", + "4fb385e9635baeff.png": "STA=\\frac{1}{n_{sp}}X^{T}y", + "4fb63086c0b9856c.png": "\\overline{a}_{\\overline{n|}i}", + "4fbb4eb61810e725.png": "\\sqrt{(}t)", + "4fc017f71a776244.png": "(\\begin{matrix}n\\\\ n\\end{matrix})", + "4fc0c5a8824c6bd2.png": "\\frac{\\partial f}{\\partial x}=y", + "4fc2bda6d98d64ea.png": "\\Xi_{g}^{d}", + "4fc68bc61ab9e446.png": "\\overline{x}=\\frac{1}{n}\\sum_{i=1}^{n}x_{i}", + "4fcb1c28a046b6be.png": "\\sum_{k=1}^{p}A(i,k)B(k,j)", + "4fcd42084c61fdb0.png": "cos^{2}z-1=0", + "4fce3405f6cd8a68.png": "c=st(x_{i_{0}})", + "4fd1233e76ba1956.png": "\\gamma=(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "4fd165a6fbc6e05b.png": "[(n:=n+1)*]", + "4fd44e9a0380f96f.png": "\\omega_{H}=\\sqrt{\\gamma\\frac{A^{2}}{m}\\frac{P_{0}}{V_{0}}}", + "4fd6d48ec7b3b4d7.png": "\\tilde{\\gamma}(0)=p", + "4fde1b919ac4d1b2.png": "\\frac{xy}{x+y^{3}}", + "4fe11c7d329f8afa.png": "D=\\prod_{i=1}^{K}d_{i}", + "4fe6535f4e2f6c5b.png": "k_{0}^{2}=\\omega_{p}^{2}+\\vec{k}^{2}", + "4fe8beeb3ece3593.png": "[X/G]\\rightarrow X//G", + "4ff5399074c81081.png": "K_{D}=\\frac{C_{E}\\cdot V_{E}}{C_{B}\\cdot t}(6d)", + "4ff777f83efba42b.png": "W=\\int V(P)dP", + "5006736ad5cfefdc.png": "C_{1}\\otimes C_{2}\\in C", + "500a44869a3ef0d4.png": "\\tilde{B}_{n}", + "500c9eef0a9fd552.png": "A_{eff}=\\frac{P_{o}}{PFD}", + "500cfab45c6bc780.png": "\\tilde{A}_{3}", + "500d9cd0420a6c13.png": "\\Psi_{v}^{\\varphi}", + "5011148aa8f86a3c.png": "\\frac{d^{n}}{dx^{n}}", + "50131e41cd14714e.png": "X(f)=L_{X}f", + "50165ebe279b1167.png": "I(Y_{1};Y_{2};Y_{3};Y_{4})", + "5017fdeccf818002.png": "[\\begin{matrix}4&4\\\\ 6\\end{matrix}]", + "501a38c613475854.png": "E(Y|X)=\\frac{3}{10}X", + "501ac7077446462a.png": "R^{n}\\rightarrow R^{n+1}", + "5021e79c0bc3dff0.png": "[\\begin{matrix}a&b\\\\ 0&0\\end{matrix}]", + "5023c5f9d43eac4b.png": "e^{it^{T}\\mu-\\sqrt{t^{T}\\Sigma t}}", + "502da27b60aeddb7.png": "-log_{2}p(X=x)", + "50327c78bc0ca281.png": "E", + "503c6ef2d756c32e.png": "p(1/x)=0", + "503eb67092fc7782.png": "P(\\epsilon_{n}=\\pm1)=\\frac{1}{2}", + "5041415c53b6d46a.png": "=\\int udx-\\int vdx", + "50424b199b6e8bae.png": "\\prod_{i=1}^{n}", + "504fb1fce26caace.png": "I(X,Y;Z|W)", + "50511212d1745847.png": "\\hat{L}", + "5053aab8bd11525e.png": "\\sqrt{dx^{2}+dy^{2}}=ds", + "50553292aa86c419.png": "z^{2}+qz-\\frac{p^{3}}{27}=0", + "5061d15394d91149.png": "B_{T}=2(\\Delta f+f_{m})", + "506483760e4efbca.png": "p_{i}\\#=\\prod_{j=1}^{i}p_{j}", + "5065bd898cca6756.png": "\\tilde{\\sigma}_{ij}", + "506980ddf69904f6.png": "h^{(pz)}", + "506ad5d5baa4d113.png": "\\oint F\\cdot dl=0", + "506ca181b038eaa9.png": "\\psi_{\\vec{k}}(\\vec{r})", + "506cc9087e682e74.png": "\\int fd\\mu", + "5073444b36fd76c0.png": "2^{m},1,2^{m}", + "50750a8f2a679cdf.png": "\\int d\\Omega", + "50798caaaf943329.png": "\\hat{x}^{\\prime}", + "507e620f216dcedc.png": "\\frac{du}{dx}", + "50834e349cc9ff51.png": "\\frac{\\partial y}{\\partial x}", + "5087d09626dd4c84.png": "\\frac{d}{dt}N_{1}=-c_{2}N_{2}", + "508f82c23fa551d0.png": "c_{i}:=a_{i}-b_{i}", + "509228be3e233e0e.png": "S=\\int Ldt", + "509239611e8a1d55.png": "c_{k-1,0}=0", + "5092d5c1197c347e.png": "H^{n-1}(E)=0", + "509432fa72b4f06f.png": "\\Omega=E[X^{2}]", + "509c686650f1fac8.png": "\\int_{E}\\varphi<\\infty", + "50a1c9b2d8a57b37.png": "Q=A^{+}A", + "50a58b1c2f6f79fc.png": "[\\begin{matrix}1&0&0\\\\ 0&4&0\\\\ 0&0&-2\\end{matrix}]", + "50b247346c022b93.png": "M_{J}\\sim\\rho^{\\frac{3}{2}(\\gamma-\\frac{4}{3})}", + "50b5972949eabaf1.png": "2\\frac{dA}{dt}=nab", + "50b94c6363f83a7f.png": "F_{k}=\\frac{m}{R}v_{k}^{2}", + "50b956f959a2d645.png": "q_{n+1}=p_{1}q_{n}+p_{n}q_{1}", + "50bbe6ecaf1ff84b.png": "w\\sqrt{\\theta}/\\delta", + "50cb41fab5ec58bb.png": "\\sqrt{nN}", + "50cf4d7b4710e161.png": "B=\\prod B/I_{i}", + "50d2ac655e4c84d4.png": "\\underline{X}=X^{+}\\cup X^{-}", + "50d3b1ad1ac906a1.png": "A=\\frac{E\\pi d^{4}}{64}", + "50d84cf7bb9177a5.png": "\\hat{f}=e^{-\\pi\\xi^{2}}", + "50e1af8a4f02c6b6.png": "(\\begin{matrix}2m-2\\\\ m-1\\end{matrix})", + "50e1ed3bf08d929d.png": "SU(N_{f})_{L}^{3}", + "50eac1594f37433e.png": "(\\begin{matrix}N\\\\ 2\\end{matrix})", + "50edff9cd2405c6d.png": "\\int f(x)d_{h}x", + "50f6a9c8bb2977aa.png": "X^{1-o(1)}", + "50fc5a37c4c75d11.png": "\\gamma(\\rho,\\infty)=2\\gamma(\\rho)", + "51029967fb990001.png": "Tr_{R}[\\rho_{QR}]=\\rho_{Q}", + "51055159ba444a59.png": "[D,\\overline{Q}]=-\\frac{1}{2}\\overline{Q}", + "51092bff7b139ce6.png": "\\tilde{\\delta}", + "510b9ba41ca98d3b.png": "\\frac{1}{M_{s}}", + "510c85ffc4c3bdcd.png": "r=\\frac{1}{2}\\sqrt{ab}", + "510ffac1d5b52aa5.png": "T_{S}\\sqrt{\\frac{R_{S}}{D}}", + "5114a496629d3797.png": "c_{w}=(\\frac{\\lambda_{1}-\\lambda_{2}}{\\lambda_{1}+\\lambda_{2}})^{2}", + "51152c3c693587ba.png": "L(x,v)=\\frac{1}{2}|v|^{2}", + "51190a3a76c8c4d0.png": "(\\begin{matrix}m+n\\\\ m\\end{matrix})", + "511f546a2f692699.png": "\\varphi_{m}(x)=E_{-m}(x)", + "5120938dd350996f.png": "U^{\\prime}=U\\cdot\\sqrt{\\frac{1+\\beta^{2}}{1-\\beta^{2}}}", + "512293026a91df17.png": "f=(\\begin{matrix}0&0&V_{s}\\end{matrix})^{T}", + "51250a1f442b5b2e.png": "\\nabla T_{m}=\\frac{\\Delta T_{m}}{\\Delta x_{stack}}", + "5129c7bdc01c7498.png": "\\frac{1}{8}(x^{3}+2x^{2}+x)", + "5129fcd5a4d4c7ee.png": "A_{HP}=A_{LP}=\\frac{R_{1}}{R_{G}}", + "512ab572f69cfd4d.png": "Z_{in}=\\frac{V_{i}}{I_{i}}=\\frac{Z}{1+A_{v}}", + "513276ba3b4fbf6e.png": "\\hat{7}", + "51338df7ae8373e9.png": "\\frac{d}{dx}", + "5139edcd0b4b98c8.png": "\\frac{\\partial F}{\\partial x}=I", + "513a9fd71b3f346d.png": "-1\\le\\xi<1", + "513e05cb461d53ce.png": "L^{2}\\le\\frac{\\pi}{4}area(\\partial P)", + "513ea09ea7b52878.png": "sI_{t+n}^{i}", + "514b1fe07ac32721.png": "E\\hat{\\sigma}^{2}=\\frac{n-p}{n}\\sigma^{2}", + "51527a012ef1242d.png": "\\sigma_{8}^{w}", + "5152d54a1532f5fd.png": "y=\\sqrt{x}", + "51580f42f522ced8.png": "\\int v_{i}dm", + "51582a8356cffc43.png": "(\\begin{matrix}n+k-1\\\\ k\\end{matrix})", + "515a0435437bd7ad.png": "\\frac{\\partial W}{\\partial t}=F_{E}\\cdot v", + "515f925744e9517e.png": "-E=\\nabla V+\\frac{\\partial A}{\\partial t}", + "516621b32ca9a76e.png": "a:=(a_{0},a_{1},...,a_{n-1})", + "5173ccdbcab1601c.png": "\\tilde{g}_{n}=[\\begin{matrix}g_{n}\\\\ \\gamma_{n}\\end{matrix}]", + "51745fa023d1cb4f.png": "f^{\\prime}(x)=st(\\frac{\\Delta y}{\\Delta x})", + "5174c38700656b2b.png": "n=\\frac{i-r}{||i-r||}", + "51753e1b3390b081.png": "G", + "5175d88520614971.png": "B^{0}\\leftrightarrow\\overline{B}^{0}", + "51776ab6ed9fad2b.png": "G^{1/2^{m}}", + "517c06d75110835a.png": "\\int_{a}^{b}f(x)dv(x)", + "5180078272050a12.png": "\\frac{dx^{\\prime}}{dt^{\\prime}}=c", + "51a0d0347cb6b8a9.png": "\\frac{\\partial f}{\\partial x}=y", + "51a98ac8947f2c54.png": "0,c_{i},-c_{i},c_{i}^{*}", + "51ad569faee54822.png": "\\int_{S}dS", + "51b1eaf125bf5e2a.png": "\\frac{dP}{dw}", + "51b6fd90b2f8f426.png": "\\int xcos(y)dy", + "51b722c138ba94e3.png": "\\{\\begin{matrix}3,3,3,3,3,3\\\\ 3\\end{matrix}\\}", + "51ba710f251b91a8.png": "x=379;239", + "51be9049178b9714.png": "(X_{1}:Y_{1}:Z_{1})", + "51bef1f8dc76f3a9.png": "\\underline{d}(X)", + "51c29be6d628ccb3.png": "t\\equiv\\sqrt{1-1/\\xi^{2}}", + "51c6296159115661.png": "(1)", + "51c81130b498e651.png": "4-6=-2", + "51d1236e64890e26.png": "\\sum_{i=6}^{10}(\\begin{matrix}16\\\\ i\\end{matrix})", + "51d1b343e1b780c7.png": "B_{\\tilde{\\nu}}", + "51d6b4e7b9564dec.png": "\\tilde{o}", + "51d7cdcd08ff2ce3.png": "-s", + "51da08e4dd5ac9c9.png": "\\rho=\\sum_{x}p_{X}(x)\\rho_{x}", + "51dff5165115ff08.png": "\\eta(x)\\frac{\\partial w}{\\partial t}", + "51e158decfc0286d.png": "A_{f}=\\langle f|P\\rangle", + "51e4d8719d70a974.png": "\\int dx\\psi_{n}^{*}(s)", + "51e7afa65dc6de10.png": "\\frac{h-h^{\\prime}}{\\lambda}=\\frac{D}{\\lambda}=N", + "51f72c7d42c0df5a.png": "e^{\\frac{-1}{x^{2}}}", + "51fb698424694b4a.png": "c=2rsin(\\frac{a}{2r})=1", + "51fd49fbc756a8a3.png": "\\tilde{\\theta}", + "51fed86bf0af1916.png": "F", + "5203a337c5ab2e53.png": "\\partial^{l}f_{i}/\\partial x_{i_{1}}^{l_{1}}\\partial x_{i_{2}}^{l_{2}}\\cdot\\cdot\\cdot\\partial x_{i_{k}}^{l_{k}}", + "520a1f1f44df2ab8.png": "\\varphi(\\beta/\\alpha)", + "520e43f7e4d18d67.png": "\\hat{c}_{p}", + "52112681051c61e2.png": "M=(\\begin{matrix}A&B&D\\\\ B&C&E\\\\ D&E&F\\end{matrix})", + "52147cf07a4310f4.png": "\\omega_{3}^{0}\\approx2.018236", + "5215937e79079dba.png": "\\sigma=e(n\\mu_{e}+p\\mu_{h})", + "521931aeef9b1379.png": "E(e^{e^{x}})=\\emptyset", + "5219523995b8237e.png": "\\int\\frac{dC}{1-C^{2}}", + "521ada5bcf1689aa.png": "\\frac{A}{H}=\\frac{1}{(\\frac{\\omega}{\\omega_{0}})^{2}-1}", + "521dc7266587a5bf.png": "(\\begin{matrix}1&0\\\\ 0&\\frac{n_{1}}{n_{2}}\\end{matrix})", + "5227cad82fdad478.png": "y=\\int\\frac{dy}{dx}dx", + "5241e5cfa37f23c0.png": "PQ", + "524e96b4a26d00f8.png": "(19/20)^{4}", + "5255365dd8381287.png": "\\sqrt{17}", + "526b83734de4a441.png": "\\frac{\\partial V}{\\partial Y}=\\lambda", + "526c15107ae73585.png": "g(x)=\\int f(x,y)dy", + "5270e3d3b275784b.png": "\\frac{\\partial z}{\\partial x}", + "5271f5b759bbeffc.png": "\\Omega=-d\\Theta=g^{*}\\omega", + "5274590b41ea356f.png": "\\delta\\int ds=0", + "5277f2fafbf06d71.png": "u\\frac{dC_{i}}{dx}=\\nu_{i}r", + "52791487c6624498.png": "a^{2}=z(e^{z}-1)", + "527ada277765f34b.png": "\\hat{n}\\cdot\\hat{m}=0", + "527b73b7f4833c85.png": "\\frac{\\partial\\theta_{e}}{\\partial z}>0", + "527d9c4cb09f94a9.png": "-\\sqrt{\\frac{1}{14}}", + "528b7a4ff1a561b8.png": "\\underline{v}", + "528f9ac07038ef8f.png": "\\tilde{D}_{4}", + "5291cf1728074eb0.png": "(\\begin{matrix}n\\\\ n\\end{matrix})", + "5295e733550b8669.png": "f(pir^{2)}", + "52a0e1db7d505027.png": "-\\sqrt{c}", + "52a229183b034f7f.png": "b(modv)", + "52a70805d65a14d5.png": "A_{i}0", + "55bca45f36ab7ae0.png": "\\dot{w}=\\frac{\\partial w}{\\partial x}", + "55bd432ffdfffbc2.png": "[\\begin{matrix}2&0\\\\ 0&1\\end{matrix}]", + "55c104cb3a8267f1.png": "\\underline{v_{col}}=0", + "55c397f189ef2257.png": "F(x)=1-\\alpha e^{x\\Theta}1", + "55c4e6009ace188c.png": "tan\\theta=\\frac{|v|^{2}}{|g|r}", + "55c78825b0e4a7be.png": "(\\begin{matrix}1&0\\\\ 0&1\\end{matrix})", + "55cc218d2a570ce8.png": "1-\\int_{t-r}^{t}E(t^{\\prime})dt^{\\prime}", + "55da04dce89af8a5.png": "\\{A_{i}|i\\in\\underline{m}\\backslash A\\}", + "55e3a3c39aafd822.png": "p(\\cdot;\\theta+\\Delta)", + "55e6327663258197.png": "R_{U}\\in R_{U}\\iff R_{U}\\notin R_{U}", + "55e6bc5718d5dacf.png": "\\wedge", + "55eec1fafe6e4dab.png": "2+\\sqrt{5}", + "55ef286fda6c06dd.png": "(t,x^{2},...,x^{n})", + "55f06b2f5f0e1f9a.png": "(\\begin{matrix}n^{2}\\\\ k\\end{matrix})", + "55f25319dcf46aaa.png": "\\{|2\\alpha\\rangle,|-2\\alpha\\rangle\\}", + "55f3dda322318e4b.png": "F_{jm}(t)<\\epsilon", + "55f85ec48c7f76cd.png": "b_{j}=\\int fv_{j}dx", + "5612db18382adbde.png": "\\frac{\\partial}{\\partial x^{i}}", + "56130d8156ea637f.png": "\\frac{dy}{ds}=1", + "561436ccaf907463.png": "y^{\\prime\\prime}=f(t,y)", + "561599041b019548.png": "Q(A/p_{i})", + "5615e1e5b72a2440.png": "\\int_{0}^{r}4\\pi u^{2}du", + "56165cb697429185.png": "D(f)=[\\begin{matrix}0\\\\ 0\\end{matrix}]", + "561e1c895488861e.png": "l^{t}\\tilde{\\beta}", + "56203f9b07b24ce5.png": "X_{0}=-ct,X_{j}=x_{j}", + "5624c8b032d67178.png": "a(n)=\\sum_{i=1}^{n}(\\begin{matrix}n\\\\ i\\end{matrix})a(n-i)", + "56281488116c25d0.png": "J=[\\begin{matrix}0&1\\\\ -1&0\\end{matrix}]", + "562d97ba4a590f41.png": "\\hat{m}_{+}", + "5631894953b96f97.png": "n", + "56334fafa2c502cf.png": "\\alpha>-1", + "5634e87bc86c9fb6.png": "(\\begin{matrix}t\\\\ k\\end{matrix})", + "56366d3cfcb8e371.png": "Spec(\\oplus_{0}^{\\infty}I^{n}/I^{n+1})", + "563890c64978deec.png": "A(\\varphi)=-f(\\varphi)", + "563b8a525e75742b.png": "251^{251^{251^{251^{259}}}}", + "56489d6ff33e7ab2.png": "\\Sigma_{\\varphi}^{\\varphi}", + "564d3238698df19c.png": "(\\frac{a}{b})=-1", + "564f092979bf4e36.png": "C^{n}/Z^{2n}", + "5651f117bf5cafdb.png": "\\prod_{T>0}(1+B_{T}^{x})<\\infty", + "56543c657c161f9f.png": "\\frac{1}{\\omega_{0}}\\frac{P}{c^{2}\\rho}\\sim\\frac{10^{-6}}{\\omega_{0}}", + "5654a012e959a4ed.png": "(Pf)^{\\wedge}=Q\\hat{f}", + "565c75eb0ad341c2.png": "\\int sin^{m}xcos^{n}xdx", + "56644bebd8c4228a.png": "\\{\\begin{matrix}3,3,3\\\\ 3,3,3\\end{matrix}\\}", + "566565c446f7a8f1.png": "[\\begin{matrix}2&-2&-4\\\\ -1&3&4\\\\ 1&-2&-3\\end{matrix}]", + "5666dc1ec51c8d74.png": "a^{1/n}\\rightarrow1", + "566f2995a6631e69.png": "B(S_{i}^{\\prime})", + "566fe995464c002e.png": "\\tilde{C}_{6}", + "56708fc61312030f.png": "x\\notin N", + "5673e9a196d9c841.png": "\\{\\mu_{T}|T\\in A(E)\\}", + "5675cde2b5027564.png": "\\frac{d^{n}Y}{dx^{n}}", + "56767ed98c802f44.png": "W^{1-\\frac{1}{p},p}(\\partial\\Omega)", + "56775934c79eed3f.png": "\\sigma_{j}^{\\eta}", + "5679be8ecb9c9583.png": "\\hat{q}_{o}", + "567a1667d4ae3d4d.png": "f(\\underline{m})=0", + "567af92c47107f55.png": "V=\\frac{1}{\\sqrt{aa^{\\dagger}}}a", + "568343ad755a335c.png": "s-r>2R", + "5685852849a360ba.png": "F(x+b)=\\int f(x+b)dx", + "568d1df0bd652f26.png": "A(t)=U_{n}^{T}A", + "5691e637d9cfb8c1.png": "MCG(S^{2})\\simeq Z/2Z", + "56931da3ecc6f275.png": "\\sqrt{19}", + "56999db0cfac4446.png": "\\underline{f}(1)=1", + "569dfd872142880b.png": "\\hat{a}_{2},\\hat{a}_{3}", + "56a26b98fe810809.png": "H=\\{h_{a,b}\\}", + "56a9b52ac5f420ff.png": "\\hat{Y}_{j}", + "56acbc3409c1a4b1.png": "[L]^{T}[L]=[I]", + "56ada850db120274.png": "lim_{x\\rightarrow0}\\sqrt{x}=0?", + "56ade6de433048a2.png": "\\tilde{T}_{M}^{ab}", + "56b15fce168982fe.png": "\\frac{1}{\\sigma_{i}+n\\lambda}\\sim\\frac{1}{\\lambda n}", + "56b4e50360ced759.png": "(\\begin{matrix}2n\\\\ n\\end{matrix})", + "56bbd958437dba26.png": "\\hat{a}_{2},\\hat{a}_{3}", + "56c96d4bacba9fdd.png": "c_{k-1,0}=0", + "56cd75f089f81e13.png": "G\\overline{t}", + "56ce03a9cf5c87f4.png": "(\\begin{matrix}v&0\\cdot\\cdot\\cdot0\\end{matrix})", + "56cf6a7d660e40b1.png": "\\hat{R}_{P}", + "56d649717b61d642.png": "(\\begin{matrix}n\\\\ k\\end{matrix})+(\\begin{matrix}n\\\\ k-1\\end{matrix})=(\\begin{matrix}n+1\\\\ k\\end{matrix})", + "56d6764522252d1e.png": "\\hat{N}_{f}", + "56d9b1f17e9a8550.png": "\\mu_{ij}^{0}:=exp(\\beta Q_{ij})", + "56dbd8b8e5ac2522.png": "(\\overline{\\xi},\\overline{\\zeta})=(0,0)", + "56dc325ab788cd16.png": "inf_{x:g(x)\\le y}f(x)", + "56e1aa0d657b7809.png": "\\int1=1", + "56e1abd5f77bc6d1.png": "s^{2}+2\\alpha s+{\\omega_{0}}^{2}=0", + "56e40326665c74c6.png": "\\int(sinx/x)dx", + "56e778c118f97b3e.png": "\\frac{dG}{dr}=0", + "56eaf61ed5cd2fbc.png": "\\tau_{g}^{\\delta}", + "56eb3e6d305ade52.png": "\\notin C", + "56ebf34c545bc35f.png": "x=[\\begin{matrix}7.111\\\\ -3.222\\end{matrix}]", + "56ed22536c88b546.png": "p:\\tilde{X}\\rightarrow X", + "56f30159433539b5.png": "\\overline{C}(8)", + "56f4bed9391b0224.png": "Mo=\\frac{We^{3}}{FrRe^{4}}", + "56fab64c0ae75cf7.png": "\\overline{X}_{n}=\\frac{1}{n}(X_{1}+\\cdot\\cdot\\cdot+X_{n})", + "56fbab516a8ab690.png": "\\frac{P_{t+1}}{P_{t}}=1-\\frac{1}{2N}", + "5704ab861011b4be.png": "(\\begin{matrix}n-k\\\\ k\\end{matrix})", + "570550ef244df195.png": "\\frac{dx}{dt}=c", + "570841dad4907136.png": "\\tilde{h}=H_{1}(\\tilde{w},\\tilde{s})", + "570b13a9bccadd3f.png": "\\int_{0}^{t}B_{s}^{2}dB_{s}", + "5712864a4342820a.png": "\\frac{\\partial p}{\\partial z}=0", + "5714dcdc2e70e3de.png": "E^{n-1}", + "571aad01d6f0c252.png": "\\int_{a}^{b}\\rho(\\gamma(t))dl(t)", + "571e9436a0c90de4.png": "Set_{\\ne\\emptyset}\\times Set_{\\ne\\emptyset}", + "5720e569bcc88fb1.png": "\\tilde{K}_{\\pm}", + "572229c5d5534e69.png": "(\\begin{matrix}k\\\\ 2\\end{matrix})", + "5722b8ac031f7dfb.png": "\\frac{dt^{2}}{dr^{2}}", + "57269e8637d726d3.png": "\\sqrt{C}", + "572e3ab62ccec164.png": "Pr[X\\in\\partial B]=0", + "573aebc3446a46f3.png": "\\frac{\\sigma}{\\mu}=\\frac{\\frac{a-b}{2}}{\\frac{a+b}{2}}=\\frac{a-b}{a+b}", + "573d2edfb4d1fa64.png": "\\pi\\int_{l_{1}}^{l_{2}}f(x)^{2}dx", + "573ed8145e2da6ff.png": "\\beta=(g_{im}\\cdot1)/n", + "573ee281d4875d9a.png": "g(2\\omega,2\\omega_{0f},\\Gamma)", + "5745132dd73b6af0.png": "H=(\\begin{matrix}E_{+}&0\\\\ 0&E_{-}\\end{matrix})", + "574dadeea297c551.png": "\\tilde{C}_{2}", + "5757585b3d7b6008.png": "\\Delta x^{\\prime}=\\Delta x/\\gamma", + "57579fb7acc9b900.png": "[h_{i},f_{j}]=-c_{ij}f_{j}", + "575a30019f9eefb0.png": "\\sum_{k=1}^{n}\\frac{z(1-z^{k})}{1-z}", + "5763568b04228fd2.png": "b(t)=b1\\times e^{\\frac{-t}{\\tau}}", + "5766ce63e639376a.png": "(\\Delta=\\omega-\\omega_{0})", + "576dbff0f3c357e3.png": "M=-EI\\frac{d^{2}w}{dx^{2}}", + "5776008819558aab.png": "(\\begin{matrix}n-1\\\\ k\\end{matrix})", + "577699058c32bef9.png": "\\tilde{E}_{7}", + "577a0eff24c28537.png": "\\overline{R}", + "577acb7cdafba9e2.png": "1/(d_{i}d_{j})^{1/2}", + "577fa8e4440b3909.png": "(\\begin{matrix}0&-i\\\\ i&0\\end{matrix})", + "57841cc9d3a06bc0.png": "\\hat{\\alpha}<\\hat{\\beta}", + "57909f74a1c1dcb3.png": "\\frac{f_{r}}{f_{s}}=\\frac{v_{r}\\cdot x}{v_{s}\\cdot x}", + "5790e14e473f696d.png": "(\\begin{matrix}i&0\\\\ i&-i\\end{matrix})", + "57959229d6ab6c1c.png": "P_{n}(K)=(P,G,\\in)", + "5799527fa4fae94e.png": "P=\\int I(x,y)dxdy", + "57998d182d511008.png": "(\\begin{matrix}x&y\\end{matrix})", + "579afe3be5f203ac.png": "\\Delta\\alpha=\\frac{1}{k}\\frac{\\partial\\phi(x)}{\\partial x}", + "57a2c5dba3c0d679.png": "\\frac{d(e^{x})}{dx}=e^{x}", + "57a44018e01e8634.png": "[\\begin{matrix}lnx\\\\ (lnx)^{2}\\end{matrix}]", + "57a80fdd3f5b7839.png": "\\overline{A_{t}}", + "57b8b124342c2ba8.png": "\\hat{Y}", + "57bb1f732f078074.png": "\\tilde{\\phi}(xU)=\\phi(x)", + "57bce8531fadba39.png": "4:sum+=tmp", + "57bdc23118e2710a.png": "MCG(S^{2})\\simeq Z/2Z", + "57c5914db0d3646f.png": "\\hat{y}=-37+5.1x", + "57cd212e01e68ab4.png": "E\\cap\\overline{E}=\\Delta\\otimes C", + "57cd3b67bfb91c8a.png": "\\forall v\\in W(w,v)\\notin R", + "57ce44933e5f11e5.png": "C^{\\prime}\\supseteq C(\\alpha)", + "57d85e8a558a2fa4.png": "\\int d^{3}xJ^{0}", + "57da586056b06390.png": "S\\approx\\frac{\\beta}{3\\alpha+0.2}", + "57e0713ea6ea405f.png": "(\\frac{1}{2})^{4}=\\frac{1}{16}", + "57e3b03731cfea4e.png": "\\tilde{O}(log^{3}n))", + "57e9e656d40b7370.png": "\\sum_{j=0}^{n}(-1)^{j}(\\begin{matrix}n\\\\ j\\end{matrix})P(j)=0", + "57ea44fc6c12b548.png": "F(h)=-\\frac{dU}{dh}", + "57ea863b4b054875.png": "f(t)=\\sqrt{|t|}+5t^{3}", + "57ece33b1647b9ff.png": "50*(\\begin{matrix}66\\\\ 7\\end{matrix})", + "57edb349d9b52688.png": "F:M_{n}(K)\\rightarrow K", + "57eeac9eb5ca23ee.png": "\\sigma=\\sqrt{\\sigma_{i}^{2}+\\sigma_{j}^{2}}", + "57f1f667d8dd595f.png": "1_{n\\ge0}-1_{n<0}", + "57f2daee07abf86e.png": "\\int_{0}^{T}dy_{2}dt", + "57f309782c924dd1.png": "L_{n-l-1}^{2l+1}(\\rho)", + "57f3325d2abe66f4.png": "E(r)=O(r^{131/208})", + "57f718a5ee82fb35.png": "\\overline{X}\\sim N(\\mu,\\sigma^{2}/n)", + "57fbbcb19f7ce264.png": "\\tilde{O}(n)", + "57fe32bd0fd781d4.png": "\\omega Z+", + "5803cb2183e8cdc7.png": "\\hat{f}^{c}", + "58052b066ea4c603.png": "\\neg\\neg\\varphi", + "580bac5312a3a25e.png": "v_{(G;c)}(\\{1,2\\})=16", + "581948787ae62406.png": "x_{0}\\in M(t_{0})", + "581d541354baa4de.png": "\\int kdx=kx+C", + "5823114aacc63d83.png": "v_{p}=k_{p}[M][M\\cdot]", + "58238907cfce3329.png": "\\hat{V}(t)", + "58247473f8bfd1c6.png": "K_{il(m+1)}=1", + "58284d2233522c25.png": "[\\begin{matrix}0\\\\ 1\\end{matrix}]", + "58329ce15bf336a6.png": "lim_{x\\rightarrow-\\infty}F(x)=0", + "5833b9087e20e47e.png": "[f|\\partial D^{2}]\\notin N", + "5836eb8f05ee46f5.png": "\\hat{q}", + "584049826f23be65.png": "\\tilde{v}_{r}^{p_{i}},\\tilde{\\omega}_{r}^{B}", + "584093078b4392a3.png": "(\\begin{matrix}4\\\\ 7\\end{matrix})", + "58450bb4b8d637c1.png": "\\int_{0}^{1}D(x)dx", + "584a6165162ff177.png": "\\tilde{K}(p;T)=e^{-Tp^{2}/2}", + "585203e1a899d886.png": "(\\nabla I)(x;t)", + "586073a8d02467e6.png": "(\\begin{matrix}n+2\\\\ 2\\end{matrix})", + "5863a726cb62e87c.png": "\\sum_{n=1}^{\\infty}\\frac{\\zeta(2n)-1}{2^{2n}}=\\frac{1}{6}", + "5867a2a5be100d34.png": "\\int Fdl", + "5868df66e188b81a.png": "\\pi_{i}B(S^{-1}S)", + "587313d19bc69997.png": "S_{n}(\\hat{\\theta})=M_{n}(\\hat{\\theta})", + "58754116741e3ba7.png": "[\\begin{matrix}1&0\\\\ 0&1\\end{matrix}]", + "5876b9a2fe5c94d0.png": "\\frac{d}{dx}y", + "58831f94f001a396.png": "2(\\sqrt{xy}-\\frac{x+y}{2})", + "5885d4c4e7358bdd.png": "(\\frac{ds}{dt})^{2}=\\dot{r}^{2}+r^{2}\\dot{\\theta}^{2}", + "588c9d4748ce11d3.png": "\\frac{1}{r}e^{-m_{W,Z}r}", + "588e460ce513f5bf.png": "\\hat{X}^{n}", + "588ea02d291f7302.png": "(\\begin{matrix}m+1\\\\ k\\end{matrix})", + "58922ffe54abba2c.png": "(S,\\pi,K_{1},...,K_{n})", + "58a00a64fb1183fc.png": "\\frac{\\partial f}{\\partial x}=y", + "58a3583ed6fe3dea.png": "R", + "58a538700a5907c5.png": "f=\\frac{3\\pi}{4}=135^{\\circ}", + "58b2ae4b7277e5ed.png": "a\\notin\\mathbb{Q}", + "58b2c92d60a8a6c8.png": "(\\begin{matrix}3\\\\ 4\\end{matrix})", + "58c88d63949ed1a2.png": "X_{m}=\\{e_{i}|x_{m}\\in e_{i}\\}", + "58c8c9eaf5e77409.png": "V_{0}\\subset V_{-1}", + "58ca5aec0feb2af4.png": "\\prod_{i=1}^{N}x_{i}", + "58d1a5bc1a83b983.png": "y=\\int f(x)dx", + "58d853e1c6f5e860.png": "p_{2}=\\frac{q_{1}-q_{2}}{2q_{4}}", + "58d9bee07d37344e.png": "G(T=0^{-})", + "58dbcc0beb9a4c6c.png": "\\hat{f}^{c}", + "58dc255351a6b068.png": "\\tilde{\\nu}", + "58e0366e09ec2682.png": "\\frac{\\pi^{12}}{12!}\\approx0.001930", + "58e045277e828b9c.png": "l^{t}\\tilde{\\beta}", + "58ed0b5cd484ac45.png": "(\\sqrt{1-x^{2}},-x)", + "58ee25570d2fc5f0.png": "\\tilde{E}_{6}", + "58f11f3711e27ca7.png": "\\frac{f(x)}{g(x)}=\\frac{\\sqrt{x-3}}{x^{2}-9}", + "58f172b4f7337da8.png": "\\sqrt{k}v=\\sqrt{g}sec\\theta", + "58f5b571037ab180.png": "\\int e^{\\theta x}dF", + "58fc317fb8b5808f.png": "\\frac{1}{0}=\\infty,\\frac{1}{\\infty}=0", + "58fe0c1dd3a83814.png": "(CH_{2}(COOH)_{2})", + "58fe7af7c1529260.png": "2y\\frac{dy}{dx}=3x^{2}-1", + "58fed88faddbad94.png": "a,\\tilde{a}", + "5900b67c2ba54f3b.png": "A=[\\begin{matrix}1&-3\\\\ 1&2\\end{matrix}]", + "59016c39ae83ce07.png": "4log_{2}n-4", + "590635f7e2c95f01.png": "\\varphi\\vee\\psi", + "590942a35bb3473f.png": "\\tilde{\\omega}", + "590a722bf9ec3aa3.png": "\\Sigma_{\\varphi}^{\\varphi}", + "590a9f75bc9b7f01.png": "\\int_{-r}^{r}\\sqrt{r^{2}-x^{2}}dx", + "59104738c82190f1.png": "(\\begin{matrix}x&y\\\\ -y&x\\end{matrix})", + "5910b993b917c208.png": "\\prod_{i=0}^{\\infty}a_{i}", + "591243b33cf408c1.png": "J_{n}(\\omega t)\\cdot u(t)", + "5912758de16b3b6e.png": "(\\begin{matrix}1\\\\ 0\\\\ -1\\\\ 0\\end{matrix})", + "591cf42c8f2aafcd.png": "\\tilde{\\psi}(t)", + "5922816a8758ca9c.png": "r=r(r,\\theta,t)=r\\hat{e}_{r}", + "592288d909af704d.png": "\\frac{-1}{\\sqrt{2a}}sin(\\frac{\\omega^{2}}{4a}-\\frac{\\pi}{4})", + "592f29432b81bf3a.png": "(\\nabla_{X}J)X=0", + "5931564b91da665b.png": "\\tau_{g}^{\\delta}", + "594c16365a9bfef4.png": "(id_{\\alpha},id_{\\beta})", + "59535102c8a41ed2.png": "0=x-12", + "5956ab18f0d90734.png": "z<\\eta(x,t)", + "5956e39abb341643.png": "(\\begin{matrix}0&1\\\\ 1&0\\end{matrix})", + "595a1c22e49e32c4.png": "u=+\\frac{\\partial\\psi}{\\partial y}", + "595cb17d624ce941.png": "D=\\prod_{i=1}^{n}D_{i}", + "5965afc590140cbf.png": "\\tilde{S}_{i}", + "5967c7216594caa5.png": "P(T|F)=\\frac{P(T)}{P(F)}", + "596bb5986a2a5800.png": "[\\begin{matrix}1&1\\\\ 0&1\\end{matrix}]", + "596feb427f753aca.png": "\\tilde{k}\\in\\tilde{K}", + "59732f5deaeb8ecd.png": "\\varphi_{m}(x)=E_{-m}(x)", + "5976445414d386fe.png": "C\\cong B/f(A)", + "597775d363fded18.png": "\\overline{4}3m", + "597bb6e1703ab7a5.png": "lim_{k}f_{k}(x)\\ge1", + "5980beb94061f3bb.png": "F=\\phi R_{m}", + "59847f6b51ec3a2a.png": "\\frac{dx}{ds}=e^{x}", + "5986e419937b0e44.png": "f(t)=\\sqrt{|t|}+5t^{3}", + "5986f57a95f43b50.png": "(R_{3}-C_{0})^{2}=D_{0}", + "598796902ea74fe1.png": "v_{rel}=v-(+w)", + "5988c4f9474d010a.png": "\\frac{\\partial^{2}f}{\\partial\\sigma^{2}}<0", + "5989b5b1e647f5f3.png": "\\int_{-\\pi}^{\\pi}e^{-i(j-k)t}dt=0", + "598aa877621f4048.png": "EC=(\\begin{matrix}I_{r}\\\\ 0\\end{matrix})", + "598f29b7b7df91cb.png": "W:[x_{1},x_{2}]\\rightarrow R", + "5993446cb219ef8c.png": "(\\frac{N}{N_{0}})", + "59a37911e3ae2eea.png": "\\langle W^{\\prime},R^{\\prime},\\Vdash^{\\prime}\\rangle", + "59a3b4674b3b7ecd.png": "\\sum_{i=6}^{10}26^{i}10^{16-i}(\\begin{matrix}16\\\\ i\\end{matrix})", + "59a7b43adaa4f49c.png": "(y^{\\prime},x^{\\prime})\\sim(y,x)", + "59a925041e64c69f.png": "{(\\beta^{\\chi})}^{\\eta}", + "59b5ddfe255de3b4.png": "A=\\pi-A^{\\prime}", + "59b6fec84bd1a04b.png": "\\alpha\\circ\\phi(g)=\\psi(g)\\circ\\alpha", + "59bb8fdadd07db2b.png": "\\frac{P_{f}}{P}=\\theta", + "59bd8b9ba2f8b022.png": "\\hat{X_{a}}", + "59c2c0ea91bc9121.png": "\\partial_{x}=\\frac{\\partial}{\\partial x}", + "59c2c260cba09143.png": "(\\begin{matrix}3&5\\\\ 6&-1\\end{matrix})", + "59c2e8bb776d7574.png": "\\overline{a}_{\\overline{n|}i}", + "59cd0618c3960c66.png": "\\mathbb{C}", + "59ce9c0f4c909aac.png": "a=\\frac{1}{\\sqrt{2R_{c}s_{o}}}", + "59dcc5d083a1fdbb.png": "e=r_{a}/a-1", + "59dfc6a74cb0e29b.png": "u^{2}=m_{u}v_{s}^{2}/T_{e}", + "59e7d6e482b2260b.png": "f_{i}(x^{1})\\le f_{i}(x^{2})", + "59f283f6908fb9b2.png": "\\tilde{D}_{6}", + "59f68d4374b35285.png": "g(\\tilde{x})", + "5a06a7bc717cf1a1.png": "\\hat{U}|\\psi_{i}\\rangle", + "5a095263f4135bfe.png": "\\hat{f}:E^{\\prime}\\rightarrow E", + "5a0c77c183aec18a.png": "A1:=28.552", + "5a132045c2f88a38.png": "ss\\{\\begin{matrix}2\\\\ 4\\end{matrix}\\}", + "5a147b4783ba6406.png": "\\tilde{\\nu}=0", + "5a149aabe43d7c5b.png": "((\\begin{matrix}n+1\\\\ d\\end{matrix}))", + "5a1fe42fe086f620.png": "\\frac{dS}{dT}", + "5a2113f929488c86.png": "\\hat{\\pi}", + "5a2282f13958f5ba.png": "20\\sqrt{3}", + "5a25de678d9da02c.png": "\\epsilon_{p,ij}=\\epsilon_{p,ij}^{h}-\\epsilon_{w,i}b_{j}", + "5a2d0ca592ab6f8d.png": "2(\\alpha-\\chi)=\\Gamma", + "5a2d832697293ef0.png": "A=\\int_{0}^{a}e^{x}dx", + "5a30ffb6f7823068.png": "T\\underline{A}", + "5a394c5c465929ef.png": "1(2^{1}/1!!)\\pi^{0}", + "5a3c66b35b18eaa7.png": "\\gamma(t)=(\\begin{matrix}t\\\\ t^{2}\\end{matrix})", + "5a3eedbead793e13.png": "a(x)=\\int f(x)dx", + "5a423ecd1d3cdddb.png": "\\mathbb{D}", + "5a4493673df4c345.png": "C_{n}=\\int_{0}^{4}x^{n}\\rho(x)dx", + "5a499af95b902e70.png": "T_{0}=2\\pi\\sqrt{\\frac{l}{g}}", + "5a50943ef5b16dc1.png": "(\\frac{7}{10},-\\frac{1}{10})", + "5a642bc8d7cf419d.png": "S_{gen}^{\\prime}=\\frac{Q_{2}^{\\prime}-Q_{1}^{\\prime}}{T_{surr}}", + "5a6736f03d99b35e.png": "k_{\\tau}^{\\psi}", + "5a67bd1a700be71f.png": "x^{2}+0.9x-3", + "5a6c306629c1999e.png": "\\Delta S=\\int\\frac{dQ_{rev}}{T}", + "5a6f75a9cdcb8adc.png": "\\hat{u}_{i}", + "5a74172a0951ad25.png": "(\\begin{matrix}n\\\\ 2\\end{matrix})", + "5a77bf2e27b08dee.png": "\\sum_{i=1}^{N}e_{i}<\\frac{Dd}{2}(1)", + "5a78eddff02d0984.png": "\\tilde{\\gamma}", + "5a79da584430a5fa.png": "\\tilde{r}", + "5a7b2c894e217bd3.png": "C_{ij}=(-1)^{i+j}M_{ij}", + "5a86095dfc704657.png": "\\int_{P_{0}}^{P}\\omega", + "5a8ede7b6ee0e706.png": "(\\begin{matrix}p\\\\ 1\\end{matrix})", + "5a9de14343d888ec.png": "\\sigma_{8}^{w}", + "5a9e9d85b9b62a70.png": "\\Omega_{x}=E(X^{\\prime}X)", + "5aa8226b5adbb972.png": "\\tau=\\prod_{i=1}^{K}\\sigma_{i}", + "5aa8528f7af09493.png": "\\frac{1}{k(k+1)\\pi}", + "5aa9ca02f6c2d9db.png": "x^{2}+0.9x-3", + "5aadffa646cfbffd.png": "\\hat{L}_{z}", + "5ab163930ace66a7.png": "\\frac{\\sigma}{\\mu}=\\frac{\\frac{a-b}{2}}{\\frac{a+b}{2}}=\\frac{a-b}{a+b}", + "5ab3e4108ffd716f.png": "||.||_{1}=||.||_{\\infty}", + "5ab536a74a394e01.png": "U=[\\begin{matrix}U_{1}&U_{2}\\end{matrix}]", + "5ab5ecb7c55b4320.png": "f(\\hat{x})", + "5ab6278360b6468b.png": "sin(2(\\theta_{i}-\\theta_{f}))", + "5ab7ffd11e5b3773.png": "\\frac{sinx}{x}=\\prod_{n=1}^{\\infty}cos\\frac{x}{2^{n}}", + "5ab8759135ed5e73.png": "\\int\\frac{e^{x}}{x}dx", + "5aba8769857e157d.png": "-\\int\\frac{du}{u}", + "5abc30e227fdda78.png": "A=(\\begin{matrix}1&1&2\\\\ 3&1&-1\\\\ \\end{matrix})", + "5abc3f7604e7ba3c.png": "[\\begin{matrix}1&R\\\\ 0&1\\end{matrix}]", + "5abc9d7e5d264e94.png": "R_{g}^{2}=\\lambda_{x}^{2}+\\lambda_{y}^{2}+\\lambda_{z}^{2}", + "5abf2c021572020d.png": "(0,0)\\in M_{1}", + "5ac0be943b914c8b.png": "|\\underline{P}\\rangle", + "5ac57c8f98011de7.png": "\\tilde{E}=E\\times\\mathbb{Z}_{n}", + "5acf402263adf9a4.png": "(\\frac{N}{N_{0}})", + "5ad1de12e4e827f4.png": "c^{\\underline{k-1}}", + "5ad315306224079a.png": "E_{1}=Ae^{i(kx-\\omega t)}z", + "5ad488023edc15d0.png": "RM\\tilde{R}", + "5adbddf6cef4bfd6.png": "\\tilde{E}_{i}^{a}", + "5adf667453f8089f.png": "\\hat{c}_{V}", + "5adfe5c52a4cf89f.png": "P(\\omega)=\\frac{|X(\\omega)|^{2}}{\\Delta f}", + "5ae0545f6d7c1843.png": "I\\frac{d^{2}\\theta}{dt^{2}}=N", + "5ae26dc4a322f6f4.png": "N\\alpha=3\\frac{n^{2}-1}{n^{2}+2}", + "5ae2b73dde15205d.png": "(\\begin{matrix}x&y\\\\ z&v\\end{matrix})", + "5ae49fa4abdb63ce.png": "[\\begin{matrix}lnx\\\\ \\frac{1}{x}\\end{matrix}]", + "5ae88f583968a253.png": "V^{*}(a\\otimes h)=\\Phi(a)h", + "5aea5508454db9be.png": "F_{3dB}\\approx K/T_{r}", + "5aeb386069e9869e.png": "G/N\\cong Z_{2}", + "5aebe956da5aae1f.png": "\\frac{dx}{du}du", + "5aed237d2dcefda2.png": "F(X)=\\prod_{i=1}^{s}f_{i}(x)", + "5afaea73d8f7151c.png": "W=\\int PdV", + "5afb21c6540d840b.png": "\\sum_{k=1}^{+\\infty}T^{k+\\frac{1}{k}}", + "5b0608f21b6c13c1.png": "\\tilde{W}\\approx(\\tilde{Z}\\tilde{Z}^{T})\\tilde{Z}\\tilde{S}^{T}", + "5b1b74cf7cd72b71.png": "1.3\\frac{a}{d}\\sqrt{n}", + "5b1c1dab6998dbb3.png": "i\\notin(2+i)", + "5b1c8f1b54d16e74.png": "\\tilde{B}_{3}", + "5b26374fb8197937.png": "(\\begin{matrix}a&b\\\\ c&-a\\end{matrix})", + "5b2767b97f1c216c.png": "\\alpha_{z}(a):=f(z)", + "5b281cbb25173fdb.png": "\\sqrt{J}", + "5b28226515f8400a.png": "\\tilde{R}_{n}", + "5b29e14b00929938.png": "\\omega=\\frac{|v|sin(\\theta)}{|r|}u", + "5b2a38783029e7ce.png": "\\tilde{G}^{K=\\pi_{1}(G)}", + "5b2cfc10a793ae13.png": "\\Delta S_{vap}=\\frac{\\Delta H_{vap}}{T_{vap}}", + "5b2fda81fd44f2f1.png": "\\sqrt{\\pi}", + "5b36024582fa5c04.png": "C/S", + "5b39efc087295db6.png": "\\frac{\\partial V}{\\partial R}", + "5b3ed5d577df4c50.png": "\\delta^{*}\\approx\\frac{1.72x}{\\sqrt{Re_{x}}}", + "5b41a50fa97a277f.png": "E=\\frac{1}{2}v^{2}-cosx", + "5b44f69d363fb896.png": "R^{(3)}=h^{ij}R_{ij}^{(3)}", + "5b45ee6f84ed6b39.png": "\\{\\begin{matrix}3\\\\ 5/2\\end{matrix}\\}", + "5b48fbe09756e500.png": "\\int_{0}^{1}\\frac{dx}{\\sqrt{x}}", + "5b49954b8e9eac6b.png": "C=p_{t}+C^{\\prime}(x,p)", + "5b4aa74720521bc0.png": "2^{5}-32=0", + "5b4bfafc9fcbd71c.png": "Q(x_{i},f(x_{i}))", + "5b4ce1de11198149.png": "p(1/x)=0", + "5b533fcd12b19cc1.png": "O(kn+1.274^{k})", + "5b57cb1b0ef82554.png": "\\sqrt{s}", + "5b677419e8ab702b.png": "\\overline{w^{\\prime}c^{\\prime}}", + "5b68cfd53f3f7321.png": "\\int n_{e}(s)ds", + "5b706d27f53ed437.png": "M/X=(M^{*}\\backslash x)^{*}", + "5b72361ae894e5d2.png": "0=f^{k}(y)=x", + "5b7280515c27c10d.png": "C_{*}(\\tilde{X})", + "5b73552e5c268b72.png": "(y^{\\prime},x^{\\prime})\\sim(y,x)", + "5b735a82853d0e27.png": "x-7\\times(x/100)", + "5b8390f9019278bc.png": "u\\notin\\Phi(V)", + "5b851c51235eb133.png": "(\\begin{matrix}2m-2\\\\ m-1\\end{matrix})", + "5b855f28519718fa.png": "\\varphi_{\\delta}^{6}", + "5b8887b50b2864a6.png": "S(t)=|t|^{3}", + "5b8b4c2110124cbb.png": "\\overline{Y}_{x}", + "5b91228d3fabb0c8.png": "\\prod_{i=1}^{n}f(x_{i})", + "5b91b563a8ad71bc.png": "y=(\\begin{matrix}v\\\\ u\\\\ p\\end{matrix})", + "5b957cb4fcd3ec7a.png": "\\hat{u}_{i}", + "5b9b8b0b14b45466.png": "\\mu(=k\\theta)", + "5ba3d6510509b549.png": "u=e^{i\\theta_{1}}cosr", + "5ba827ff3cee2789.png": "A=[\\begin{matrix}1&-3\\\\ 1&2\\end{matrix}]", + "5bb2422c2c702450.png": "\\sqrt{2}^{\\sqrt{2}^{\\sqrt{2}^{\\cdot^{\\cdot^{\\cdot}}}}}", + "5bb313b17bc9d521.png": "2+\\frac{12}{\\sqrt{13}}", + "5bb336812d28959a.png": "\\hat{c}_{V}", + "5bb3b9ed303df12d.png": "p_{k}(d\\sigma_{k}|\\eta)", + "5bc0d00f48f36198.png": "T_{n}n!=n^{n-2}n!", + "5bc51156715dfe14.png": "\\int f(x,y)dx", + "5bc78a7471fac718.png": "\\alpha e^{xS}S^{0}", + "5bce5be60553c77b.png": "OV_{i}V_{i+1}", + "5bcfe7ecde2c7744.png": "\\frac{\\partial f}{\\partial x_{j}}(x)", + "5bd18a92816c6e66.png": "E[\\epsilon|X]=0", + "5bdafa955e898f05.png": "[\\begin{matrix}1/4&0\\\\ 0&-1/4\\end{matrix}]", + "5bdc294911ccc252.png": "p+B^{2}/2\\mu_{0}", + "5bdc4ce8387cbdef.png": "\\frac{2\\pi}{5}\\frac{3\\pi}{5}\\frac{3\\pi}{5}", + "5bdf67734a3b1bb3.png": "\\{p(x),x\\in[0,1]\\}", + "5be1bad52281d864.png": "(\\begin{matrix}p\\\\ r\\end{matrix})", + "5be526ba70a9aaaa.png": "Re(s)>n-\\frac{1}{2}", + "5be9ac7cc441b172.png": "\\int e^{x}sin(x)dx", + "5be9dcb869e32a3f.png": "\\Delta l=l_{2^{\\prime\\prime}}+l_{2}^{\\prime}+l_{1}^{\\prime}", + "5bf22027389e6f02.png": "\\theta_{1},\\theta_{2}>\\theta_{12}>0", + "5bf2c43b0ccd227f.png": "(X,=)", + "5c015f79f65a0f48.png": "Z=\\frac{1}{s^{2}kC}", + "5c08dc7d5ab942e5.png": "\\tilde{T}_{i}:G/G^{\\prime}\\rightarrow H_{i}/H_{i}^{\\prime}", + "5c0a5039babe6ee9.png": "\\frac{F}{\\epsilon^{D}}\\cdot\\epsilon", + "5c117949746cb622.png": "=\\frac{1}{2}\\frac{m}{L^{3}}v^{2}[\\frac{y^{3}}{3}]_{0}^{L}", + "5c12f26913f4eb72.png": "\\omega^{n}/n!", + "5c12f302825224ee.png": "V^{(c_{n})}", + "5c14bd8df692e65e.png": "sup_{n}|\\sum_{i=1}^{n}x_{i}|", + "5c178cef12f137bd.png": "-\\frac{\\partial\\phi}{\\partial x}", + "5c19f1a8d606a393.png": "N_{0}-N_{1}+N_{2}", + "5c1a3eff7ef914e9.png": "\\frac{d}{d\\tau}", + "5c2554e6059d9f18.png": "(\\vec{A},-\\vec{E})", + "5c2a02c611bdc6fa.png": "\\int_{Q}r^{2}dm", + "5c2dd859b85aa324.png": "(\\begin{matrix}0&a\\\\ -a&0\\end{matrix})", + "5c3240ba18cb7d91.png": "\\mu=\\mu^{\\circ}+RTln\\frac{P}{P^{\\circ}}", + "5c33d33e82b1c873.png": "=-8/4=-2", + "5c340a1242176a1c.png": "\\tilde{\\psi}", + "5c34c91ed345a3b9.png": "\\hat{g}(f)", + "5c37870d371245b4.png": "\\overline{P}(A)", + "5c3f244299deee19.png": "\\int_{0}^{1}g_{n}=1", + "5c40e1217bc16828.png": "\\tilde{D}_{6}", + "5c41613d04208f76.png": "|\\int_{\\Gamma}\\frac{1}{(z^{2}+1)^{2}}dz|", + "5c475d9e57936ba7.png": "A=4A_{0}=\\sqrt{3}a^{2}", + "5c48b2a5ad4933a6.png": "\\rho(r)\\sim e^{-2Z_{\\alpha}r}", + "5c4c9837c5957bd9.png": "\\tilde{E}_{6}", + "5c5008d85cbd491c.png": "H(t):=\\int_{0}^{t}h(s)ds", + "5c537d4d2e866871.png": "\\frac{dv}{dy}", + "5c5447369635fd89.png": "\\prod_{i=0}^{k-1}(x-i)^{n}", + "5c590285ff62042b.png": "c^{\\aleph_{0}}", + "5c5c6db689e93555.png": "\\frac{dy}{dt}", + "5c5d926fc7b336be.png": "\\frac{d}{dt}(\\frac{d}{dt}x)", + "5c65ac9946de8425.png": "\\overline{\\delta}=\\frac{\\sum c_{i}\\delta_{i}}{\\sum c_{i}}", + "5c752dfd72a99661.png": "(\\prod_{i=N-1}^{0}T_{i})\\vec{0}", + "5c7848516a47e68e.png": "\\sum F_{x}=0=R_{Ax}", + "5c7cfcc7cb53b41c.png": "\\int x^{s}\\phi(x)dx", + "5c7ec71959441b42.png": "(2t+1)^{2}=8s^{2}+1", + "5c87817bbc5b8097.png": "D_{j}=-i\\frac{\\partial}{\\partial x_{j}}", + "5c87eefe623ef574.png": "\\pm[\\begin{matrix}1&1\\\\ 1&-1\\end{matrix}]", + "5c8998feb70515e1.png": "\\hat{\\alpha},\\hat{\\beta}", + "5c8e3cc74c1f0341.png": "\\int_{S}\\vec{B}\\cdot d\\vec{S}=const", + "5c908aa8d49a38f8.png": "[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "5c91c563b50e3bd5.png": "(x\\times d)\\cdot m=|m|^{2}", + "5c95956fd81900e8.png": "e^{\\hat{n}\\theta}", + "5c9b0e5e3d699d69.png": "1=\\frac{f\\sigma}{m\\sqrt{s}}\\rho^{2/3}M^{1/3}", + "5cac893732000b40.png": "V_{in}\\approx\\frac{I}{j\\omega C}=V_{C}", + "5cb6139ab2b58f3a.png": "-\\int E\\cdot dl", + "5cb6210573854e33.png": "(\\begin{matrix}n\\\\ d\\end{matrix})", + "5cc2030a091298f2.png": "\\hat{e}", + "5cc5ec30c287dd6c.png": "G:=-\\frac{\\partial(U-V)}{\\partial A}", + "5cc6a092d46e913d.png": "m^{*}=m+c(t-\\tau)", + "5cc88813c32439cb.png": "\\frac{-10bd^{2}}{c}+bc=1", + "5ccb8acb07c564a2.png": "g_{kl}=2\\chi\\Delta n\\overline{n}", + "5ccebfe81fb6e34c.png": "\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{a^{2}-c^{2}}=1", + "5ccfdf2a02ff2377.png": "f_{xx}=-\\frac{3}{8}<0", + "5cd1a3080a6ca594.png": "u_{J}(x,y)=x^{a}y^{1-a}", + "5cd3b5beef77325d.png": "b", + "5cd4d0b529c58ad4.png": "\\gamma_{\\chi}^{\\mu}", + "5cd4d4f1915cdc80.png": "\\int\\frac{dy}{y}", + "5cd8c42934c0bf19.png": "n|10^{i}(10^{k}-1)", + "5cd8eb6a3f5daecb.png": "2\\sqrt{5}\\approx4.47>4", + "5cdaca93dc23ae19.png": "t_{max}=\\frac{1}{b}ln(a)", + "5ce3b3c2893ec4b8.png": "\\int_{0}^{t}f(u)du", + "5ceb0dd1a41cf18e.png": "\\sqrt{\\Gamma}", + "5ceece34a648aa28.png": "v_{1}=(\\begin{matrix}1\\\\ 0\\end{matrix})", + "5cf98e972718f8f7.png": "a,\\theta,b,c:=0", + "5d05deae539c7f66.png": "N\\backslash S\\notin W", + "5d0687f0dce81b1e.png": "O(|E|+|V|\\sqrt{log|C|})", + "5d0b38480ef46261.png": "G=\\sum_{nm}G_{nm}", + "5d0f4bb338914670.png": "d\\in D^{n},r\\in R", + "5d193135c9dcbb44.png": "-\\hat{k}", + "5d198c89dd6a2e49.png": "(\\begin{matrix}1&N\\\\ 1&1\\end{matrix})", + "5d1fa24e0ca3dc46.png": "\\psi(r+a_{i})=C_{i}\\psi(r)", + "5d1ff51f83b36a06.png": "i\\notin F", + "5d207acdcc3aeddf.png": "\\frac{d\\theta}{ds}=\\frac{s}{R_{c}s_{o}}", + "5d22115b233749f1.png": "(x+y)^{n}=\\sum_{k=0}^{n}(\\begin{matrix}n\\\\ k\\end{matrix})x^{n-k}y^{k}", + "5d24ea25b7d9eb3b.png": "\\tilde{f}_{ij}", + "5d28b6639a0f30f1.png": "\\overline{P}(Cl_{2}^{\\le})=Cl_{2}^{\\le}", + "5d2bfdecfd07fc18.png": "g(x)\\int f(x)dx", + "5d2d17a74ad33ef1.png": "f:x\\mapsto cx^{r}c,r\\in R", + "5d380ac403029a36.png": "[\\begin{matrix}0&1\\\\ 0&1\\end{matrix}]", + "5d3afd842fd6a918.png": "\\frac{\\partial u}{\\partial t}", + "5d3d3353c895c885.png": "R_{\\eta}^{5}", + "5d5464b66a659fb8.png": "s\\{\\begin{matrix}2\\\\ 2\\end{matrix}\\}", + "5d5469144f86279c.png": "A(w)=\\sum_{n=0}^{\\infty}a_{n}w^{n}", + "5d5551d846a6880b.png": "1,1+x", + "5d590290df1753b0.png": "\\hbar\\frac{dk}{dt}=-eE", + "5d592d4b060a8086.png": "J=J_{1}(4)\\oplus J_{2}(16)", + "5d5be971e1cc1938.png": "cos(\\omega_{0}n)u[n]", + "5d5e12a30c008eb7.png": "\\cap_{n=1}^{\\infty}C_{n}=\\{x\\}", + "5d5ea938fc9e4211.png": "\\frac{d}{dx}", + "5d5fb952fd410c74.png": "\\hat{w}=\\hat{p}\\times\\hat{q}", + "5d63a40632973788.png": "\\frac{d^{c}u^{c}u^{c}e^{c}}{\\Lambda^{2}}", + "5d6463ec64324f2c.png": "D=\\frac{2|E|}{|V|(|V|-1)}", + "5d6ba91583557a08.png": "10^{1,000,000n}", + "5d757ae6594fe4d7.png": "/c^{2}", + "5d7ffee16fed6b2c.png": "\\overline{H}(y^{n}|x^{n})", + "5d8397ed10673873.png": "\\Delta^{t}(\\Delta^{r}(\\Delta^{s}(\\phi_{1,1,1})))", + "5d85a70aae759551.png": "B_{n+1}=\\sum_{k=0}^{n}(\\begin{matrix}n\\\\ k\\end{matrix})B_{k}", + "5d85c2d406a9005f.png": "(2x)/x=2", + "5d8cee9292c538f9.png": "[\\begin{matrix}a&r\\\\ d&s\\end{matrix}]", + "5d92d49ef6e31d51.png": "J=[\\begin{matrix}0&I\\\\ -I&0\\end{matrix}]", + "5d9d7a8eda2335a5.png": "f_{|M}:M\\rightarrow R", + "5d9edc0696771664.png": "H", + "5da0e5aa87f90b1c.png": "\\hat{T}", + "5daefda98bf287b1.png": "G(y)=\\int_{0}^{y}g(z)dz", + "5db4f0e19b34eda0.png": "[\\begin{matrix}x\\\\ \\frac{1}{x}\\end{matrix}]", + "5db7796042e29555.png": "A^{0}(\\overline{x},G)=G\\overline{x}", + "5db8e6a2ee3458d9.png": "V(r)=\\frac{1}{2}m_{0}\\omega^{2}r^{2}", + "5dbada0cff4ed803.png": "Tr\\rho^{p}K^{*}\\rho^{1-p}K", + "5dbe8f8e43d40b1e.png": "y=px-f^{*}(p)", + "5dc4fb7051d7f67e.png": "\\forall u(wR_{i}u\\Rightarrow u\\Vdash A)", + "5dd264763724ed0c.png": "(\\begin{matrix}n\\\\ 5\\end{matrix})", + "5dd36bba2b37c73b.png": "\\hat{n}", + "5dd419d9a0ee6f2a.png": "s\\notin T", + "5dd8557501384503.png": "-r_{2}e^{-i\\theta_{2}}s^{2}(1-s)", + "5ddf965492c89c56.png": "X\\cdot Y:=\\eta_{\\mu\\nu}X^{\\mu}Y^{\\nu}", + "5de057ef65664432.png": "(2e^{0i})^{0.5}=\\sqrt{2}", + "5de3ceadb9accfd3.png": "M\\otimes_{R}M^{*}\\cong R", + "5de74ba1d860c1cf.png": "\\hat{\\alpha}>0", + "5def474c77fadade.png": "(f\\circ i_{j})_{j\\in J}", + "5deffeab5d757ad9.png": "(\\begin{matrix}p+q\\\\ p\\end{matrix})", + "5df4fd7d83af38f2.png": "[\\begin{matrix}1&0\\\\ 0&-1\\end{matrix}]", + "5df820f2493dcb42.png": "\\int_{h(C)}fds", + "5df841f396395024.png": "\\int x(t)dt|_{t=z}", + "5dfe0360d40d7108.png": "PB-C=\\sqrt{\\gamma}Q", + "5e00fd483abd5853.png": "\\tilde{v}_{ij}", + "5e027914bdce1a4b.png": "\\hat{x}^{o}", + "5e12096ea850b73b.png": "\\hat{M}^{\\prime}", + "5e1a8c6fa9aed4bf.png": "y=a\\frac{d-c}{a-b}+c", + "5e1eb62de0087d65.png": "\\int e^{\\theta x}dF", + "5e1f6d45e01a9bd1.png": "\\int_{\\gamma}\\rho|dz|", + "5e1f98ecad576e7d.png": "\\rho_{N_{1},N_{2}}=\\rho_{\\epsilon_{1},\\epsilon_{2}}", + "5e2136e028d57f50.png": "exp_{2}^{i-2}(n^{O(1)}))^{\\Sigma_{j}^{P}}", + "5e247178976ea1b3.png": "\\tilde{O}(log^{4}q)", + "5e25790243ba94f7.png": "\\int_{-\\infty}^{a}", + "5e3100e25ded0e34.png": "\\tilde{D}_{9}", + "5e3242e0e11d147a.png": "\\sum_{n=0}^{\\infty}x_{1}^{n}x_{2}^{n}", + "5e34feb2dd7abe21.png": "y^{+}=\\frac{yu_{\\tau}}{\\nu}", + "5e35a1ec78cdec9b.png": "\\Psi=e^{i(k\\cdot r-\\omega t)}", + "5e3c31d4f1c75e46.png": "\\tilde{P}_{r}", + "5e45a7d8a1665cbf.png": "\\rho_{k}=k\\frac{U_{MN}}{I_{AB}}", + "5e470986e0717a54.png": "0,\\frac{1}{2},\\frac{\\sqrt{2}}{2},\\frac{\\sqrt{3}}{2},1", + "5e4b417e15ceaab4.png": "\\tau=\\sqrt{t^{2}-x^{2}}", + "5e51f9412168609a.png": "\\int_{p}fdx", + "5e54119e4ecd5b00.png": "\\sqrt{2n}", + "5e59ff58889b4275.png": "\\tilde{X}:=f\\circ X", + "5e5be8384283080a.png": "P(\\vec{y}|\\vec{x})P(\\vec{x})", + "5e5e9c97ca5e7f96.png": "H(x)=1_{(0,\\infty)}(x)", + "5e5f99f201845bd0.png": "\\frac{d}{dx}(\\mu y)=\\mu q(x)", + "5e605022bd7bf4ae.png": "\\int_{\\gamma}f(z)dz=0", + "5e6849a40d406a14.png": "-\\pi^{-\\pi}", + "5e72715d85fc515c.png": "\\overline{A_{t}}", + "5e7ab97d44642692.png": "x^{p}\\notin G^{\\prime}", + "5e7c0507b075301b.png": "s\\{\\begin{matrix}2\\\\ 3\\end{matrix}\\}", + "5e84893f9a4fe330.png": "g\\frac{\\partial\\eta}{\\partial x}=fv", + "5e8f41b53c430230.png": "\\sum\\frac{\\kappa}{sin(\\theta)^{3}}=0", + "5e93de30955fd98a.png": "=c+v+s", + "5e9420865e4a8284.png": "N(t)=\\int ndxdydz", + "5ea441cebf3f0c1c.png": "F[y]=\\prod y", + "5ea50b3eaa674948.png": "n", + "5ea684cd207d0bd8.png": "\\{a^{n}b^{n}c^{n}d^{n}|1\\le n\\}", + "5ead5544a36c534f.png": "S_{i}=\\sum_{j}d(v_{i},v_{j})^{2}", + "5ead8ebbd7258967.png": "s\\{\\begin{matrix}2\\\\ 4\\end{matrix}\\}", + "5eaf0683339b06f1.png": "Q(H)=\\prod_{i}Q_{i}(H_{i})", + "5eafa8cef97ebb74.png": "S=\\frac{\\partial M}{\\partial logt}", + "5eb1d4bef7272116.png": "p_{M}=e^{-\\Delta U/k_{B}T}", + "5eb3fc30b7017406.png": "df=(\\nabla f)\\cdot dx=0", + "5eb4288e8379e1ca.png": "\\hat{\\nu}", + "5eb50554b4624636.png": "Ra_{x}^{*}=\\frac{g\\beta q_{o}^{\\prime\\prime}}{\\nu\\alpha k}x^{4}", + "5eb75b2ff2a8fd3f.png": "I=\\int Fdt", + "5ebb48398667f402.png": "(e_{1}\\leftrightarrow e_{2})", + "5ebd0a995bc33cc2.png": "P(\\omega<\\frac{X}{a})=\\alpha", + "5ebde82b96c28250.png": "(\\begin{matrix}6\\\\ 3\\end{matrix})", + "5ec404d57586e40e.png": "K_{X}\\sim\\pi^{*}K_{Y}+R", + "5eccf65a217bae7c.png": "E_{-}0", + "5eea6f8f0f01a3d7.png": "v=v^{i}(x)\\partial/\\partial x^{i}", + "5eef0cd358521e7f.png": "\\tilde{s}", + "5eeff5d98f437e4a.png": "\\{z:||z||=-a^{2}\\}", + "5ef56b1784049925.png": "\\int_{0}^{t}p^{\\prime}(s)p(t-s)ds", + "5efd18bf67ccdc07.png": "C[]", + "5f02444239aaf90d.png": "(\\begin{matrix}9\\\\ 4\\end{matrix})", + "5f05d98f826ba5b2.png": "t_{E^{d}}=-t_{E}", + "5f100604039baf91.png": "\\hat{V}", + "5f12d88891ba5cb9.png": "\\hat{x}_{1}", + "5f164a277f5527df.png": "(\\begin{matrix}n\\\\ m\\end{matrix})", + "5f2c830c0010e297.png": "x=\\frac{\\pi}{3},\\pi", + "5f2d98007970cbe0.png": "\\partial_{t}L=\\frac{1}{2}\\nabla^{2}L", + "5f32af4f64199a52.png": "Q(H)=\\prod_{i}Q_{i}(H_{i})", + "5f32d73575d1a8c2.png": "(\\begin{matrix}0&0\\\\ 0&1\\end{matrix})", + "5f3987a9918f0e51.png": "(\\begin{matrix}n\\\\ 1\\end{matrix})_{F}=(\\begin{matrix}n\\\\ n-1\\end{matrix})_{F}=F_{n}", + "5f39d16a5eed3bce.png": "|\\langle m|e^{ik\\cdot r}|n\\rangle|^{2}", + "5f3d3a458eb588a5.png": "-\\frac{dz}{z}", + "5f454144039977cc.png": "t=\\frac{X_{o}^{2}}{B}+\\frac{X_{o}}{B/A}", + "5f4b0f531569e32d.png": "B=\\prod_{i=1}^{n}[a_{i},b_{i}]", + "5f4e67b9cb24d986.png": "MR", + "5f4f2b6340da0f38.png": "(\\begin{matrix}U_{1}\\\\ U_{2}\\end{matrix})", + "5f500d1c85fe058f.png": "\\sqrt{2t}", + "5f54a4ab96664482.png": "[\\hat{Y},\\hat{I}_{\\pm}]=0", + "5f5a69d06bcee576.png": "(1-m_{k})", + "5f5b5d1b20cb0a93.png": "V_{\\alpha+1}=P(V_{\\alpha})", + "5f60f2b1a85d56fb.png": "|G:H|=\\frac{|G|}{|H|}", + "5f65c6560df122c3.png": "\\frac{1}{2}\\sqrt{r-r^{2}}", + "5f668ded242de37f.png": "T(p)=\\frac{1-z_{a}}{1+z_{a}}", + "5f66a22466dc076d.png": "c_{1}\\overline{V}_{1}+c_{2}\\overline{V}_{2}=1", + "5f6cc81434c3ab0e.png": "A(w)=\\sum_{n=0}^{\\infty}a_{n}w^{n}", + "5f774e4af6047db8.png": "L=-\\tilde{F}\\dot{v}^{2}+2\\dot{v}\\dot{r}", + "5f780aeeaf5afda2.png": "s\\{\\begin{matrix}2\\\\ 3\\end{matrix}\\}", + "5f7bd045b1f47a28.png": "G=H-TS_{int}", + "5f8307aa6227754b.png": "\\frac{\\partial F}{\\partial y}=J", + "5f859dfa2eb73103.png": "\\{\\begin{matrix}4\\\\ 4\\end{matrix}\\}", + "5f880776aed46c7b.png": "\\Phi^{t}(x_{0})=e^{tA}x_{0}", + "5f88754156c1414b.png": "\\varphi\\vdash\\psi", + "5f88c5cd7f852480.png": "\\langle J(0)\\rangle_{F_{e}}=0", + "5f8a273007dccffb.png": "FT^{t}=M^{t}F", + "5f8c21da36308d81.png": "\\frac{a}{b}=\\frac{dy}{dx}", + "5f90125e1d4507cf.png": "Uf(T)U^{*}", + "5f90eb747f7dab53.png": "\\Delta\\vec{F}=A\\Delta\\vec{p}", + "5f966fbb9ef1e339.png": "A(-1)=a", + "5f9911936bffd4c4.png": "\\int r^{2}\\rho(r)d^{3}r", + "5f99f6cc91bce1a0.png": "\\tilde{L}", + "5fa447599ecd62a2.png": "\\{\\hat{f}_{n}\\}_{n=1}^{\\infty}", + "5fa80654bedf78a7.png": "(1,2,3)\\ne(3,2,1)", + "5fa90909d8c3e203.png": "m=e/(u_{1}^{z})", + "5fabcf8af97e8939.png": "O(|E|+|V|\\sqrt{log|C|})", + "5fb0b45fab31a279.png": "Q\\sqrt{5}", + "5fb4cc17cb8f67e9.png": "u_{2}=[\\begin{matrix}0\\\\ 1\\end{matrix}]", + "5fb57d4990be23e7.png": "(\\begin{matrix}6\\\\ 3\\end{matrix})", + "5fb5a3d1cf796a66.png": "\\frac{1}{2}\\hbar\\omega_{q}", + "5fb7456c72d3c643.png": "d=(1/2)b_{2}", + "5fbc47d2504b1b31.png": "\\sqrt{(1-x^{2})^{-1}}", + "5fbe33f3c33c47f5.png": "(x,y)\\mapsto(x,-y)", + "5fc5bf09627bc9a1.png": "\\alpha(t)=\\frac{|t|!}{t!|S_{t}|}", + "5fd055b7dbec11cb.png": "\\int_{E}f\\mu", + "5fdb6cd8071849ca.png": "z-\\hat{z}", + "5feeab36b21b4de4.png": "2^{n-4}+2^{\\lfloor(n-4)/2\\rfloor}", + "5ff06c351083d279.png": "c_{w}=(\\frac{\\lambda_{1}-\\lambda_{2}}{\\lambda_{1}+\\lambda_{2}})^{2}", + "5ffda3c030c89e4e.png": "MSD=6D_{a}t^{\\alpha}", + "5ffdf51feaaeb15a.png": "(\\begin{matrix}N\\\\ 2\\end{matrix})", + "60044f38f5ffc921.png": "tr(e^{-tD^{2}})<\\infty", + "6004b13b8dc7985b.png": "S_{x}=x(H)", + "60059847820defc1.png": "-\\frac{8}{945}h^{7}f^{(6)}(c)", + "600909e70b979e87.png": "\\int_{\\Omega}|f\\varphi|dx<+\\infty", + "600ded194042afd2.png": "lim_{n\\rightarrow\\pm\\infty}x^{2}f(x)=0", + "600f4ff37c25cb86.png": "12\\sqrt{25+10\\sqrt{5}}", + "60137da7a85d15cc.png": "x_{0}=\\frac{S^{2}-1}{S^{2}+1}", + "60147ceb36daa546.png": "Q_{\\chi^{3}}", + "60199d10b2be666c.png": "C_{E_{2}}^{J}=-\\epsilon_{1}^{1}\\epsilon_{2}^{3}/D", + "601a825685c11877.png": "|E(F_{q})|=q", + "601fc087f4bac1a1.png": "h_{J}\\leftarrow\\hat{h}", + "60273c8e937195f2.png": "\\hat{L}^{2}", + "602808076a6b565a.png": "z_{\\alpha}\\sigma/\\sqrt{n}", + "6028cdfa7160c46a.png": "(1-x,1-y)", + "602968f41246de45.png": "\\frac{dq}{dt}=\\frac{M}{B}", + "602a2ebf268d9129.png": "B_{\\tilde{\\nu}}", + "6030eb0212bb5e74.png": "(\\begin{matrix}N+I-1\\\\ I-1\\end{matrix})", + "6032d6c2e88be599.png": "x_{n}K_{\\alpha}", + "605d1a5602f1eddf.png": "W_{r}^{\\omega}", + "606cdd223c746d6b.png": "(\\begin{matrix}n+2\\\\ 2\\end{matrix})", + "6076f2c1da7c6640.png": "12^{m}\\cdot(\\#\\phi)", + "607d13d4db312090.png": "\\hat{R}", + "607eb9584d62ff5a.png": "O_{R}P", + "6080b55e0ebc9b13.png": "k\\frac{QdL}{x^{2}L}\\hat{x}", + "6080e4a495c97eb5.png": "\\hat{u}_{R}", + "608117eaafb01584.png": "\\tilde{g}=e^{2\\varphi}g", + "6082ff58413e9f22.png": "\\overline{E_{0}}", + "6083ba0ee7365aca.png": "\\int_{0}^{\\infty}e^{ax}cosxdx", + "60852bb251cba465.png": "w(2)=\\frac{2}{\\sqrt{\\pi}}", + "608666662277eef2.png": "\\int e^{-x}cos(x)dx", + "608b82fa0b47dfbc.png": "\\Psi_{v}^{\\varphi}", + "60955e336155e3d1.png": "s\\{\\begin{matrix}3\\\\ 3\\end{matrix}\\}", + "6095962582e49e87.png": "\\frac{d}{dx}", + "6097b11af73c34ae.png": "\\partial_{\\mu}\\hat{A}^{\\mu}", + "6098a808fb191487.png": "1/2<\\sigma<1", + "6098af1500477c5a.png": "\\frac{h-h^{\\prime}}{\\lambda}=\\frac{D}{\\lambda}=N", + "609a8abe07cced4d.png": "\\int_{S}1dS", + "609bacca22e1f3bb.png": "\\lambda\\frac{1}{k_{1}^{2}}\\frac{1}{k_{2}^{2}}\\frac{1}{k_{3}^{2}}\\frac{1}{k_{4}^{2}}", + "609caf3497a8e493.png": "\\prod_{i\\in X}Y_{i}", + "60b20b0bb8589bd4.png": "Q_{A}=10^{R_{A}/400}", + "60bafe34ad61ba73.png": "(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "60be7994e03c85bb.png": "dx\\rightarrow dx(1+i\\sigma/\\omega)", + "60c945a70998100a.png": "V_{T+1}(k)=0", + "60d07bd2db412c15.png": "u^{h}(x^{h},z^{h})", + "60d62798784ac8db.png": "(n+1)^{2}-n^{2}", + "60d722cfee552a90.png": "\\hat{a}_{i}", + "60dca5d9016849dc.png": "degi=(1,-1)", + "60e56d372cc460ed.png": "2^{k}\\le\\frac{2^{n}}{(n2^{b-1}+1)}", + "60e7e35b4962deda.png": "\\langle\\mu\\rangle=\\frac{\\int\\mu dP}{\\int dP}", + "60e9edce25452468.png": "\\hat{a}_{t}", + "60fb833b4baaed28.png": "(\\partial_{t}+\\gamma)^{2}", + "60fe7d9e5b5a3d31.png": "A_{(0,0,1)}(x)=x^{2}", + "6101a391917ccac6.png": "\\hat{\\nu}", + "610ba43accf2b12f.png": "\\frac{dy}{dx}=st(\\frac{\\Delta y}{\\Delta x})", + "610d4d5bad59b19f.png": "{(\\Lambda^{\\psi})}^{\\nu}", + "610f3858745ff5af.png": "\\frac{dB}{dG}=0", + "61100d5cb52a6e20.png": "S=\\int ds", + "61135f4472856cf3.png": "\\int_{0}^{\\infty}f(x)dx", + "61184976e3a87d93.png": "(0.999)x-y=2", + "6126876f869fb5b4.png": "g_{mm^{\\prime}}^{-1}=g_{m^{\\prime}m}", + "613792e42fcf821c.png": "(\\begin{matrix}n+1\\\\ 1\\end{matrix})", + "613882e383503b22.png": "e=\\frac{\\Delta L}{L}=\\frac{l-L}{L}", + "613b08e1435d49b8.png": "c(E)=A_{C}(E-E_{C})^{a_{C}}", + "613f668456693251.png": "M=(\\begin{matrix}A&B\\\\ C&D\\end{matrix})", + "6144a62e9a62f5c8.png": "\\tilde{D}_{6}", + "6148d60c0cf260f8.png": "\\int_{a}^{b}dx", + "6149645f112a3e9f.png": "\\mathbb{H}", + "614ff7b80bf0830e.png": "(\\forall x\\in V^{P})p\\Vdash_{P}f", + "6150916369819aac.png": "L_{n+l}^{2l+1}(\\rho)", + "615604447fe89da5.png": "[\\begin{matrix}4&4\\\\ 6\\end{matrix}]", + "6158b6a0a1ab1289.png": "\\hat{H}=\\hbar\\omega(\\hat{a}^{\\dagger}\\hat{a}+1/2)", + "615a0fee542c0928.png": "E_{u}[Y_{t}(u)-Y_{c}(u)]", + "615b4a3cec5ce1a3.png": "\\tilde{M}=U\\tilde{\\Sigma}V^{*}", + "615bb25e5904138f.png": "\\hat{q}_{i}", + "615ed67ade540bf4.png": "(\\begin{matrix}n+k-1\\\\ n-1\\end{matrix})", + "6162988a6f6887b5.png": "a\\hat{x},a\\hat{y},a\\hat{z}", + "616630c8118d101e.png": "G=\\bigcup_{i\\in I}{t_{i}}^{-1}H", + "61689960393f3294.png": "|\\Omega|=\\frac{d\\theta}{dt}=\\omega(t)", + "616b44eddfd09f61.png": "y=20+3\\epsilon_{4}+4\\epsilon_{8}", + "616c3557d4f1cc5b.png": "A", + "616d6bbbea6a08c8.png": "\\int xe^{2x}dx", + "61762357330c09f4.png": "\\hat{L}_{a}", + "61771470f37a7a73.png": "\\eta=1-(\\frac{1}{r^{(\\gamma-1)}})", + "617d995f2f56be65.png": "\\hat{\\pi}", + "617e58d6c14ec911.png": "(\\nabla_{X}J)X=0", + "61828db918384f45.png": "q^{\\prime\\prime}=h(T-T_{\\infty})", + "6183016cde0bb8f4.png": "\\sum_{k=1}^{\\infty}(\\frac{1}{k^{3}})", + "61874e98b8b4608a.png": "c=\\sqrt{a^{2}+b^{2}}", + "618c45a9cbfc1188.png": "F=\\sqrt{1-\\alpha}", + "6195c341830aa129.png": "\\int_{0}^{1}g_{n}=1", + "6197571aec2caafa.png": "\\tilde{f}_{1}", + "619b1c16bd82118b.png": "\\hat{f}_{i}", + "619cf0736c240241.png": "[\\begin{matrix}x&y\\\\ z&v\\end{matrix}]", + "61a5dc0eebefaa88.png": "\\prod_{i\\in I}S_{i}", + "61aaa23fc49a8c89.png": "\\hat{v}^{*}", + "61afa681544a4144.png": "J=J^{-1}=J^{*}", + "61afd27e10df9196.png": "\\tilde{f}", + "61b089effd5bd921.png": "\\int d^{3}r", + "61b5d60dc826eed3.png": "X=A,\\overline{A},A\\overline{A}A,", + "61bbecb143b08579.png": "\\frac{dN}{dt}", + "61c15ddcfd761e5f.png": "\\hat{d}", + "61c26e30216dda69.png": "E_{0}=(\\frac{a^{2}}{2\\pi L_{B}})v^{2}", + "61c8ab8dee0dc1f2.png": "\\hat{1}", + "61cd630dbc364f59.png": "C=-c^{2}", + "61e30bc224e386ee.png": "A=(\\begin{matrix}0&1\\\\ 1&0\\end{matrix})", + "61ea447fd53e990e.png": "T=r_{a}r_{b}=rr_{c}", + "61ee112bb36cf2d1.png": "-i[\\hat{n}\\times\\partial\\hat{n}]", + "61f4e64fc7b950df.png": "\\frac{dg(z)}{dz}=\\frac{1}{(cz+d)^{2}}.", + "61f661b01a527543.png": "\\sqrt{n}D_{n}>K_{\\alpha}", + "61fadde434688597.png": "\\prod_{k=1}^{x}f(k)", + "61fbbb6e449a61ff.png": "I=\\prod_{i=1}^{n}P_{i}^{a_{i}}", + "6207bd9240ca17f1.png": "\\int_{L}^{*}", + "6208e6db5f1c2fbc.png": "(\\begin{matrix}n\\\\ k\\end{matrix})_{q}", + "620e37b00495a00c.png": "T_{r}H=HT_{r}\\forall r", + "621100e9ef710b1a.png": "\\langle\\Psi_{motion}|", + "62149e0aa2b1ec1b.png": "A_{q}(n,d,w)=1", + "621d92889f603a4a.png": "p:\\dot{\\phi}\\mapsto(p|\\dot{\\phi})", + "621db6d0b1f6acff.png": "C_{\\alpha_{1}...\\alpha_{2s}},C_{\\dot{\\alpha}_{1}...\\dot{\\alpha}_{2s}}", + "62204c62fe821e6f.png": "\\int Mvds", + "62267b5eed0d3fa9.png": "\\frac{1}{2}(z+1)", + "622773f555a3502c.png": "f_{0}(\\vec{x})\\ne0", + "622b1db4e3b0e0bd.png": "2\\epsilon\\sigma T_{a}^{4}-\\epsilon\\sigma T_{s}^{4}=0", + "62324e52f8332c11.png": "v^{2}=u^{2}+2as", + "623492f4266ac559.png": "\\sqrt{N}\\le Mk_{B}T_{i}", + "62468a616d1fc4f3.png": "(x_{i1}-\\overline{x}_{i})", + "624c27e36f069af8.png": "G_{\\lambda}(\\sigma)=\\frac{1}{\\sigma+n\\lambda}", + "624d4b59f383e293.png": "\\tilde{\\Omega}", + "6250a1fd98ed338e.png": "(\\begin{matrix}n\\\\ b\\end{matrix})", + "6250d9fa594ae332.png": "X=e^{\\mu+\\sigma Z}", + "625113d422115ae3.png": "a=\\frac{1}{2n+1}", + "625369fcf9945504.png": "s_{n}^{2}=\\frac{Q_{n}}{n-1}", + "6256ec71fabfc250.png": "(1|1)", + "6258425474b0abd5.png": "(\\begin{matrix}0&0\\\\ 0&1\\end{matrix})", + "6263e7f4376627d1.png": "(\\begin{matrix}0&1\\\\ -1&0\\\\ \\end{matrix})", + "62664462bc51efd5.png": "\\prod_{k=1}^{n/2}2(2k-1)", + "626d30b1ece9359b.png": "X_{n}=M^{n}X_{0}", + "626f70c224758b94.png": "\\xi_{-1}(-\\hat{z})=(\\begin{matrix}-1\\\\ 0\\end{matrix})", + "627de29874bf3f86.png": "\\vec{t_{2}}\\langle s^{\\prime\\prime}\\rangle=\\vec{t_{2}}\\langle s^{\\prime}\\rangle", + "6280f995aa6962ca.png": "\\hat{\\theta}\\in\\Theta", + "628518c978d250db.png": "-log_{2}p(X=x)", + "628536c4a5bd053a.png": "\\frac{\\partial u}{\\partial t}=0", + "62896b47ed57a5bd.png": "W_{\\alpha}\\equiv\\overline{D}^{2}D_{\\alpha}V", + "628e78d6e081fe62.png": "\\int_{0}^{\\infty}e^{ax}cosxdx", + "628ec2c7fe5e4125.png": "a_{p}^{N-1}\\equiv1(modN)", + "62962a60b5563d0c.png": "A_{i}0", + "62d9213f57d5f524.png": "A=\\int2\\pi R(s)ds", + "62dd74df0b0a985e.png": "n=\\frac{(4\\cdot l^{2}+1)}{4}", + "62dda838e31a6f2b.png": "\\frac{d}{dt}N_{1}=-c_{2}N_{2}", + "62de530c9a473c1a.png": "\\{\\begin{matrix}3\\\\ 8\\end{matrix}\\}", + "62ee0895245324cd.png": "R_{\\mu\\nu}=\\frac{\\Lambda}{\\frac{D}{2}-1}g_{\\mu\\nu}", + "62f17c7db20d3072.png": "F_{\\overline{z}}", + "62fe96daf9094aad.png": "[\\begin{matrix}1&-1\\\\ -1&-1\\end{matrix}]", + "63014603d1625d7b.png": "a]=\\{x\\le a\\}", + "630343be16860355.png": "T\\ne U/c", + "6305772aa5122b3d.png": "S=-mc\\int ds", + "63088388f572142f.png": "\\hat{V}_{n}", + "630bb806a0c21583.png": "\\omega_{\\hat{M}\\hat{N}P}", + "630f4830448a5a10.png": "(\\begin{matrix}x\\\\ y\\\\ 1\\end{matrix})", + "63103cc4e745fee1.png": "(\\begin{matrix}k\\\\ r_{1},r_{2},...r_{n}\\end{matrix})", + "631902d5f44d3b28.png": "\\Xi_{q}^{z}", + "631bf713f85b721d.png": "\\int e^{x}dx=e^{x}+C", + "631c8f7085682f7c.png": "\\int rcos\\theta dm", + "632268c654f39942.png": "\\dot{p}_{i}=\\{p_{i},H\\}", + "63278e8b5760bb4f.png": "r=\\frac{h}{2}+\\frac{c^{2}}{8h}", + "6329ed237af76f13.png": "\\int_{S}1dS", + "6329ee78e013d56d.png": "0=0", + "6334ffdf7f1e4314.png": "1+6(\\frac{1}{2}n(n-1))", + "633988197e7cf33e.png": "P(r)=\\frac{1}{Z}e^{-\\frac{F(r)}{kT}}", + "633f30dd4661d774.png": "\\frac{d^{2}s}{dt^{2}}=-k^{2}s", + "633ff21de32b42dc.png": "\\sqrt{K}", + "634558d8320d64fd.png": "\\int_{0}^{T}y_{2}dt", + "63478b8c59f57855.png": "T=\\sqrt{N_{0}/2^{k}}", + "6349531e743ee197.png": "2d+1>n", + "6349c3738eea5c2d.png": "A=U(\\begin{matrix}I_{r}&0\\\\ 0&0\\end{matrix})V", + "634c03ed1a8a8141.png": "\\frac{du}{ds}=0", + "634f5a4de7370e70.png": "\\lambda^{3}=(\\begin{matrix}1&0&0\\\\ 0&-1&0\\\\ 0&0&0\\end{matrix})", + "6354ea3c91fb0c42.png": "E_{n}=aP+bH", + "6356a2be76baf637.png": "I_{R}(B)=(B:B)", + "6359e1ee1aa7636e.png": "x_{0}=\\frac{S^{2}-1}{S^{2}+1}", + "635e2896915c8045.png": "-\\sqrt{\\frac{1}{14}}", + "635f1108c16c700b.png": "\\sqrt{p}", + "636616f7980e3cc1.png": "3/\\tilde{4}", + "6366284fc62aa50e.png": "\\hat{f}_{i}", + "6367f4be5132e580.png": "[\\begin{matrix}x\\\\ x^{2}\\end{matrix}]", + "6368af9a6b64342a.png": "\\hat{H}=1+\\frac{1}{2}(slope)", + "6374587aea8238ab.png": "T_{2}=T_{1}e^{\\mu_{s}\\beta}", + "637968238d8ab99b.png": "h_{n}=-\\frac{f(x_{n})}{f^{\\prime}(x_{n})}", + "6379ae4f62bbb73f.png": "\\Omega=N!/N_{1}!N_{2}!", + "637b3e67ab1fb3e7.png": "\\int_{\\gamma}f(z)dz=0", + "637e27da9eca9f44.png": "a,\\tilde{a}", + "6381c5f1ddeac5d2.png": "e_{a}:=e(f_{a}):=e_{a}^{\\mu}\\partial_{\\mu}", + "63888f0f1a436e7c.png": "\\frac{g_{\\mu\\nu}-\\frac{k_{\\mu}k_{\\nu}}{k^{2}}}{k^{2}-m^{2}+i\\epsilon}", + "6389999878f19b5e.png": "\\hat{\\nu}_{i}", + "638b02e7b1d32d21.png": "\\tilde{g}=F^{T}gF", + "638c3bfebf749b38.png": "\\int_{J}f(x)g(y)dx", + "638cd1675194db56.png": "P_{i}\\ne O", + "638eafde1106e20b.png": "AM", + "6397633ab01bc9eb.png": "I(k)=\\delta(|k|)", + "6397df8c2b5f82a2.png": "\\tilde{\\mu}", + "6398ad42ca55368c.png": "L=\\bigoplus L_{i}", + "639aee1eba036557.png": "P_{e}^{(n)}\\rightarrow0", + "639eed83750f46c4.png": "\\tilde{6}/2", + "63a5c85fe9c4a342.png": "0\\notin\\mathbb{N}", + "63b57c480e039114.png": "\\kappa^{+}\\rightarrow(\\alpha)^{2}", + "63b75e98c549c65d.png": "\\hat{h}", + "63c060a3b48f5c1d.png": "(\\begin{matrix}n\\\\ m\\end{matrix})=\\frac{n!}{m!(n-m)!}", + "63c125ec041b11f2.png": "((\\infty),[c,d])\\notin I", + "63c1a627af802f97.png": "\\overline{L}^{\\dot{\\alpha}\\dot{\\beta}}=T^{\\dot{\\alpha}\\dot{\\beta}}", + "63c5fdd0b02fe649.png": "\\sqrt{-1}", + "63d17f2eb2294596.png": "(\\begin{matrix}1&2\\\\ 2&1\\end{matrix})", + "63d5f7340f12f563.png": "\\hat{N}_{f}", + "63d6434715d36914.png": "\\langle\\overline{z}\\rangle=e^{i\\mu-\\gamma}", + "63d867d18a42526c.png": "Y_{\\alpha,\\beta}^{1/\\gamma}", + "63d95cc027569285.png": "\\prod_{i\\ne\\beta}X_{i}", + "63e19afb785479cb.png": "\\frac{\\partial y}{\\partial x}", + "63e955d53e70f3a6.png": "[\\begin{matrix}a&b\\\\ c&d\\end{matrix}]", + "63eadb99edd86a07.png": "E(\\overline{K})", + "63f586e3f64c4af4.png": "G=e^{-(log_{e}2)x^{2}}", + "63f8f25dce249bdc.png": "(cos(\\theta))", + "64023c7b362428bc.png": "\\int_{0}^{t}B_{s}^{2}ds", + "6415181e9f7c0194.png": "V_{i}^{L}||V_{i}^{R}=V_{i}", + "6415968e6fa1a04b.png": "e^{\\gamma}\\cdot log_{|b|}(log_{|b|}(n))", + "641aac54be14ef19.png": "\\dot{y}=\\frac{1}{\\mu}x", + "641e12eb87ab20c8.png": "\\hat{a}_{t}", + "641e62570435d0ba.png": "(\\begin{matrix}\\alpha\\\\ k\\end{matrix})", + "64206324464bcf1a.png": "(g\\circ f)^{-1}=(f^{-1})\\circ(g^{-1})", + "6422d55d4c965a8a.png": "W_{i}=V,W_{1-i}=\\{\\}", + "6429bc1cd70043a9.png": "\\{\\begin{matrix}q\\\\ r\\end{matrix}\\}", + "642ed47ff4489905.png": "\\overline{Y}=X", + "643d767c44fcd8c4.png": "\\frac{1}{2}\\sqrt{r-r^{2}}", + "643daefd18d2be36.png": "C", + "644557b2f3b0d28f.png": "\\frac{2\\pi d}{\\lambda}\\ge\\pi", + "644be8f9d6585574.png": "\\int_{1}^{5}2xdx", + "644ce1d0a32d7633.png": "C\\propto1/\\sqrt{B}", + "644e66a66c9c61d7.png": "\\underline{w}=(s_{i_{1}},s_{i_{2}},...,s_{i_{l}})", + "645e8c46dc026e99.png": "X_{n}=M^{n}X_{0}", + "64622a5627ecbaeb.png": "\\sqrt{x}+O(\\sqrt[4]{x})", + "646f610feb7c5d60.png": "-1\\cdot\\cdot\\cdot>\\tau_{m}\\ge0", + "651352f579fcf6cb.png": "(Z_{2})^{2}", + "651ff820d3481410.png": "(x\\otimes y_{1})\\oplus(x\\otimes y_{2})", + "6525ebfe824f97ff.png": "\\pi\\tilde{f}=f", + "652b85e844e14ba7.png": "R=-V/I", + "652ea6ca37ba1227.png": "E[R]=\\sum_{i=1}^{n}R_{i}P_{i}", + "65346af865369c12.png": "0=\\nabla\\gamma\\cdot\\hat{t}", + "6537cc21270cb182.png": "(2^{r}+1)|(2^{rs}+1)", + "65385ddf526e923b.png": "\\tau_{\\tilde{H}}(\\tilde{G})=\\tau_{H}(G)", + "6538a08ca8cab2f5.png": "\\frac{dp_{o}}{p_{o}}", + "653fe3b0f341765c.png": "f(x)=-\\sqrt{x}", + "65436c564f8de0ca.png": "0\\le u_{1},u_{2},v<256^{l}", + "6549bbac3825462f.png": "\\prod_{i=1}^{r}(n-i+1)", + "654a59d128015277.png": "\\hat{e}_{j}", + "654f339aac07d7be.png": "|+\\rangle=\\frac{1}{\\sqrt{2}}(1,1)", + "6550cf08976305bb.png": "P(A^{c})=1-P(A)", + "6554c87d801b8943.png": "(\\begin{matrix}n+2\\\\ 2\\end{matrix})-2n-1", + "6556aa5f72019392.png": "\\sqrt{2}-1", + "655f1e19d331ad71.png": "P(X_{n}\\rightarrow X)=1", + "656805db4ec58d8d.png": "Q=\\int j_{0}a^{3}d^{3}x", + "656854316edf68cd.png": "\\int d^{D}x\\sqrt{-g}G", + "656b965ea9085878.png": "\\hat{r}=\\vec{r}/r", + "6571c391671dbb7b.png": "\\gamma_{m}^{j}", + "6573d94653f456b3.png": "q=s^{s/(s+1)}", + "657960b3a1a43813.png": "L^{2}\\le\\frac{\\pi}{4}area(\\partial P)", + "6580546f6fdadef5.png": "\\int_{0}^{a}sinxdx", + "658ad2a7b0790006.png": "H", + "6593b1fc08a2bb9e.png": "\\hat{f}j=f", + "65967908dd057b48.png": "t\\{\\begin{matrix}5\\\\ 3\\end{matrix}\\}", + "659f77dfcae3c196.png": "(\\theta_{*}(\\mu_{\\cdot}))_{S}=i_{*}(\\mu_{\\Sigma})", + "65a358845947fd3b.png": "\\overline{P_{e}}=\\sum_{j=1}^{k}p_{j}^{2}", + "65a599a18c46ecdc.png": "x=y=\\frac{i}{\\sqrt{2}}", + "65af697fa7f66ba6.png": "n=p_{1}^{k_{1}}p_{2}^{k_{2}}...p_{l}^{k_{l}}", + "65b03d785400ba6f.png": "i:\\underline{A}", + "65b94709ac04c955.png": "U=(A^{T}A)^{1/2}A^{-1}", + "65b9e00af09e5879.png": "f:R^{n+m+1}\\rightarrow R^{n}", + "65bcc84029912b35.png": "f_{p-int}", + "65bf86dc2b7f9472.png": "J(u_{n}-c_{n}\\Delta_{n})_{i}", + "65c3946e4510bc0d.png": "\\langle U^{*}x,y\\rangle=\\overline{\\langle x,Uy\\rangle}", + "65c4ce96fcde6583.png": "L_{z}\\Phi_{s}=\\pm\\Lambda\\hbar\\Phi_{s}", + "65cad5ad1b57bc27.png": "\\mathbb{L}", + "65cb5a1132f793e0.png": "k[X]", + "65cd62a543695e01.png": "\\int_{Z}i^{*}\\alpha", + "65ce8b1f3722ac33.png": "v_{i}(x)-p_{i}\\ge0", + "65d02e6657fb6df5.png": "u_{xt}-(uu_{x})_{x}=u_{yy}", + "65d401e0aa3b6dc2.png": "(\\begin{matrix}4\\\\ 2\\end{matrix})", + "65daa35476e05ff5.png": "\\hat{p}_{x}", + "65dadeb06a766146.png": "t_{1}s_{2}\\overline{t_{1}s_{2}}^{-1}=(123)", + "65dbf86a3b0a6ad7.png": "e=\\frac{A}{mk}=\\frac{|A|}{mk}", + "65de108c9c5f8546.png": "(x,y)\\in Z_{n}\\times Z_{n}", + "65e05c48bc99ee25.png": "[c]=LT^{-1}", + "65e12c9a1fa19c1c.png": "\\frac{\\partial y}{\\partial t^{\\prime}}+u\\frac{\\partial y}{\\partial x}=d\\frac{\\partial^{2}y}{\\partial x^{2}}", + "65e2eb1dd6f06e66.png": "\\frac{dy}{y}=-f(t)dt", + "65e39ed3e556bf5d.png": "(T,T+H]", + "65e3c15e6329ebc9.png": "\\sqrt{10}\\approx3.1", + "65eb5667cfb1145c.png": "[0,1]^{2}", + "65ecd65480243216.png": "\\overline{hv^{2}}+\\frac{1}{2}k_{ap}g_{z}h^{2}", + "65ee009363747293.png": "f(x,q_{k+1})\\le r_{k+1}", + "65f00922776f1e08.png": "(\\begin{matrix}d\\\\ k\\end{matrix})", + "65f9c1073764f0c2.png": "\\frac{G(\\chi)}{|G(\\chi)|}", + "65fbdf16334d2009.png": "\\tilde{\\eta}", + "65fda81426fecb26.png": "\\underline{x}=(x_{1},...,x_{d})", + "66054b108862e1d1.png": "F_{X}=0.5", + "660d29ea1d1bb2cd.png": "(\\begin{matrix}n\\\\ 2k\\end{matrix})", + "66123f19d20aa83a.png": "s\\{\\begin{matrix}2\\\\ 5\\end{matrix}\\}", + "661bd1fecd8043a7.png": "\\sqrt{3}", + "66207ea818662865.png": "0=\\frac{3x-1}{2\\sqrt{x}}", + "66257033d51c805e.png": "\\sqrt{10}(4\\rho^{4}-3\\rho^{2})sin2\\theta", + "6625ed097bc650c8.png": "\\hat{z}=\\pm\\hat{p}", + "66264d9d9aa11669.png": "16", + "662a1151b7e73f74.png": "(\\begin{matrix}0&-1\\\\ 1&0\\end{matrix})", + "662bf6f1ea254d84.png": "\\int_{C}=0", + "662edbbcf7f4d311.png": "(\\overline{\\xi},\\overline{\\zeta})=(0,0)", + "663b2a21acb5be30.png": "\\frac{ds}{dt}=0", + "664298dda8722dd3.png": "\\int fdg", + "6642cb08ebe87148.png": "\\prod_{n=1}^{\\infty}(1+a_{n})", + "6645bd2b40c7cdb7.png": "E=-\\vec{\\mu}\\cdot\\vec{B}", + "664bd4dfe67b474d.png": "Set_{\\ne\\emptyset}\\times Set_{\\ne\\emptyset}", + "664c67af0e164242.png": "\\int_{0}^{h}exp(x^{2})dx", + "664eaba29bbe1fa6.png": "\\frac{dG}{dr}=0", + "664f13e2a5236ebe.png": "B\\rightarrow\\langle E(B)x,y\\rangle", + "6650617092646c56.png": "\\sum_{j}|c_{ij}|^{2}=1", + "6650a717edc24b92.png": "|\\Psi\\rangle=e^{T}|\\Phi_{0}\\rangle", + "6651b286868d4c35.png": "\\mu(=k\\theta)", + "6655ffe7fd7bd96e.png": "x,||x||_{p}\\le n", + "66578d74a18d96fe.png": "L_{X}dz=f(z)dz", + "665a1d1ece55b2b6.png": "I(.)", + "66633f3b44cd3726.png": "n>0\\Rightarrow q=\\lfloor\\frac{a}{n}\\rfloor", + "666a976a026f3bd8.png": "(\\prod_{i=1}^{N}\\tau_{i})\\frac{\\partial^{N}\\sigma}{\\partial t^{N}}", + "667407adaeaafc1c.png": "\\sqrt{\\frac{a^{2}}{b^{2}}-1}", + "6680b14a597db623.png": "\\tilde{O}(log(n)^{10.5})", + "6696738f96ac2324.png": "N=(\\begin{matrix}n+d\\\\ d\\end{matrix})-1", + "669c890dc1f8a21b.png": "\\chi_{j}^{v}=1-\\psi_{j}^{v}", + "669d350e420be8a3.png": "\\frac{d^{2}x}{dt^{2}}", + "669d7e6df1827a6d.png": "s\\{\\begin{matrix}2\\\\ 4\\end{matrix}\\}", + "66a0e80341b1e83d.png": "R_{j}=\\frac{1}{2\\sigma_{j}^{2}}I_{d\\times d}", + "66aca79201ef7f42.png": "U=[\\begin{matrix}M\\\\ N\\end{matrix}]", + "66acffa17b9935ba.png": "J=[0,1)^{s}", + "66b869d8df1c7751.png": "f=\\frac{x}{1-x-x^{2}}", + "66bade501d4e393d.png": "L=Q(\\zeta_{p^{n}})/Q", + "66bca83350c6ddbb.png": "\\omega_{N}^{n}=e^{-\\frac{2\\pi i}{N}n}", + "66bf49011d1f8678.png": "L_{*}x=b-Ux", + "66c58553a3548388.png": "F(r)=-\\frac{k}{r^{3}}", + "66cd1383bdc6f50c.png": "\\underline{Z}=Zcos(\\phi)+jZsin(\\phi)", + "66cfc24b8e05c586.png": "p(x)|(x^{r}-1)", + "66d276daeea9ea11.png": "\\frac{dW}{dt}", + "66e2a5e505cd5f41.png": "I=\\int xcos(x)dx", + "66f25cf64931ca87.png": "F(E/As,l/A)=0", + "66f914c74efa31e7.png": "\\hat{\\alpha}>\\hat{\\beta}", + "66fc1b878e8e105d.png": "\\tilde{t}_{i}", + "66fcb05f7f5c9afe.png": "\\gamma(t)=(t,f(t))", + "66fd3200f101ff3d.png": "c(1-\\frac{r_{S}}{r})", + "6705aed8b51bd994.png": "(a_{0},...,a_{N-1})", + "6707e5e965fd26b9.png": "r(u):=0.2", + "6709d121cdbd862f.png": "[\\hat{Y},\\hat{I}_{\\pm}]=0", + "670c6a5373289c4f.png": "\\frac{dN}{dE}", + "670c7c2ff606375f.png": "\\int_{1}^{\\infty}\\frac{dx}{x}", + "6712a8565c1443ca.png": "\\tilde{D}_{9}", + "6715f1e320367e32.png": "x^{2l-1}+1", + "6717e022edd2506f.png": "\\hat{p}_{i}", + "671ba7070a49d044.png": "D=\\mathbb{Z}[\\sqrt{3}]", + "6720eb281c79e2ac.png": "[\\begin{matrix}1&0\\\\ 0&1\\end{matrix}]", + "6725a7f1c70acb6a.png": "N/K\\subseteq_{s}M/K", + "6728a6de18e5c6cf.png": "\\delta\\vec{x}(t)\\approx H\\cdot\\delta\\vec{x}_{0}", + "672d74dca827aa14.png": "\\frac{sinx}{x}=\\prod_{n=1}^{\\infty}cos\\frac{x}{2^{n}}", + "6737c9226cba30b0.png": "det(1-zL_{w})", + "673a177241b31b0e.png": "\\int_{X}||f||_{B}d\\mu<\\infty", + "6742fb8695ce8ca1.png": "\\tilde{C}_{3}", + "67437eaf5013082f.png": "(\\begin{matrix}6\\\\ 2\\end{matrix})=15", + "6747f523735fcb07.png": "\\chi^{2}>\\chi_{k-1,\\alpha}^{2}", + "674982c13d11b49e.png": "\\rho_{ij}\\rightarrow-1", + "674c2a58ec67997f.png": "(\\begin{matrix}1&0\\\\ 0&0\\end{matrix})", + "675317799f4038e9.png": "+j1.14", + "67550d5d5858e7e4.png": "[S_{0}]=[S]+[A_{ad}]", + "6755e6a11a527793.png": "(D^{2}-\\alpha^{2})\\Psi_{i}=0", + "675d1c826ec9118a.png": "\\int n_{e}(s)ds", + "675ed8a6bfe42e53.png": "|\\tau_{cap}(\\omega)|^{2}", + "6765993b4d683778.png": "\\overline{K}_{n}", + "676820c09c87d08e.png": "h(z)=h_{1}(z)(z-c)", + "676cc70c5c4a74dd.png": "\\underline{\\varphi(\\beta/\\alpha)}", + "6773de3582b90308.png": "\\frac{(n-1)(n-2)}{2}", + "6775e149f19cc4a6.png": "\\int f(x)dx=1/M", + "67772eb4c7741dbe.png": "H_{f}(a)=f^{-1}(a).", + "67783f871890ca2a.png": "\\zeta(0,x)=\\frac{1}{2}-x", + "677e111987fb41b4.png": "v_{a}(t)=e^{i\\omega(t+a)}", + "677fe03b1694d8d3.png": "[\\begin{matrix}1&0\\\\ sC&1\\end{matrix}]", + "67813f945793fcd4.png": "u_{b}^{\\psi}", + "6787e3f68811c220.png": "B_{n+1}=\\sum_{k=0}^{n}(\\begin{matrix}n\\\\ k\\end{matrix})B_{k}", + "678e08e05cb281a8.png": "A=[\\begin{matrix}2&1\\\\ 1&2\\end{matrix}]", + "678ea5ddf47fde4f.png": "-s", + "679c710c87b7f0f4.png": "\\frac{dy}{dx}=0", + "67a1a4cdd5fcc650.png": "\\Omega^{\\prime},\\Omega_{0},\\Omega_{1}", + "67a1cddb7e1793c6.png": "-log_{2}p(X=x)", + "67a29c25912dffa0.png": "N\\overline{x}", + "67ab1cf9b2bc2135.png": "(\\nabla_{X}J)X=0", + "67b7f324fe43cc95.png": "x_{n}/||x_{n}||", + "67b938c475b49869.png": "\\mathbb{N}", + "67bfb6ba11b3088f.png": "\\frac{\\partial f}{\\partial y}", + "67c37ede8b33a135.png": "cosx=1-\\frac{x^{2}}{2}", + "67c993788cacfaa8.png": "M=\\int_{V}\\rho dV", + "67ca183401c37630.png": "\\prod_{i=a}^{b}", + "67cc3969aa04f795.png": "q(1)^{2}+q(1)-1", + "67cd7710c0efb79c.png": "[m/2^{p},n/2^{p}]", + "67d018492688d2e9.png": "x^{-}=\\frac{t-x}{\\sqrt{2}}", + "67d5d7f7c1ecb4bb.png": "s\\{\\begin{matrix}3\\\\ 4\\end{matrix}\\}", + "67d656c45cfde4ca.png": "\\{1,3,5,...,2^{w-1}-1\\}P", + "67d9f227775c8e75.png": "T=\\sum_{n=1}^{N}\\lambda_{n}\\langle f_{n},\\cdot\\rangle g_{n}", + "67de3d220a27ef1f.png": "A_{f}=\\langle f|P\\rangle", + "67eab0f7a6789f35.png": "\\int fg=f(x)\\int g", + "6801752a70d601c1.png": "\\tilde{C_{n}^{m}}=-\\frac{C_{n}^{m}}{\\mu R^{n}}", + "68028e316575c008.png": "s_{x}^{\\epsilon}", + "6802e5f1b96f9422.png": "\\hat{h}", + "680d0cbf5c78d6fd.png": "(x)O(\\underline{x}:G)", + "6810aff2b4621590.png": "A^{\\prime}(z)", + "6812775b7dc0679c.png": "\\int f(x,y)dx", + "68154361bd134fae.png": "Si", + "681e0c3cc82e5358.png": "\\frac{dR}{dP}=0", + "6820ec9d5b37b988.png": "[\\begin{matrix}1/4&0\\\\ 0&-1/4\\end{matrix}]", + "6821daa3982554fa.png": "\\int\\sqrt{1+1/x^{2}}dx", + "68246e8ed2408aba.png": "s\\{\\begin{matrix}7\\\\ 3\\end{matrix}\\}", + "6825e8ef097758e4.png": "C^{\\varphi_{\\mu}}", + "68276abd3c46c685.png": "E_{u}[Y_{t}(u)-Y_{c}(u)]", + "6827ff0703cd0548.png": "\\tilde{G}(s)", + "682e266b7146e944.png": "P(z_{\\Lambda_{1}})P(z_{\\Lambda_{2}})", + "6838fd84ca8533da.png": "Q=I_{Q}\\tau_{F}+Q_{J}", + "6840930aaf8a2a99.png": "\\int_{X}1d\\mu", + "68434b79b6a46c30.png": "\\tilde{e}", + "6843c7ba27b65c7e.png": "(\\begin{matrix}a\\\\ r\\end{matrix})", + "684a7ed3b3f4a123.png": "\\sigma=\\sigma_{0}e^{-(T_{0}/T)^{1/4}}", + "68559b9a49523152.png": "\\int_{-1}^{1}x^{-2}dx", + "6856612b4907842f.png": "M\\int vds", + "685da4270354ffc6.png": "-\\int_{P_{1}}^{P_{2}}VdP", + "68647063626e0a25.png": "(n+1)^{2}-n^{2}", + "68647b6eaa09fc4b.png": "bk_{B}T-2a", + "686731b983c489ad.png": "c_{0}/c_{1}-1", + "686c746c1e0484e9.png": "(\\begin{matrix}5+1\\\\ 1+1\\end{matrix})=15", + "686e1d43ab25042b.png": "P^{D}(\\tilde{t}_{i})", + "686f0786cd914505.png": "P(A)+P(\\neg A)=1", + "6870dc35bbaeadb0.png": "\\iint_{S}FdS", + "6870df2079dfb1ca.png": "\\frac{dP}{dx}", + "687df5626fb71871.png": "E[uu^{\\prime}]=\\sigma^{2}I_{n}", + "68800d34ebabdd65.png": "x\\mapsto\\{\\langle e_{k},x\\rangle\\}_{k\\in N}", + "688062147a29197c.png": "|\\omega_{i}|=q^{1/2}", + "68822ffe46e765eb.png": "A^{\\prime}=x^{2}A", + "68897d5a4ac69bf9.png": "01(01)^{*}\\cup100^{*}", + "68900562e66eec4e.png": "R_{+}M=M", + "68903cf961a4409b.png": "X=\\langle X,F\\rangle", + "6897a3ed68351198.png": "\\vec{u}(||\\vec{x}_{m}||=a)=\\vec{U}", + "689bf35fe033748d.png": "\\langle\\psi^{\\prime}|=\\langle\\psi|\\hat{U}^{\\dagger}", + "689c72bfd3b662c9.png": "\\{\\begin{matrix}p\\\\ q\\end{matrix}\\}", + "68a861353cede0bb.png": "-\\frac{dz}{z}", + "68ad77bba651f939.png": "\\omega_{0}=\\sqrt{\\frac{k_{c}}{m+m_{A}}}", + "68be7cd68cb4be4d.png": "d=|(I_{t}-\\mu_{t})|", + "68bfb022bf380839.png": "\\omega=\\frac{d\\theta}{dt}=\\frac{v}{r}", + "68c10e1c708d9aa9.png": "\\{c_{P}|c_{P}\\ne0\\}", + "68c173f2aa15d208.png": "\\frac{EQ}{EQ^{\\prime}}=\\frac{ES}{ES^{\\prime}}", + "68c21f4df955c79f.png": "v_{0}=[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "68c387a0a73e8e4e.png": "A^{*}:H_{2}\\rightarrow H_{1}", + "68c9448b4304b304.png": "0\\notin[l_{n},u_{n}]", + "68ca5b3a70a9c4a4.png": "\\int_{0}^{3}|x^{2}-4|dx", + "68d55d274b29138a.png": "\\tilde{A}_{9}", + "68d6314a47f71247.png": "f^{\\phi}=\\frac{f^{\\prime}-\\frac{f}{I}}{2}", + "68dbfbc260c9ccc7.png": "\\int_{C}x^{2}dy", + "68dfccb4ddab7314.png": "\\frac{dC}{dt}", + "68e05b7d86d2b766.png": "(\\begin{matrix}\\alpha\\\\ k\\end{matrix})", + "68e1356dc29216a3.png": "C[x,y]/(x,y)\\cong C", + "68e19e979f8dee5e.png": "\\int d^{4}xF(x)", + "68efd95bb3bc6f93.png": "\\hat{z}(t)", + "68fed1d4e21350dc.png": "F_{i},i=1,2", + "69112e9b8649e19d.png": "T(\\theta)=\\frac{M(\\theta)-C_{1}}{C_{2}}", + "69146e5955ffd753.png": "\\underline{F}", + "691a21279994ac8c.png": "[\\begin{matrix}1&2\\\\ 1&1\\end{matrix}]", + "691a256d18cc8765.png": "l:=L_{\\rho}(\\Gamma)>0", + "691a31337abcccf0.png": "\\int_{0}^{1}F(x)dx=0", + "691dd33ce0c624ed.png": "A_{p}(g)=A(g,p)", + "691fc798193c9f8f.png": "S_{gen}^{\\prime}=\\frac{Q_{2}^{\\prime}-Q_{1}^{\\prime}}{T_{surr}}", + "6926ae9943359013.png": "T\\ne U/c", + "692828e235d39b50.png": "r=\\frac{s}{2}\\sqrt{d}", + "692973f2cca3ac5a.png": "\\varphi", + "6929939cb1d43d64.png": "1-\\frac{10^{3}}{11^{3}}=\\frac{331}{1331}", + "692e96acb99be815.png": "=\\frac{1}{2}\\frac{m}{L^{3}}v^{2}[\\frac{y^{3}}{3}]_{0}^{L}", + "6934176f48188596.png": "[1;\\frac{2t}{t^{2}+1};\\frac{t^{2}-1}{t^{2}+1}]", + "693a6c30fe6600ff.png": "(x,r)=(0,r_{o})", + "693b245d72d6c4d0.png": "a,b\\in\\hat{R}", + "693e24de748353b5.png": "\\sqrt{\\Sigma}", + "693eab6ad5d46a4e.png": "u=-\\phi(y)(2)", + "69468010cb45687d.png": "\\int_{S}F\\overline{F}", + "694e4c03766de5d5.png": "A=[\\begin{matrix}4&1\\\\ 6&3\\end{matrix}]", + "69516ed0e0b0fb35.png": "(4)\\frac{du}{dt}=\\frac{-u}{1+u}", + "6954cbffb1cf9d3b.png": "\\rho_{k}=k\\frac{U_{MN}}{I_{AB}}", + "695528a1c47d14a4.png": "\\int dy=\\int f^{\\prime}(x)dx", + "695775e0a27c6fb6.png": "m=\\prod_{k=1}^{j}m_{k}", + "6962d8c30df2b381.png": "-1^{\\sqrt{2}}", + "69640387b7f08f6c.png": "St=\\frac{f\\cdot\\frac{D}{2}}{V}", + "696a3ec6d6b04fd9.png": "\\sqrt{2t}", + "6988519ce6fb7e58.png": "F(x)=\\int_{a}^{x}f(t)dt", + "6988833250cf1929.png": "[0,", + "6989f7494a24d974.png": "V=\\sqrt{P\\bullet R}", + "698a604fe86cf561.png": "\\hat{N}", + "698b94dcdcfd28b0.png": "\\int_{A}P_{A}dA=1", + "69941d4e504bd682.png": "F=lim_{\\alpha\\rightarrow0}\\alpha E_{\\alpha,0}(1)", + "6994a82b58c8135a.png": "\\varphi(x,y)=\\overline{\\varphi(y,x)}", + "699908dcb08c3739.png": "C=-c^{2}", + "699ac570bbe7f845.png": "\\frac{1}{\\sqrt{5}q^{2}}", + "69a4df981d617016.png": "\\frac{\\partial L}{\\partial t}=0", + "69a69608b28630d3.png": "\\tilde{r}", + "69adbad12ea827c8.png": "\\frac{1}{T}=\\frac{dS}{dE}", + "69b85cf53723a8e1.png": "\\sum_{k=1}^{n}\\frac{z(1-z^{k})}{1-z}", + "69b9942179a60324.png": "\\Delta K=\\Delta\\sigma Y\\sqrt{\\pi a}", + "69b9acfc2a7ad17d.png": "\\mathbb{X}", + "69ce4e101b535509.png": "f_{p-int}", + "69cf7c5776f3ed15.png": "1-Q_{1}(\\frac{\\nu}{\\sigma},\\frac{x}{\\sigma})", + "69d36074905f939f.png": "FV(xy)=\\{x,y\\}", + "69d6299bf878777a.png": "lim_{x\\rightarrow3}\\frac{x^{3}-27}{(x-3)}", + "69de43172ba03eac.png": "x=\\prod_{i}p_{i}^{e_{i}}", + "69e5cbba011056a5.png": "C=\\cup_{p}F_{p}C", + "69efcd80ceacaa39.png": "P=\\frac{\\rho\\cdot R^{*}\\cdot T}{M}", + "69f40b352d7e7174.png": "\\tau^{(\\epsilon_{\\psi})}", + "69f48675f38785fd.png": "\\tilde{g}_{lk}", + "69f63210499b5ae2.png": "-r^{-1}cos\\theta", + "69f7d60c844a5622.png": "\\int e^{x}sin(x)dx", + "69fc866b455981fd.png": "\\hat{y}_{i}", + "69ffebc310c2a33a.png": "\\underline{m}=\\{1,2,...,m\\}", + "6a014f194b2460a2.png": "v=\\frac{dr}{dt}", + "6a04cc07c4bb29fa.png": "\\sqrt{1}=-1", + "6a0600330e380068.png": "(\\begin{matrix}2n-2\\\\ n-2\\end{matrix})", + "6a08cf8fd6c49913.png": "g=T_{e}G", + "6a149bffdee4a885.png": "\\frac{\\partial^{2}C}{\\partial S^{2}}", + "6a16b29781abf0d3.png": "F(A^{p})\\rightarrow F(A^{p+1})", + "6a1acc7a3e246f71.png": "\\hat{g}(f)", + "6a1dd65e07637d1c.png": "(a:a:a):\\tilde{4}/3", + "6a1e18550070cfde.png": "\\sqrt{\\eta}", + "6a22bb2bb5dd8e51.png": "(\\begin{matrix}2&-2\\\\ -2&2\\end{matrix})", + "6a29d94e95741de7.png": "\\frac{dF}{dx}+2xF=1", + "6a30ba71a94a3844.png": "(ax+b)^{5}=c", + "6a346902ac4149f0.png": "2(\\sqrt{xy}-\\frac{x+y}{2})", + "6a3c9b6178b09857.png": "BP=(\\begin{matrix}I_{r}&G\\\\ 0&0\\end{matrix})", + "6a48e1091de42bd6.png": "\\frac{d\\rho}{dr}=-\\frac{\\rho(r)g(r)}{\\Phi(r)}", + "6a50302d87e1a36c.png": "-\\sqrt{\\frac{2}{35}}", + "6a569edd49752486.png": "\\Pi(t)=e^{it\\sqrt{D}}.", + "6a5c20618b70186e.png": "e_{a}=\\frac{\\partial}{\\partial x^{a}}", + "6a5d79c794183595.png": "a(1+\\frac{e^{2}}{2})", + "6a62e8f679bd6d17.png": "\\overline{y},\\overline{y}^{\\prime}", + "6a650c944a63d8ce.png": "\\vec{\\Omega}=\\frac{\\vec{R}\\times\\vec{V}_{r}}{\\vec{R}\\cdot\\vec{R}}", + "6a65a34cabbffc11.png": "\\underline{\\neg\\neg\\varphi}", + "6a6bfab5433b8dc2.png": "J=\\int f(t,x,y)dt", + "6a6d7146dfcb4652.png": "\\hat{e}=y-X\\hat{\\beta}", + "6a7291de82d654ff.png": "\\frac{\\partial\\theta}{\\partial z}>0", + "6a72b6ab39c6217a.png": "|1\\rangle=(\\begin{matrix}1\\\\ 0\\end{matrix})", + "6a778e9c8affcd22.png": "Q\\sqrt{5}", + "6a78db03fcf8435f.png": "2n=2(2k+1)", + "6a7b9afc2c6cae1a.png": "U=[\\begin{matrix}U_{1}&U_{2}\\end{matrix}]", + "6a7cc695e6ec22d1.png": "BA=(\\begin{matrix}1&0\\\\ 0&0\\end{matrix})", + "6a868f6b7a4c5094.png": "\\lambda=e^{2\\pi}=1^{-i}", + "6a8d4aa7d3a53873.png": "(\\begin{matrix}k\\\\ n\\end{matrix})=0", + "6a955194548e66ad.png": "G_{r}=G_{r}^{+}+G_{r}^{-}", + "6a9a9c7431fa2289.png": "\\chi_{\\mu}^{A}(1)\\chi_{\\nu}^{B}(1)", + "6aa07a01b500a550.png": "A=(\\begin{matrix}1&0&2\\\\ 0&2&0\\\\ 1&1&0\\end{matrix})", + "6aa4e59366a83065.png": "Y_{0}\\approx1/\\sqrt{S}", + "6aa4efb7b007750a.png": "150\\sqrt{1.4}=177", + "6aa9f1f3f38ae277.png": "\\frac{P_{f}}{P}=\\theta", + "6aaef8bf1283dcb3.png": "\\Gamma", + "6ab6a3f68a8b73a0.png": "-6=7\\times(-6/7)", + "6ab82faa92bfe060.png": "(\\begin{matrix}k+n\\\\ n\\end{matrix})-1", + "6abcb3a7317fa132.png": "125+55(n-2)", + "6ac70fd97ebce1c6.png": "S=\\int ds", + "6ace65b8f3ab1c99.png": "\\int dy=\\int f(x)dx", + "6ad1f6f05a5ee85d.png": "F(r)=-\\frac{k}{r^{3}}", + "6ad2f6b8fc897d51.png": "\\Delta E^{tot}=Q+W", + "6ad33656341487a2.png": "b)\\overline{a}", + "6ad47321bbcf7f5a.png": "\\int_{E}|f|<\\epsilon", + "6ad769f02d392a25.png": "\\int_{E}w(x)dx", + "6ad968ea974264d2.png": "\\{\\begin{matrix}8\\\\ 8\\end{matrix}\\}", + "6aeb621aad714942.png": "(\\begin{matrix}1&-1\\\\ 1&0\\end{matrix})", + "6af1d7ea7f9a66bb.png": "k([\\overline{x}])=i^{r-1}([y])", + "6af29815c0106818.png": "\\langle r|\\Psi\\rangle=\\Psi(r)", + "6afa53a497f55dba.png": "(\\begin{matrix}n\\\\ n\\end{matrix})", + "6b02298a6de6f74a.png": "J=J^{-1}=J^{*}", + "6b04d48cb7d7cfcb.png": "\\hat{d}", + "6b0d2faac1605852.png": "0.5M_{\\sigma,\\epsilon}", + "6b226b082938dc7f.png": "\\Phi=\\frac{k_{f}}{\\sum_{i}k_{i}}", + "6b34718bf0a7441c.png": "\\varphi_{*}(x_{\\varphi^{-1}(K^{\\prime})})", + "6b370e278f7df75f.png": "P^{-1}FP", + "6b409f8d8265519d.png": "\\tilde{t}_{i}", + "6b44b25d3eb59c0e.png": "xD(1)=x*\\frac{d}{dx}(1)=0", + "6b49297b98dc9618.png": "T_{i_{1}i_{2}...i_{k}}", + "6b4a7bc21076860a.png": "\\hat{C}", + "6b4ae2f3eb450b2b.png": "\\int x^{x}dx", + "6b4cb52da10a2776.png": "1/\\sqrt{1-(v/c)^{2}}", + "6b4ed4af30d3b508.png": "(p_{1}+...+p_{n})^{4}", + "6b4fe6044d96e3e0.png": "g(x)^{\\prime}\\in G", + "6b53243332ef82b1.png": "\\mathbb{F}", + "6b54cc9c9c8ff85a.png": "(\\begin{matrix}m\\\\ r\\end{matrix})_{q}", + "6b56f8e70473ef24.png": "(-\\pi<\\theta\\le\\pi)", + "6b5887bfa7ceeedc.png": "\\{\\begin{matrix}6\\\\ 6\\end{matrix}\\}", + "6b5e590a8713d0e9.png": "(\\begin{matrix}n\\\\ 0\\end{matrix})=1", + "6b5f4b64e065e3ed.png": "(\\tau_{h}S)[\\varphi]=S[\\tau_{-h}\\varphi]", + "6b61a6901534f9b0.png": "\\int\\Psi\\Psi^{*}dV=N_{s}", + "6b62a021d5aff7fd.png": "\\partial", + "6b653a79caab4241.png": "hc\\sim2\\cdot10^{-23}Jcm", + "6b6612f0cd61aa64.png": "a\\notin Z", + "6b687ddc001a0521.png": "\\frac{dM}{dx}=V", + "6b691bde18ecaece.png": "\\frac{dA}{db}=p", + "6b6b2551869e920e.png": "\\underline{a}_{1},...,\\underline{a}_{r}", + "6b70091aeae7c4c4.png": "(0<\\frac{dB}{dt}<\\infty)", + "6b71d8160d1d6bf6.png": "\\frac{n\\cdot(n-1)}{2}", + "6b7b1ad293b2af83.png": "\\frac{dt}{dx}=C_{1}e^{-\\int f(x)dx}", + "6b7d075a572e4835.png": "OD", + "6b8146cb1eb4b47a.png": "F=S\\int udt", + "6b8ddd37736ac62f.png": "\\langle W^{\\prime},R^{\\prime},\\Vdash^{\\prime}\\rangle", + "6b8f94b02bcba14e.png": "C^{N/2}", + "6b95a25b10e5fd79.png": "F_{r}=\\frac{v}{\\sqrt{g\\frac{A}{B}}}", + "6b972baf14a9ef5f.png": "\\int Fdx", + "6b9944c7c593dc5d.png": "\\tilde{\\chi}", + "6b996ad65dd80928.png": "\\{\\begin{matrix}p\\\\ q\\end{matrix}\\}", + "6b9983c60dd132cd.png": "\\hat{S}_{1}\\cdot\\hat{S}_{2}", + "6b99b3f522dabb44.png": "+j1.14", + "6ba2716f8f6c1d1a.png": "b_{t-1:T}=TO_{t}b_{t:T}", + "6ba32594d281a5db.png": "N", + "6ba5a3e473415d40.png": "f(g^{a}h^{c},g^{b}h^{d},\\tau)", + "6bb6f96ce1d232ab.png": "\\delta\\int d\\tau=0", + "6bb85313e1b56fd7.png": "P=1,2,3,...,n", + "6bc1f10eeb7980fa.png": "g_{00}=1+\\frac{2\\varphi}{c^{2}}", + "6bc9831caa30d86d.png": "E(X)=\\int_{\\Omega}XdP", + "6bc9cd1dfffee6e6.png": "(\\begin{matrix}N\\\\ 2\\end{matrix})", + "6bd0f302a41658dd.png": "|\\frac{y_{1}+y_{2}}{2}-x|^{2}\\ge\\delta^{2}", + "6bd18f8261e0b2ca.png": "\\underline{c}^{A}(t)", + "6bd81e5a9f77ba2f.png": "[\\begin{matrix}B&AB\\end{matrix}]", + "6bdaa94dbc462b0b.png": "T(z)=z+c\\int_{0}^{1}tdt", + "6beb600e022513ac.png": "ML", + "6bec16f019924399.png": "q^{\\prime}\\notin\\delta(q,a)", + "6bed1f1733ab89e9.png": "\\Omega(Sp/U)\\simeq U/O", + "6bf8ed0aa1981d75.png": "Z_{P}=\\frac{d_{2}^{3}-d_{1}^{3}}{6}", + "6bfde8de116158df.png": "-(2\\alpha+1)x", + "6bff8fe105b662f6.png": "a^{i}b^{j}(ba)^{k}", + "6c091302ca70ce5a.png": "(-b+\\sqrt{b^{2}-4c})/2", + "6c0a54f218d55377.png": "e_{m+1}=\\sum_{i=1}^{m}c_{i}e_{i}", + "6c121324c70bd07b.png": "\\overline{K_{0}}", + "6c1479f571775682.png": "\\overline{p_{in}^{2}}=\\frac{1}{2}P_{0}^{2}cos^{2}(kx)", + "6c2b9de3a942147b.png": "a(x)\\ge c>0", + "6c2bb3ff6578d961.png": "m\\frac{d^{2}x}{dt^{2}}=f(x)", + "6c2ca8ef677dfc35.png": "r(K_{m}+\\overline{K_{n}},K_{p}+\\overline{K_{q}})", + "6c2d6678a63ad724.png": "(x_{i1}-\\overline{x}_{i})", + "6c2d8a2f032fba25.png": "H(t):=\\int_{0}^{t}h(s)ds", + "6c2e10294b36053f.png": "\\tilde{C}[0,1]", + "6c2e3518cb0b085b.png": "f_{u}=L_{uu}^{\\dagger}(L_{ul}Y)", + "6c2f05d94b855d30.png": "-e,\\sqrt{2},3,\\pi", + "6c300e5473effcd2.png": "\\chi_{imp}=\\frac{C}{T+\\theta}", + "6c344f3edc141a4a.png": "(p(N<0;\\mu)=0)", + "6c34879d245a95d3.png": "\\hat{c}_{V}", + "6c3703e109c3762b.png": "\\frac{V}{V_{e}}=\\sqrt{\\frac{\\rho_{0}}{\\rho}}", + "6c3baa7ba3dd0dd8.png": "\\int_{0}^{L}F(x)dx", + "6c404342e210a166.png": "b_{\\mu^{7}}", + "6c44cfe1cde319ae.png": "(\\epsilon_{i})\\in\\{-1,1\\}^{\\infty}", + "6c46fa9d0e9172b2.png": "V:=p^{\\perp}/[p^{\\perp},p^{\\perp}]", + "6c478cef7242eb0a.png": "\\Delta=\\frac{\\partial^{2}}{\\partial x^{2}}+\\frac{\\partial^{2}}{\\partial y^{2}}", + "6c4decf91f8165d0.png": "lim_{s\\rightarrow\\infty}e^{-st}", + "6c577a9569f7e92b.png": "X\\rightarrow f(Y,Z,...)", + "6c583e016aeaa9ec.png": "\\frac{1}{y}\\frac{dy}{dx}=ln2", + "6c5bba4f1bb30cf4.png": "Y_{0}\\approx1/\\sqrt{S}", + "6c6046d4c049638a.png": "\\frac{g_{\\mu\\nu}-\\frac{k_{\\mu}k_{\\nu}}{k^{2}}}{k^{2}-m^{2}+i\\epsilon}", + "6c60c034693f12e9.png": "\\int_{-\\infty}^{x_{1}}", + "6c67d0c0d66765a0.png": "\\varphi=\\frac{d\\varphi}{dz}=0", + "6c6a891027583fe5.png": "(\\tau_{1}^{-1},...,\\tau_{g}^{-1})", + "6c6d909b3fa7d4f3.png": "\\int_{E}f(t)d\\mu(t)", + "6c7233e9fae478ae.png": "\\dot{\\varphi}^{2}+\\dot{\\psi}^{2}=1", + "6c73c3a678ecdb96.png": "\\int dx=x+C", + "6c7d7a2433b306ea.png": "\\frac{\\partial u}{\\partial t}=F(u,t)", + "6c7da33caed7885f.png": "v_{i}=(\\begin{matrix}n\\\\ i\\end{matrix})", + "6c8075009e36dbdf.png": "c_{3,1}(\\hat{a},T,\\hat{d})", + "6c817d3ce402002c.png": "\\frac{d\\langle T\\rangle}{dt}=0", + "6c84a66dbfb155d0.png": "\\frac{d}{dx}", + "6c8d9ca04a66e1f0.png": "\\{v_{1},v_{2}\\},\\{v_{2},v_{3}\\}", + "6c92addff844a89f.png": "C_{i}=N_{i}/V", + "6c94469b5893a091.png": "[\\begin{matrix}2&2\\\\ 3\\end{matrix}]", + "6c94c06f987377b9.png": "S(\\rho)=S(U\\rho U^{*})", + "6c9e8ceaf0360fb1.png": "f(x)=0,g(x)=x^{2}", + "6ca02740e51a9e9a.png": "\\hat{v}^{*}", + "6ca15ea5f83b8a07.png": "[\\begin{matrix}0&0\\\\ 1&-1\\end{matrix}]", + "6ca995b501d309e4.png": "F=(\\begin{matrix}1&0\\\\ 0&N\\end{matrix})", + "6ca9e3d29b244c59.png": "G_{n}(x_{1},...,,x_{n})", + "6cac88749fb060a4.png": "\\eta=1-(\\frac{T_{1}}{T_{2}})", + "6cae3ab4c8229ce9.png": "exp(tX)g", + "6cb0f436e73c4ebc.png": "L_{n}(p,q):=p*q", + "6cb1d08c2346e22e.png": "\\int\\int_{X}\\int_{Y}^{Z}", + "6cb20534cd4a5d44.png": "Z_{0}=\\sqrt{\\frac{L}{C}}", + "6cb22090763e9468.png": "\\tilde{A}_{5}", + "6cb85615832500f6.png": "(\\begin{matrix}0\\\\ 1\\end{matrix})", + "6cbfa80abce43070.png": "0<\\langle k\\rangle>lnN", + "6cc07751908d85bc.png": "\\sqrt{\\Lambda}", + "6cc4a3a0593411a2.png": "(\\sqrt{a}x+\\sqrt{c})^{2}", + "6cc50b5ac0f43953.png": "n=(\\begin{matrix}2k-1\\\\ k\\end{matrix})", + "6cc90bc356ed7696.png": "10^{-k}\\cdot\\cdot\\cdot>\\tau_{m}\\ge0", + "6f49265ec545b8a9.png": "\\int_{\\Omega}fw=0", + "6f55dcf9e4070fbf.png": "(\\frac{1}{2})^{4}=\\frac{1}{16}", + "6f56773ac23c9827.png": "(N^{\\prime}-1)!", + "6f57c923f9c77215.png": "\\frac{\\partial V}{\\partial h}=0", + "6f57ee1dd3313662.png": "\\tilde{A}_{8}", + "6f5807a5f547be6f.png": "S=\\int_{M}BF", + "6f588f29d8f79600.png": "\\int_{a}^{b}f(k)dk", + "6f595ae2cbf7dc58.png": "(x,y,w)\\in R_{*}^{3}", + "6f5c9bff696c2eb0.png": "(X_{1}:Y_{1}:Z_{1})", + "6f60c2939325caea.png": "x,x-20", + "6f6da98c0e22ab5e.png": "\\hat{t}<0", + "6f7faea896b05bbb.png": "w_{k}=V_{k}^{T}(U-M)", + "6f827acb7d441c0c.png": "\\int xsinx^{2}dx", + "6f888c0038eb505e.png": "A^{2}=1+\\xi^{2}", + "6f8937335e861eb6.png": "\\frac{2}{n}\\times x_{i}^{2}", + "6f8b7f4d4aa348e0.png": "\\int_{a}^{b}...", + "6f91e7cdbb21f16e.png": "|f|_{0,\\alpha}", + "6f9536da53a5225e.png": "\\Lambda_{0}^{3}C^{6}\\cong C^{14}", + "6f982f76f2cfc489.png": "\\frac{\\partial}{\\partial x}f(x,t)", + "6fa74f32706f414c.png": "H(x)=[x>0]", + "6fabc7415fad601c.png": "\\frac{13}{52}+\\frac{12}{52}-\\frac{3}{52}=\\frac{11}{26}", + "6faefe4b5b031564.png": "[\\begin{matrix}ac\\\\ bd\\end{matrix}]", + "6fb1d43fd695f579.png": "e^{x^{2}-5x-7}-3=0", + "6fb33ce149f23aae.png": "[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "6fba996505101b27.png": "\\theta=\\int(\\frac{M}{EI})dx", + "6fbc772df8b358c6.png": "9", + "6fcc5a447b058d08.png": "G_{X}(t)=e^{\\lambda(t-1)}", + "6fcd8ef4cd30eb3f.png": "\\hat{G}", + "6fcdc314002e3a3c.png": "a=0.3+i0.3", + "6fd5bb9ef5ee9cd5.png": "\\varphi_{cb}(a)=a^{b-c}", + "6fd5f74d66c986dc.png": "\\hat{F}(x)", + "6fdc30598b5ced36.png": "p<\\frac{(1-\\epsilon)lnn}{n}", + "6fdde973e12a65bf.png": "-1\\le\\rho_{ij}<1", + "6fe2216cab8dcfa2.png": "z=z\\times z^{\\prime}=z^{\\prime}", + "6fe34298ce1f338c.png": "(-1)^{N_{y}+N_{z}}", + "6fe66182b9bf1397.png": "\\hat{C}_{I}", + "6ff22355610197f9.png": "(\\begin{matrix}p\\\\ 1\\end{matrix})", + "6ff32c8827dfd30e.png": "\\neg\\varphi", + "6ff8a1d4255d3f6f.png": "u_{1}=[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "6ff9b51b999e3e63.png": "C=\\frac{\\partial P}{\\partial\\rho}", + "6ffeea3da64cfd59.png": "[\\begin{matrix}x\\\\ x^{2}\\end{matrix}]", + "7006253187b7ad02.png": "(\\begin{matrix}u&v\\\\ v^{*}&u^{*}\\end{matrix})", + "7007d31a33709560.png": "\\sqrt{2\\pi}\\cdot\\delta(\\omega)", + "700de268103efb51.png": "\\Omega^{\\prime},\\Omega_{0},\\Omega_{1}", + "700fe4078a48e255.png": "s_{a}^{*}(t)\\cdot e^{j2\\pi f_{0}t}", + "701055eca48f4388.png": "\\frac{\\partial q^{i}}{\\partial x_{j}}", + "7015cb3e4892db9a.png": "\\sum_{i,j}a_{ij}(x)c_{i}\\overline{c_{j}}\\ge0", + "701ea7e9f4c01768.png": "q=(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "701f97b235168171.png": "\\hat{f}^{c}", + "70219369abbd44d3.png": "(U\\Psi,U\\Phi)=(\\Psi,\\Phi)", + "70260b386654df82.png": "(\\theta_{*}(\\mu_{\\cdot}))_{S}=\\mu_{S\\circ\\theta}", + "702693a59f732acc.png": "n^{*}=\\sqrt{2E_{i}}/Z^{2}", + "7029f76a5c417d82.png": "\\prod U_{i}", + "702af6d8957ebc72.png": "\\kappa\\notin\\{\\lambda,\\mu\\}", + "702b2b439869dd24.png": "e^{in\\mu-|n|\\gamma}", + "704269200a01b84d.png": "[\\begin{matrix}4&6\\end{matrix}]", + "70550c0541b8aeee.png": "\\hat{H}_{I}=\\sum_{i}\\hat{S}_{i}\\otimes\\hat{B}_{i}", + "7055e21b70103603.png": "(\\begin{matrix}X\\\\ k\\end{matrix})", + "7057ec09a6529247.png": "M\\int vds", + "7058fc5e6c11e481.png": "\\pm\\sqrt{csc^{2}\\theta-1}", + "7059419882845a31.png": "|1\\rangle=(\\begin{matrix}1\\\\ 0\\end{matrix})", + "7059f1281bef21b5.png": "\\underline{P}X\\ne\\emptyset", + "705aff4849f7b549.png": "\\hat{x}^{o}", + "705ed69a35175bd3.png": "(\\begin{matrix}t\\\\ 2\\end{matrix})", + "70611d7a36b57cd8.png": "=0.28\\times10,000", + "70638abf49691c89.png": "[\\begin{matrix}0&1\\\\ 0&1\\end{matrix}]", + "706830fbf64fcb7f.png": "\\tilde{X}\\in T_{e}E", + "706b9aa9ba46d1db.png": "x_{i}=\\frac{2X_{i}}{S^{2}+1}", + "707021f085ca9e24.png": "V_{A}\\sqrt{\\frac{W_{2}}{W_{1}}}", + "7070fc6fbf9ad355.png": "R_{+}^{d}-min_{x\\in M}f(x)", + "70745a3e9d29d1b5.png": "\\tilde{\\eta}", + "7076e61686455a46.png": "\\tilde{f}_{i}\\tilde{e}_{i}", + "707cf8d99519b5fa.png": "=x(p)=x", + "707e74d6bf9beb99.png": "[\\begin{matrix}p&t\\\\ q&u\\end{matrix}]", + "7082f6754288f7c2.png": "sin[R]=[-1,1]", + "7086957c2944b0f2.png": "x", + "7088ba36401e2daa.png": "\\frac{du}{dx}=6", + "708f1d81692b89a5.png": "P_{E}dE=P_{p}\\frac{dp}{dE}dE", + "709490db233c0f77.png": "|\\epsilon_{n+1}|\\le M{\\epsilon_{n}}^{2}", + "7097b22ce87a5072.png": "\\sum_{\\langle i,j\\rangle}=\\frac{1}{2}\\sum_{i}\\sum_{j\\in nn(i)}", + "709b18203b596a97.png": "\\int_{-r}^{r}|y-s|dx", + "709d611b79f014b4.png": "Ra=\\{ra|r\\in R\\}", + "709ec39f43daa172.png": "-1F_{0}", + "71cd820b9c74eb3a.png": "\\int dx=x+C", + "71d08c50f57fe27d.png": "i=(\\begin{matrix}0&-1\\\\ 1&0\\end{matrix})", + "71d544246ba5bb99.png": "6\\sqrt{2}\\approx8.49", + "71da5b6094378996.png": "P(A_{1})\\le P(A_{1})", + "71df8855a0f7f3cd.png": "\\frac{a_{1}}{1-\\lambda_{1}t}+\\frac{a_{2}}{1-\\lambda_{2}t}", + "71e5e8faaeb37508.png": "\\tilde{Y}^{n}", + "71e6f0ec1c8df88c.png": "W=\\int P(V)dV", + "71ec9db729806f8f.png": "\\Phi^{t}(x_{1})=x_{1}+bt", + "71efe155aa1fd05e.png": "\\Phi_{1}+\\Phi_{2}+\\cdot\\cdot\\cdot=0", + "71fa472bae74de40.png": "(R_{1}^{T})^{-1}b", + "71fb360ab6a7e1fa.png": "H_{pot}=\\sum_{n=2}^{\\infty}C_{n}q^{n}", + "72010df359ea3495.png": "(\\begin{matrix}12\\\\ 3\\end{matrix})=220", + "720520102c2c3d4b.png": "A=", + "72067cd6a131bed4.png": "(\\begin{matrix}a&b/2\\\\ b/2&c\\end{matrix})", + "7208da0eb66baf2e.png": "\\int_{0}^{1}F(x)dx=0", + "720ee1868160f88e.png": "[\\begin{matrix}a_{11}&0&0\\\\ 0&a_{22}&0\\\\ 0&0&a_{33}\\\\ \\end{matrix}]", + "720fbab906ed2804.png": "[\\begin{matrix}0&-1\\\\ 1&1\\end{matrix}]", + "7210efa1a53bebef.png": "\\hat{y}\\in\\{-1,1\\}", + "721c0434f075af18.png": "\\hat{\\beta}", + "721d570834f732f5.png": "g=T_{e}G", + "722402785ef7de4e.png": "\\Phi_{n}(x)=\\prod(x-\\zeta)", + "7228ab92b15eeaef.png": "A=\\frac{1}{2}(b+d)a", + "7228da6f5afb9ed9.png": "\\langle N|J^{\\mu}|N\\rangle\\langle e|J_{\\mu}|\\nu\\rangle", + "722cee9d58d558bb.png": "[\\begin{matrix}1&k\\\\ 0&1\\end{matrix}]", + "72378c5b831bdd64.png": "2^{m},2^{m},1", + "7239585da2c028ce.png": "\\int_{A}(g-f)d\\mu=0", + "723b8974df0b06c0.png": "lim_{x\\rightarrow0^{+}}lnx=-\\infty", + "723d139812d37650.png": "x,||x||_{p}\\le n", + "7245ec9148f00ca6.png": "\\frac{1}{2}x^{2}lnx", + "72501f6539055084.png": "\\frac{dE_{2}}{dE_{1}}=-1", + "72502b71c8a694f0.png": "C_{Y}W^{T}=C_{YX}", + "72527717b144d8a4.png": "T^{\\mu}=\\frac{\\partial x^{\\mu}(s,t)}{\\partial t}", + "72537038b81713bf.png": "\\tilde{L}=\\sqrt{\\nu}(C-||C\\varphi||)", + "7259ee9ffd76fc66.png": "e\\overline{\\psi}\\gamma^{\\mu}\\psi A_{\\mu}", + "7259f2607d06c5db.png": "F(\\underline{x}_{0},\\underline{u})", + "725a9a97c33a8d15.png": "\\overline{A}_{x}", + "725b0986bfa4b404.png": "a\\mapsto a_{u}^{\\#}:g\\rightarrow T_{u}P", + "725b5c705357218e.png": "(xx)(x(xx))", + "725cf6e5c013638f.png": "\\tilde{D}_{9}", + "726adc5444462d88.png": "\\prod(p(i)-1)", + "72757d4df82d204a.png": "\\frac{dG}{dr}=0", + "727c5b991a5435af.png": "\\int2xdx=x^{2}+C", + "727f93938d38a3ab.png": "\\frac{\\omega_{1}}{\\omega_{2}}\\notin\\mathbb{R}", + "72823fc5d1b8660a.png": "e_{2}=(\\begin{matrix}0&-1\\\\ 1&0\\end{matrix})", + "7283a4b5eee5de76.png": "A:=(a_{i,j})", + "7287d000fe0b478f.png": "S\\subseteq[n],|S|\\le d,j\\notin S", + "728a7b865669bd01.png": "=\\partial_{\\mu}A_{\\nu}-\\partial_{\\nu}A_{\\nu}", + "728b3351bfcee925.png": "\\sqrt{\\beta}", + "7292cafc117b6ec3.png": "\\frac{dc}{dt}=1", + "729e203a538896b1.png": "\\frac{dC}{dt}", + "729e89e014dad224.png": "(G:H_{i})=p", + "72a078dfeb8e6027.png": "\\sqrt{\\frac{2}{\\pi}}cos(ut)", + "72a3880d7afd5d2a.png": "\\overline{MR}", + "72a422f9238cd1ba.png": "K_{k}(\\tilde{M})", + "72a5abbe52bc7600.png": "H^{2}(CP^{1},Z)", + "72a7a91148169b78.png": "2^{10}=1,024", + "72aca9434d11b57c.png": "(1)Z(V,0)=1", + "72b0015727ef638e.png": "(x,y)\\mapsto x+y\\sqrt{-1}", + "72b167040fb30649.png": "\\varphi", + "72b70e4a1f613bfc.png": "(n-1)|(m-k)", + "72b750ba4b5fe8f6.png": "5=\\frac{e^{x}}{x^{2}+4}", + "72bfb050e87e5080.png": "g^{(2)}(r_{1},r_{2})", + "72bfbd626974d28e.png": "2x=O(x)", + "72c477cf39f2eaf2.png": "Z=\\int_{x}f(x)dx", + "72c936a0854dba3c.png": "\\int e^{ix}", + "72cac1b3052f3d08.png": "2^{m-n+c}", + "72cbbfc090983b28.png": "\\hat{m}_{-}", + "72cea15f43523cbd.png": "(p_{1}+...+p_{n})^{4}", + "72cfd8e30f59c293.png": "\\int_{-1}^{1}x^{-1}dx", + "72d23c6a1df20963.png": "(\\begin{matrix}n\\\\ n\\end{matrix})", + "72d5e39c7ded3c0d.png": "\\frac{dy}{dx}", + "72d7c59c795c58e5.png": "\\frac{P_{Rx}}{P_{Tx}}=\\frac{c_{0}F_{g}}{d^{\\gamma}}", + "72daef81c5b10ee1.png": "1-P(M|E)=0", + "72db3c6398745892.png": "H^{1}(R^{n})", + "72dc6c97aea1d3ea.png": "(\\begin{matrix}t\\\\ k\\end{matrix})", + "72dee48731478dfc.png": "\\alpha\\in\\tilde{P}_{i}", + "72e2cf887c4a92b0.png": "\\langle\\rho=\\rho_{2},Z_{2}\\rangle", + "72e3517962ac83f7.png": "I_{r,r-1}=[\\begin{matrix}I\\\\ O\\end{matrix}]", + "72e4b04711094739.png": "\\prod_{i\\in X}Y_{i}", + "72ef2c4e4aca05b3.png": "\\frac{\\partial y}{\\partial x_{1}}dx_{1}", + "72ef3eaac72a8da5.png": "\\oint_{K}\\kappa ds>4\\pi", + "72f369b88cd6a64d.png": "U((n+1)\\Delta t)", + "730221907f79ca35.png": "(\\begin{matrix}N\\\\ M\\end{matrix})", + "73029ac9fa64ba29.png": "\\tilde{u}(x,z,t)", + "7309e5733ae0baa1.png": "\\frac{\\rho v^{2}}{2}+\\rho gz+p=C", + "730b933ff7ffe10b.png": "0\\notin\\{1,2,3,4,5\\}", + "730d9d0b16abc793.png": "W^{1-\\frac{1}{p},p}(\\partial\\Omega)", + "730f0943ea85a52d.png": "\\int x^{2}dxdydz", + "7312f862bb1e2684.png": "\\prod_{i\\in I}R_{i}", + "73146762032c6c67.png": "\\forall y\\notin J\\cup\\{z\\},w_{iy}=0", + "73163abcd1a0d76d.png": "\\rho V\\int_{0}^{c}x\\gamma(x)dx", + "73165aa584bd6ad2.png": "a(x)\\ge c>0", + "731721ee3632b5f4.png": "\\hat{S}_{a}", + "731fb433c2164247.png": "P=[\\begin{matrix}0.1&0.9&0\\\\ 0.1&0.9&0\\\\ 0&0&1\\end{matrix}]", + "7324ca349572d196.png": "\\int_{0}^{5}xdx", + "7328dd7c995c6e8f.png": "P=-(\\frac{\\partial F}{\\partial V})_{T}", + "732a06fc633bd4ec.png": "\\theta=\\frac{2}{3}\\Sigma\\frac{\\theta_{i}}{2}", + "732d50456830347f.png": "\\frac{dx^{\\prime}}{dt^{\\prime}}=c", + "7331a6afd3b9334c.png": "\\int_{0}^{\\pi}sinxdx", + "733330247ce167b1.png": "G=KAN.", + "7337c75bfb39584f.png": "\\frac{1}{M(1,\\sqrt{2})}", + "733837c83685cb00.png": "[K]\\{d\\}=\\{-f\\}", + "73385c56071245b4.png": "\\int_{0}^{5}xdx", + "73388ff8e6bb17fd.png": "\\sigma_{i+1}^{2}\\le\\frac{\\sigma_{i}^{2}}{i^{\\alpha}}", + "7339885b82fa6480.png": "\\hat{\\phi}=Y_{D}\\circ F", + "734687a540eb3a05.png": "Y=(\\begin{matrix}-y&0\\\\ 0&y\\end{matrix})", + "734adbf7a0085008.png": "\\int x^{2}d(cosx)", + "7350d27b65eaa693.png": "\\frac{\\partial L}{\\partial x}=0", + "7351e1bf16eaa122.png": "\\hat{T}", + "735245749e1f00ab.png": "\\frac{1}{y}\\frac{dy}{dx}=ln2", + "735f8df68101ce30.png": "U((n+1)\\Delta t)", + "7372b02426d92348.png": "\\frac{\\partial c}{\\partial t}=\\nabla\\cdot j(x)", + "737d4e3f4581733b.png": "\\hat{R}", + "737de97faa087af0.png": "X=\\prod_{i\\in I}X_{i}", + "73821e0838f2b7cf.png": "2^{m}\\ge2^{n}(an+1)", + "7384b99257ae44f9.png": "\\tilde{Y_{k}}", + "7386ac09c8e90d39.png": "\\frac{dV}{dt}=Q_{0}", + "7388f15d5cb7453f.png": "r=1/\\varphi^{1/\\varphi}", + "7391ad7b052911a2.png": "(A\\times B)^{\\sigma}", + "7392ca4a34fad2db.png": "\\nu^{h_{5}}", + "7393db39a481060f.png": "lnn\\#=n+o(n^{\\alpha})", + "73a45373a8f66cb2.png": "\\hat{N}_{C}", + "73a537292f26e582.png": "X_{1},X_{2},...:\\Omega\\rightarrow R", + "73aa01549b8ec3ee.png": "K_{il(m+1)}=1", + "73ac10cc3237a1d1.png": "E[\\hat{\\sigma}^{2}]=\\frac{n-1}{n}\\sigma^{2}", + "73b4f2dc9d062f79.png": "f:\\{0,1\\}^{*}\\rightarrow Z_{n}", + "73becbea42ecdac4.png": "\\frac{1}{r}e^{-m_{W,Z}r}", + "73c0b9a325e3f8d3.png": "\\infty k\\delta(s)\\hat{z}", + "73d8210ce590177f.png": "G(y)=\\int_{0}^{y}g(z)dz", + "73dfd61fc15d01bd.png": "\\sigma_{xx}-\\sigma_{xz}+\\sigma_{xy}", + "73e1d7c808b2e7dd.png": "\\tilde{K}_{\\pm}", + "73edf48545edabfe.png": "\\int sin^{m}xcos^{n}xdx", + "73ee494ce5d1d258.png": "(\\begin{matrix}x\\\\ k\\end{matrix})=\\frac{(x)_{k}}{k!}", + "73f0b1d37ae70a47.png": "2.5\\le\\epsilon_{r}\\le25", + "73f8b76bcbc0a709.png": "(\\begin{matrix}k\\\\ 2\\end{matrix})-m", + "73f9b17f93e7df4e.png": "\\mathbb{I}", + "74006ed8f447ed41.png": "f\\in[D\\times D^{\\prime}\\rightarrow D^{\\prime\\prime}]", + "7402066f00e0cc4d.png": "(\\begin{matrix}4\\\\ 2\\end{matrix})", + "7409947213a8ce48.png": "\\tilde{q}_{i}", + "74099941420a9569.png": "N=max(m,n)", + "740cc91bae2a7dc1.png": "X,T=AX", + "740cedf125e5a5de.png": "\\overline{Y_{v}}=P_{\\overline{x}}\\overline{X_{v}}", + "740eae6c8c659cc1.png": "x\\notin Y\\cup Z", + "740f61ee2eadc6da.png": "\\eta=1-(\\frac{T_{1}}{T_{2}})", + "740fa2f36a664133.png": "\\tilde{U}", + "7412618681e9798d.png": "(0.999)x-y=2", + "74129fda084c5e04.png": "\\sqrt{67}", + "7413def1ebb4de4b.png": "R=a_{z}z-a_{r}b", + "7414b61f62201ead.png": "\\frac{q}{A}=-k\\frac{dT}{dx}", + "7414c094cbefa018.png": "L=9.75m/s^{2}", + "7415c3e3dc3ec31c.png": "\\phi_{e}\\notin F", + "7416c1a193707a3e.png": "\\lambda=\\sqrt{\\frac{r_{m}}{r_{i}+r_{o}}}", + "7417406fbd836e93.png": "\\sqrt{z}", + "741755af21598561.png": "\\tilde{f}_{1}", + "741b13d1672081ed.png": "[\\hat{Y},\\hat{I}_{\\pm}]=0", + "741cc1d0a2c247ef.png": "(\\begin{matrix}7\\\\ 5\\end{matrix})", + "7420825f80c02b7a.png": "\\frac{M\\mu_{0}}{B+\\lambda M}=\\frac{C}{T}", + "742c01da889863db.png": "\\frac{\\partial\\delta}{\\partial x_{j}}(x)", + "742cb1253125d31f.png": "Y^{T}A_{i}Y\\sim\\sigma^{2}\\chi_{r_{i}}^{2}", + "7431cf135e7a8a85.png": "\\frac{\\partial u}{\\partial x}", + "743397dcff905765.png": "\\langle f,\\varphi\\rangle=\\langle T_{f},\\varphi\\rangle", + "7435f1ed4adda7ff.png": "H=(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "74366ae795e95a2a.png": "\\hat{\\gamma}", + "74369a030d4fcacc.png": "(\\begin{matrix}c_{i}\\\\ i\\end{matrix})=0", + "7436c666a1c653af.png": "\\tilde{A}_{2}", + "7438dcd0bfcbce7e.png": "\\hat{X}(z_{1k},z_{2k})", + "743bf15baed19fbe.png": "(\\nabla^{2}+k_{0}^{2}n^{2})\\psi=0", + "743f4e96d74a0bf5.png": "e\\notin S", + "743fff68dafa2ae5.png": "\\partial_{t}L=\\frac{1}{2}\\nabla^{2}L", + "7441ddd050811e06.png": "\\tilde{E}_{n}", + "7445374e4cce2554.png": "\\mu y=\\int\\mu q(x)dx", + "74486156377ccce9.png": "\\hat{D}(\\alpha)", + "744c00c870c28f93.png": "\\vec{P}_{m}=(x_{m},y_{m},z_{m})", + "744d77c6f47d3901.png": "-\\mu_{e}E", + "7451e7c5c801468f.png": "\\frac{d}{D}", + "7452cbb897003b9e.png": "\\hat{p}", + "745bd363958ed628.png": "2\\pi/c_{ij}", + "745ef67628c55599.png": "=\\frac{1}{2}I\\omega^{2}", + "7461e512aec7ac48.png": "(2f(x))^{-2}", + "74624ff7823c59ca.png": "M=\\frac{y_{2}-y_{1}}{X_{2}-X_{1}}", + "74626aa6b955c0b5.png": "EL(\\Gamma)=w/h", + "7468313927121cb0.png": "2\\sqrt{5}\\approx4.47>4", + "74731bc3178cfcbf.png": "(s)_{+}=max(s,0)", + "74737bf3b1e0f18e.png": "\\underline{R}", + "747589baebecde8b.png": "O(n^{2}log\\frac{1}{\\delta})", + "7476dcbea98dffb5.png": "r\\{\\begin{matrix}3\\\\ 3\\end{matrix}\\}", + "747ce17014ba6157.png": "(\\begin{matrix}m\\\\ n\\end{matrix})", + "747ed34caf9579dc.png": "mr^{2}\\dot{\\theta}", + "74846bde4bca902e.png": "\\frac{dV}{dh}=0", + "7485a008eafdf072.png": "-2\\int E\\cdot dl", + "7488831a3bdc120d.png": "cos\\nu=\\frac{d_{1}-d_{2}}{2a}", + "748c59c4e60fcd9f.png": "\\sum_{\\langle i,j\\rangle}=\\frac{1}{2}\\sum_{i}\\sum_{j\\in nn(i)}", + "7490903d6f1543f4.png": "\\tilde{T}_{2}(gG^{\\prime})=t_{3}^{-j}H_{2}^{\\prime}", + "74909715d06165fb.png": "\\Delta T=\\dot{Q}R", + "74916d4bf30d0cce.png": "\\frac{dV}{dt}=Q_{0}", + "749226c7c3dff114.png": "g\\frac{\\partial\\eta}{\\partial x}=fv", + "74aa3972ec65f132.png": "g(x)\\int f(x)dx", + "74b1379fd50d13a8.png": "(\\begin{matrix}x&-y\\\\ y&x\\end{matrix})", + "74b572f9ec02041c.png": "\\varphi(e^{-\\pi})=\\frac{\\sqrt[4]{\\pi}}{\\Gamma(\\frac{3}{4})}", + "74b6d74036634d25.png": "lim_{n\\rightarrow\\pm\\infty}x^{2}f(x)=0", + "74b9d47e1be01d75.png": "\\tilde{E}", + "74baa232d9fc0d51.png": "(q+1)-\\frac{q}{d}", + "74bbff7e274b7883.png": "[\\begin{matrix}2&p\\\\ q&2\\end{matrix}]", + "74be0f7524d8bb48.png": "(-b+\\sqrt{b^{2}-4c})/2", + "74bf9422af109ea7.png": "a_{i}-a_{j}=a_{k}-a_{l}", + "74c8cb9f84f0482d.png": "\\frac{dC_{A}}{dt}\\ne0", + "74cbbc399a0c3c12.png": "lim_{p\\rightarrow-\\infty}a_{p}=-\\infty", + "74ccd2db0476b63e.png": "C_{n}=\\int_{0}^{4}x^{n}\\rho(x)dx", + "74cd4566e78cbfec.png": "C_{R}=\\sqrt{\\frac{h}{H}}", + "74da511cd23a9dc2.png": "\\delta_{u}(t):=\\delta(t-u)", + "74dd4f0a8dfcff80.png": "\\tilde{a}_{k}=a_{k}^{*}", + "74ddd50baee227c8.png": "q_{(\\theta_{j})}", + "74e47f377e1af3b8.png": "\\overline{\\vec{\\xi}^{2}}\\approx\\lambda_{c}^{2}", + "74e6909ba750c966.png": "\\sum_{Z}n_{Z}[Z]", + "74fb950935800ed1.png": "\\langle J(0)\\rangle_{F_{e}}=0", + "74fc89ee1e12645b.png": "(v_{0},v_{1})=-(v_{1},v_{0})", + "74feba13685f13e1.png": "-\\int E\\cdot dl", + "7501290d58980cf5.png": "\\int d^{D}x\\sqrt{-g}G", + "75017b515e8ab9c7.png": "\\frac{dt^{2}}{dr^{2}}", + "7505a4597273520c.png": "\\int_{G}fd\\mu", + "7505ec356ea6f73e.png": "y=\\frac{\\int xe^{-x}}{e^{-x}}", + "7507cc5ac5b98dfd.png": "(\\begin{matrix}X\\\\ k\\end{matrix})", + "75086c249caf3d42.png": "F(a)=\\frac{xa^{2}}{2}", + "75104607b8439f95.png": "C_{pq}^{-}", + "7513138fab901fb9.png": "\\mu=\\frac{(-3)(-1)}{-2}=-\\frac{3}{2}", + "7514059b2b529da0.png": "-i\\frac{d}{dx}", + "7517d23e5625c665.png": "\\sigma^{2}=(\\pi s)^{2}/3", + "751b37cc068a1d1b.png": "v", + "751e08215c1fdeb2.png": "\\Omega_{u}^{\\phi}", + "751ef0bf1262e691.png": "\\sqrt{N}", + "752088483e6fc281.png": "C([x])\\subset[x]", + "7525595bafb75a46.png": "\\Rightarrow r=-\\frac{3}{4}\\pm\\frac{\\sqrt{17}}{4}", + "75268c994a32b25b.png": "\\pi_{w}^{\\eta}", + "752c710311ffc053.png": "\\oint dS=\\oint\\frac{dQ}{T}=0", + "752dd7c8d3056bbd.png": "A^{?}=A+1", + "752ee1325058aaa1.png": "\\tilde{W}_{t}=W_{t}+\\frac{\\mu-r}{\\sigma}t", + "7530d352b8d43a8b.png": "\\dot{y}=\\frac{dy}{dt}", + "75338b4b4fd6ab8b.png": "\\frac{d}{dx}(\\rho\\frac{v^{2}}{2}+p)=0", + "75366a1c06c936b9.png": "f_{d}", + "75370edbf91a0c53.png": "C[g]^{G}", + "7538995bc32f9ba6.png": "\\vec{a}(\\theta_{k})\\gamma_{k}", + "7539efa693cea1fa.png": "\\tilde{T}_{H,K}:H/H^{\\prime}\\rightarrow K/K^{\\prime}", + "753abaeeeea46630.png": "a=\\tilde{x}\\iff f(a)=f(\\tilde{x})", + "753d5a1a75c98401.png": "-\\sqrt{x}", + "753e2b03f8a49bab.png": "\\sqrt{50}", + "75415b13038e0362.png": "p=-\\frac{1}{\\sqrt{3}}z", + "75439c362293d411.png": "m_{\\tilde{t}}", + "7549d2889810f238.png": "E\\{\\hat{x}-x\\}=0", + "75625743328102dd.png": "\\delta^{*}\\approx\\frac{1.72x}{\\sqrt{Re_{x}}}", + "7565240cbafe12fc.png": "(q+1,q-1)", + "756b7e46dea04d95.png": "\\underline{n}", + "756caaf7ed0d15dd.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "756d710ada0603ea.png": "\\frac{337m}{11}-2=x", + "756e0dec67c58c51.png": "\\prod_{i\\in I}A_{i}", + "7570bb53cc001aee.png": "G(R)=\\sigma^{+}-\\sigma", + "7570c08cfec97c04.png": "(\\begin{matrix}d-1\\\\ n\\end{matrix})", + "7573fc5b48b852a8.png": "\\int_{a}^{b}f(x)dx", + "75763cd42a380240.png": "\\theta_{0}=2\\pi r_{0}^{2}H_{0}", + "7578b552f9b6e6c2.png": "\\tilde{a}_{1},...,\\tilde{a}_{m/n}", + "757cd59c45a0b929.png": "-j\\sqrt{\\frac{1}{2}}", + "7580cf2866599666.png": "(X,Y,Z,aZ^{4})", + "75844de197e7e782.png": "\\Gamma_{00}^{i}=U_{,i}", + "758471b0070f2ebb.png": "x^{2}+q=px", + "758712cc0e4d936a.png": "(\\begin{matrix}0&1\\\\ -1&0\\\\ \\end{matrix})", + "7596343c3c09b734.png": "1/2<\\sigma<1", + "759a054f7d34bc72.png": "E=\\frac{1}{2}(t-y)^{2}", + "759da8ab4a6eb6b5.png": "\\int_{L}f(z)dz", + "759e1dc04492f701.png": "[\\begin{matrix}1&R\\\\ 0&1\\end{matrix}]", + "75a11bd054423d6c.png": "\\gamma=lim_{\\epsilon\\rightarrow0}\\frac{lnf(\\epsilon)}{ln\\epsilon}", + "75a6c3416c45e1e4.png": "y=\\int_{0}^{2}xdx", + "75aa72bf68cf0244.png": "\\tilde{C}_{8}", + "75aaa36a5652f830.png": "b\\overline{z}", + "75b21bf7fffe0517.png": "F(a)=\\frac{xa^{2}}{2}", + "75b25bbae65e378c.png": "F\\underline{A}", + "75bee5bd77b3b5cf.png": "\\beta=(g_{im}\\cdot1)/n", + "75c200f3b04bd251.png": "\\frac{\\partial\\psi}{\\partial t}=P\\psi", + "75c6735a848043fd.png": "\\int_{0}^{r}4\\pi u^{2}du", + "75c8f0efef185763.png": "[\\begin{matrix}0&-1\\\\ 1&1\\end{matrix}]", + "75c9b864fa76ab1c.png": "\\mu_{n}=\\int x^{n}d\\mu", + "75ca13864ee768b0.png": "2\\sqrt{5}\\approx4.47>4", + "75cb5b0973f06f08.png": "\\exists!n\\in N(n-2=4)", + "75ce71395eead72f.png": "\\frac{\\partial^{2}z}{\\partial t^{2}}", + "75d6216bf77386ed.png": "\\Rightarrow\\frac{1}{c}=\\frac{-ln(z)}{W(-ln(z))}", + "75e728a88bc25869.png": "V_{i}^{L}||V_{i}^{R}=V_{i}", + "75e9534d8c8dec67.png": "x=y=\\frac{-i}{\\sqrt{2}}", + "75e95bc357074f5a.png": "\\int x(t)dt|_{t=z}", + "75eb45b8efbc08da.png": "(\\begin{matrix}5\\\\ 2\\end{matrix})=5\\times\\frac{4}{2}=10", + "75ebc41d5bfc1410.png": "\\int_{-\\infty}^{\\infty}e^{-x^{2}}=\\sqrt{\\pi}", + "75f1f4bd420b2539.png": "lim_{x\\rightarrow0}f(x)/g(x)=1", + "75f2f5b959ff1474.png": "\\frac{\\partial V_{1}}{\\partial C_{1j}}=\\frac{\\partial V_{2}}{\\partial C_{1j}}", + "75fbf1bc07aa0e3a.png": "(P(n))_{n\\in N}", + "76015e864b235b8a.png": "\\{\\vec{x}:\\vec{y}\\}", + "760318c1f04b590e.png": "(\\begin{matrix}x\\\\ k\\end{matrix})", + "760389264d07ca95.png": "F(x):=\\int_{-\\infty}^{x}dp", + "760b128abbbfe276.png": "I(a)^{2}", + "760d25f17bbd505e.png": "\\int_{0}^{t}Z_{s}ds", + "761308cb3d70d6b7.png": "\\{\\begin{matrix}p\\\\ q+r\\end{matrix}\\}", + "761c216b26ceeae5.png": "\\sqrt{10}(4\\rho^{4}-3\\rho^{2})cos2\\theta", + "7622ac8d70bd60a8.png": "(\\frac{1}{s},0,0)", + "762b82cee3872d3d.png": "E(\\overline{K})", + "7631d57843020bb6.png": "f_{1}=(x,y,0)/norm", + "7639d67745573234.png": "V_{i}=O_{[g]}^{\\chi}", + "763bf20d9c561450.png": "\\vec{p}_{0}=\\frac{1}{\\sqrt{1-\\omega^{2}r^{2}}}\\partial_{t}", + "76469bff00656234.png": "[0,\\frac{3}{8}]\\cup[\\frac{5}{8},1]", + "76471d218d4d120a.png": "Ra=\\{ra|r\\in R\\}", + "7647d457fe5a56f0.png": "{v^{\\chi}}^{\\varphi}", + "76493fcb12ecad01.png": "\\int_{\\partial\\Omega}", + "764d4e783e5fe867.png": "(-1)^{N_{y}+N_{z}}", + "764d9b68af4415a4.png": "|x-x_{0}|>\\epsilon", + "764dc9dd7e54d9a5.png": "z=\\pm\\sqrt{R^{2}-r^{2}};", + "765f30c62ca82973.png": "g(Q-I)=0", + "76604ef08c7f23b5.png": "\\hat{z}_{a}", + "7665c92bf0b0cdb1.png": "A=4A_{0}=\\sqrt{3}a^{2}", + "76684c6e7f5b4c89.png": "\\int_{c}^{d}f(x)dx", + "766bd191e5797207.png": "\\int_{-r}^{r}\\sqrt{r^{2}-x^{2}}dx", + "766c3618ab4041ed.png": "g", + "766fc3cf504863cf.png": "x\\notin C", + "767179c66e6053e7.png": "w\\notin\\{u,v\\}", + "767850c8dc197e38.png": "\\forall p\\forall x(x\\notin p)", + "767aa0a0dafe84e8.png": "a\\notin w", + "767b173567a5a725.png": "\\gamma_{0}=[\\begin{matrix}0&1\\\\ 1&0\\end{matrix}]", + "767bbb676ea47878.png": "\\sum_{k=0}^{n}(\\begin{matrix}n\\\\ k\\end{matrix})p^{k}(1-p)^{n-k}=1", + "767c8ef05531f307.png": "\\hat{p}_{y}", + "7682432fad8cc3ca.png": "(\\frac{p-1}{2})(\\frac{q-1}{2})", + "7684ac6b7a2463d3.png": "A=(\\begin{matrix}2&1\\\\ -1&0\\end{matrix})", + "768590580f0288dc.png": "\\int_{a}^{b}dx", + "768b915d266f9d64.png": "g(x)=\\int_{0}^{x}f(t)dt", + "769bbbb97a81e1ff.png": "0\\le[f]", + "769ca4850c4c9731.png": "\\int e^{-x^{2}}dx", + "76aaec143c8d5281.png": "C_{i}^{\\prime m}(r)", + "76adb1c3f6a209c6.png": "\\tilde{U}", + "76af87476b3029e1.png": "\\Psi(r)=\\sqrt{\\frac{N}{V}}e^{ik\\cdot r}", + "76b197515e8bcf4c.png": "J^{2}=j(j+1)I_{2j+1}", + "76b3058b4803a8d1.png": "\\sqrt{nc}", + "76b4cf6be8ac54ff.png": "\\frac{\\partial h}{\\partial z_{j}^{-}}", + "76bf6a3090ff1dd6.png": "W=-\\int Fdx", + "76c7eaf2fec7a44a.png": "\\sqrt{6}", + "76cba4685bc1d60a.png": "f(t)=L^{-1}\\{F(s)\\}", + "76d69bac010ce2b1.png": "10^{-10^{100}}", + "76db05914b294da2.png": "\\frac{\\delta J}{J}=\\epsilon_{S}^{2}\\frac{\\delta S}{S}", + "76dc67eb7a29ce28.png": "\\hat{x}_{k}", + "76e2f681be1ef544.png": "f(0,\\overline{u})=g(\\overline{u})", + "76e3488817866ba3.png": "V=\\sqrt{r_{1}^{2}+r_{2}^{2}}", + "76e66289ffe43894.png": "(\\begin{matrix}3\\\\ 4\\end{matrix})", + "76e8c3b97df4aff8.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=(\\begin{matrix}n-1\\\\ k\\end{matrix})+(\\begin{matrix}n-1\\\\ k-1\\end{matrix})", + "76e9fad718f1ca82.png": "\\frac{dy}{dx}", + "76eaabe807630803.png": "u=\\int\\frac{du}{dx}dx", + "76eb6ccbd87a34d9.png": "\\sum_{n=0}^{\\infty}a_{n}x^{n}\\sim\\frac{1}{1-x}", + "76efb6c6b4170e04.png": "(\\begin{matrix}k\\\\ r_{1},r_{2},...r_{n}\\end{matrix})", + "76f287f77f4737bd.png": "k=\\frac{m}{x^{\\prime2}+y^{\\prime2}}", + "76fb5d2bedeec1bf.png": "\\overline{Y}", + "7702b16973ab0d32.png": "r=1+\\frac{a_{c}}{100}", + "770419c651654e21.png": "p(x)=\\prod_{j}(1-xX_{j})", + "77054697f667fd71.png": "\\hat{M}", + "77083393ba3c9e8d.png": "(\\begin{matrix}c_{k-1}\\\\ k-1\\end{matrix})\\le N-(\\begin{matrix}c_{k}\\\\ k\\end{matrix})", + "7724f47caf4efcff.png": "\\partial_{g}(U|\\Psi_{0}\\rangle)", + "77285b00405abeae.png": "\\frac{\\hbar}{ea_{0}^{2}}", + "7735ea70095cdec1.png": "\\{|j,m_{j}\\rangle\\}", + "773692a415d97063.png": "[\\begin{matrix}2&2\\\\ 3\\end{matrix}]", + "7745bc97b2b25cfb.png": "\\frac{d^{2}y}{dt^{2}}", + "7753b4e8dcadb351.png": "E\\cap\\overline{E}=\\Delta\\otimes C", + "7758f7ba7d6582ea.png": "A\\overline{D}", + "775cd2d3c4720133.png": "R=0,C_{abcd}=0", + "775ddc08379b569a.png": "B^{\\mu},W_{j}^{\\mu}", + "77634176b6e1a31d.png": "\\frac{2}{3}(ln(ln2x))", + "77656ee0f92fec8e.png": "\\frac{20n}{4^{10}}", + "776af78a0624dc62.png": "(\\begin{matrix}n\\\\ m\\end{matrix})", + "776c158be9f12650.png": "Z=\\frac{\\partial}{\\partial z}", + "77730b20f4871997.png": "g=\\frac{dv}{dx}", + "7774873e9c44b5d8.png": "\\frac{2e}{h}U_{DC}", + "7775d14304673d8d.png": "\\hat{\\epsilon}=\\frac{D_{0}}{E_{0}}=|\\epsilon|e^{-i\\delta}", + "777a48a8dcf70cbe.png": "n(x,0)=0,x>0", + "778430da0372fd86.png": "2^{127-23}", + "7788870067c426e3.png": "\\int_{E}w(x)dx", + "778b00d66796e0a9.png": "W_{1-2}=\\int PdV", + "778c14f6d1f0bb43.png": "f(-10,1)=0", + "778c37d7450b48f4.png": "\\prod_{i=1}^{4}i=24", + "779349280b030844.png": "j\\notin I", + "77a482f515a1d302.png": "cos(\\theta(\\hat{n}))", + "77ac3a751d76e934.png": "\\tilde{C}_{n}", + "77acf9541ee8e7a6.png": "\\overline{x}\\in X", + "77c04783a0d6e20f.png": "S=\\int Ldx_{3}", + "77cfe7368c65f2e1.png": "y", + "77d089a73bd13170.png": "\\tilde{0}", + "77d889661cf87efb.png": "h_{k}=f_{-k}", + "77e0c9ac7f99850c.png": "f_{yy}(x,y)=-e^{y}", + "77e5d042d5a0f400.png": "x=\\sqrt{y+(1/4)}-(1/2)", + "77ea40336df395d4.png": "K=V_{star}sin(i)", + "77ea46678c7b1429.png": "V=-\\frac{h^{2}}{m}sech^{2}(x)", + "77ed8e8000bccf11.png": "F=\\frac{\\pi}{4}P_{max}DL", + "77ee505b45bd65f1.png": "F(\\underline{x},-)", + "77f1a282c4c3a6dc.png": "\\alpha_{2}=\\frac{4\\alpha_{0}+1\\alpha_{1}}{5}", + "77f1bd18b64c2858.png": "P^{2}\\psi=e^{i\\phi}\\psi", + "78034b5cb446aec7.png": "\\gamma=\\sqrt{\\alpha g}", + "78066a45ce69b320.png": "H_{2^{n}}=F_{n}^{T}F_{n}", + "7813addc620a95c6.png": "(\\begin{matrix}n\\\\ i\\end{matrix})2^{-n}", + "7815178519924bf4.png": "\\Psi=e^{i(k\\cdot r-\\omega t)}", + "7815e2ed8ba8ee9c.png": "V_{R}=IR=C\\frac{dV_{C}}{dt}R", + "78181ad4e91c3b8b.png": "F(r)=-\\frac{k}{r^{3}}", + "78192dd0314fd7ed.png": "\\frac{1+x}{((1+x)^{2}+1)^{3/2}}", + "78196cb85e532fc4.png": "e^{2}/\\hbar c\\approx1/137", + "7819f682fe3c856c.png": "\\frac{1}{10}x^{5}+\\frac{1}{2}x", + "781c4f2074e36a50.png": "\\sqrt{1}", + "781f93569a9bc67d.png": "\\hat{v}_{i}", + "7824303422aebf78.png": "\\sigma_{j}^{\\eta}", + "7825b171b02ab64c.png": "M_{unit}=\\frac{y^{2}}{2}+\\frac{q^{2}}{gy}", + "782608e7eaf4bed7.png": "D(-\\infty,\\infty)", + "78277b3659498d79.png": "\\frac{q}{A}=-k\\frac{dT}{dx}", + "7829ad39e993d63b.png": "\\sqrt[n]{\\prod_{i=1}^{n}r_{i}}", + "782bbf94753ef3d1.png": "(\\begin{matrix}11\\\\ 4\\end{matrix})", + "78352cf33e0c6569.png": "(\\begin{matrix}n+1\\\\ k-1\\end{matrix})", + "783a8820eed77518.png": "\\frac{a}{a+b}+\\frac{b}{a+b}=1", + "7840ac5f29a13c76.png": "[\\begin{matrix}x^{\\prime}\\\\ y^{\\prime}\\end{matrix}]", + "78431728c7ce47d5.png": "\\frac{dF}{dx}", + "7844355c71442f7d.png": "EC=(\\begin{matrix}I_{r}\\\\ 0\\end{matrix})", + "7844e04cfc796c1e.png": "\\int_{-N}^{N}f(x)dx", + "7850faa6212c9e02.png": "C_{1}=C_{2}=C>0", + "7851393f9baff140.png": "T(\\theta)=\\frac{M(\\theta)-C_{1}}{C_{2}}", + "7857666d838837fa.png": "\\phi,\\tilde{\\phi}", + "785987dc65f3e287.png": "\\bigcap_{i=1}^{\\infty}m^{i}=\\{0\\}", + "785d610deb287504.png": "n^{\\overline{m}}", + "7860497030c154ba.png": "f(t)=L^{-1}\\{F(s)\\}", + "78635425dcd975e9.png": "\\frac{1}{(1/X-1)^{n}+1}", + "7864083ccffa8ee0.png": "\\sqrt{yz}", + "78669844844de505.png": "F[y]=\\int_{E}ytdt", + "786e40a25ae086b5.png": "\\overline{P}(Cl_{2}^{\\le})=Cl_{2}^{\\le}", + "787400f0f7b2f028.png": "p^{2}+(1-p)^{2}", + "787450d00ef7b197.png": "(\\begin{matrix}m\\\\ r\\end{matrix})", + "7876b84f57e692df.png": "\\int_{-3}^{4}f(x)dx", + "78816859651b85b2.png": "\\frac{dz}{z}", + "788f3cf02e033808.png": "\\hat{se}_{\\theta}", + "78929297363ed09e.png": "\\tilde{x}_{0}", + "789b7772d5183e31.png": "2^{7}+17^{3}=71^{2}", + "78a387a5c543c47b.png": "w^{*}=\\frac{c_{min}}{c_{max}}", + "78a6b673857d5c7e.png": "l", + "78ab9d1032569821.png": "P(n,x):=P^{n}(x)", + "78adcfd5f1896839.png": "W=\\int Fdx", + "78afb3217d312de2.png": "j(\\{y\\in V_{\\alpha}|\\phi_{3}\\})", + "78bbfbfefd810682.png": "|B^{\\prime}|\\le w(X)", + "78bcf38e7cddb559.png": "A_{i}^{2}=B_{j}^{2}=I", + "78c13b39fdb8411c.png": "r(\\underline{x},t)", + "78c265999e5078b9.png": "A:x\\mapsto2\\sqrt{x}", + "78c6d148d5fe2225.png": "E\\mapsto\\int_{E}fd\\mu", + "78cb3918e1896fce.png": "\\hat{J}^{2}", + "78ce255d3fc59f4c.png": "I^{m}M/I^{m+1}M", + "78d093bf5da63d9c.png": "\\frac{\\partial f}{\\partial x}=y", + "78db2f1199164d1b.png": "V(r)=\\frac{1}{2}m_{0}\\omega^{2}r^{2}", + "78dcdbfdb87d0c62.png": "\\int_{x}^{1}f^{\\prime}(t)dt", + "78e0770092d34329.png": "\\|\\lambda_{\\hat{\\theta}}-\\lambda_{\\theta}^{*}\\|_{T}", + "78f1334149f66d2c.png": "x=\\hat{X}", + "78fa294dc6923141.png": "\\overline{W}_{t}", + "78faee30fa4cf751.png": "x\\mapsto\\{\\langle e_{k},x\\rangle\\}_{k\\in N}", + "78fda67b4cd6fa76.png": "u=e^{i\\theta_{1}}cosr", + "7900a06ffbfdd8e5.png": "\\sum_{i=1}^{k}\\sum_{w\\in V}f_{i}(s_{i},w)", + "7900e70061245a99.png": "\\frac{dS}{dz}=0", + "79010d3405cbf619.png": "0=\\dot{Q}_{H}-\\dot{Q}_{a}-P", + "790391c2e8c89892.png": "\\frac{\\partial^{2}u^{2}}{\\partial x^{2}}", + "790605e010da9443.png": "d\\in D^{n},r\\in R", + "79095843aaf6c714.png": "d(v)0}(1+B_{T}^{x})<\\infty", + "7f4b51d9b6da8b47.png": "\\int_{-\\infty}^{\\infty}", + "7f5590eb3b3fbbfe.png": "\\hat{y}\\in\\{-1,1\\}", + "7f5ac166cc17a7f3.png": "a\\notin\\mathbb{Q}", + "7f5cbebd523986d0.png": "g(Q-I)=0", + "7f6969142ec7d6bc.png": "RO_{j})", + "820509ca286e1a4b.png": "\\frac{dx}{dt}=r+x^{2}", + "820a0ab46d0754a6.png": "\\Omega=\\rho+i\\tilde{\\rho}(\\rho)", + "820bffb7774dd220.png": "W(k)\\ge\\frac{1}{2},k\\in N", + "820caadb1d227b88.png": "H=(\\begin{matrix}0&-i\\\\ i&0\\end{matrix})", + "820ff7f57bc9b4bd.png": "\\vec{F_{a}}\\cdot\\vec{x}=F_{a}x", + "82123b7caf58bb6b.png": "(q=F(\\tau-\\theta))", + "821afc631613fd70.png": "lim\\frac{x}{y}=\\frac{limx}{limy}", + "822407119b660f0f.png": "A_{c}=A_{c}^{i}T_{i}", + "822993283f55955f.png": "\\sum_{j=1}^{n}|\\gamma_{j}|\\le M+1", + "822e2b970c5906ad.png": "\\frac{dB}{dz}", + "82345eddc8b91dd8.png": "\\hat{p}=0", + "8244c25242c105a7.png": "\\frac{dX}{dt}", + "824575e096854f4d.png": "\\forall v\\in W(w,v)\\notin R", + "8253b25a7319f0d6.png": "\\prod_{1}^{p}E", + "8254c7ad66045b5c.png": "v=\\frac{max(|x|,|y|)}{n}c", + "8255041d6272658f.png": "P(X_{1}=X_{2})", + "825799b9cf498f36.png": "L(\\phi,\\partial_{\\mu}\\phi)", + "825888380e4a5e14.png": "\\tilde{O}(log^{5}q)", + "825cf749d67f34e3.png": "F=P-\\frac{\\partial V}{\\partial r}", + "8264647b4da10fec.png": "\\frac{\\partial f}{\\partial x^{i}}", + "82650010dbea7f22.png": "\\overline{AH}", + "82696f2a4edb75dd.png": "P_{rad}=A_{rad}\\epsilon\\sigma T^{4}", + "826b3726066dc558.png": "2^{c}", + "82758043345dd444.png": "(\\begin{matrix}c_{i}\\\\ i\\end{matrix})=0", + "8275caf45802b657.png": "\\overline{s}\\in\\alpha,t\\notin\\gamma", + "827e73037151266c.png": "\\rho>2b/2D", + "827f68f123933374.png": "\\Gamma^{i}=\\partial_{t}q^{i}(t,\\overline{q}^{j})", + "827fb247a067fbe9.png": "\\tilde{M}=M//G", + "828488fcb8f452a7.png": "z_{\\alpha}\\sigma/\\sqrt{n}", + "828ab1dee63f53c4.png": "m=\\prod_{k=1}^{j}m_{k}", + "828fe5486dee5a3f.png": "(\\begin{matrix}m\\\\ r\\end{matrix})_{q}", + "8296b43e0e201aeb.png": "f(f(x))=ab^{x}", + "8298bad01dafac87.png": "O_{p^{\\prime},p}(G)", + "829c72d2a36e5845.png": "\\hat{=}", + "82a0c956800a9d8e.png": "\\alpha_{12}=\\frac{1}{2}(\\alpha_{11}+\\alpha_{22})", + "82b4958517af3784.png": "\\hat{w}_{i}^{\\prime}", + "82b538ce765f9a19.png": "cos\\Phi_{r}\\rightarrow\\sqrt{\\frac{r}{2M}}", + "82bde76c7dac8699.png": "(\\begin{matrix}k\\\\ r\\end{matrix})=0", + "82c0ceea7650a689.png": "N+-", + "82c635240b3d4ae0.png": "\\int_{0}^{T}g(t)dt", + "82caa005a98dd8a1.png": "cos\\Phi_{r}\\rightarrow\\sqrt{\\frac{r}{2M}}", + "82ce9fd786d4d580.png": "U(P_{\\phi})=e^{i\\phi}", + "82d918db40780815.png": "e_{1}=(\\begin{matrix}0&1\\\\ 1&0\\end{matrix})", + "82de5c7250a915ad.png": "\\int_{0}^{r}4\\pi u^{2}du", + "82e62c53baacd74d.png": "(\\begin{matrix}d-1\\\\ n\\end{matrix})", + "82e8f7d69958a8b7.png": "(\\begin{matrix}4\\\\ 7\\end{matrix})", + "82fe7859b9eb5dc8.png": "[\\frac{\\alpha}{\\pi}]=[\\frac{\\alpha}{\\theta}]", + "82ffef2edd8ae1c0.png": "\\hat{H}", + "8302639c5b1e951f.png": "{\\prod_{i}}^{\\prime}G_{i}", + "83035be6e1468403.png": "(\\frac{5i}{3},\\frac{4}{3})", + "830c7e374ab191c3.png": "(-\\rho(X),\\rho(-X))", + "830f034300b0b6ee.png": "Rv_{i}=\\tilde{\\lambda}_{i}v_{i}", + "831133ae16dd80eb.png": "\\sigma_{b}=P\\cdot\\hat{n}_{out}", + "8313d47c7d0382eb.png": "f=\\frac{1}{2\\pi\\sqrt{LC}}", + "831b86007585b83c.png": "A=[\\begin{matrix}1&-3\\\\ 1&2\\end{matrix}]", + "831d576e820aa078.png": "\\frac{1}{4}nl^{2}\\cdot cot(\\pi/n)", + "831e37a730943f14.png": "\\{\\Omega_{x}^{(k)}\\}_{k=1}^{K}", + "8322786637fb631f.png": "\\frac{dx}{dt}=rx(1-x)-px", + "832709aad3825e40.png": "m=0,...,|n|-1", + "83285f8f5d15c4a0.png": "\\hat{w}=\\hat{p}\\times\\hat{q}", + "832f3cc0cfddd0f3.png": "-\\sqrt{\\frac{1}{20}}", + "83331e5b8cbbdc88.png": "\\beta=max\\{0,\\beta^{PR}\\}", + "83334169d01e1cbc.png": "x(\\underline{n})", + "833658b51228b436.png": "\\Omega_{t}=R^{n}", + "833f0cf212bee5f6.png": "\\alpha_{1}=\\frac{A_{32}-A_{23}}{2}", + "833f69362cef45e7.png": "\\frac{dy}{dx}=\\frac{x}{y}", + "83400eb5e124460f.png": "\\tilde{c}(\\Pi)", + "834136bb745b8265.png": "\\Omega_{u}^{\\phi}", + "8345a87c358ae9b9.png": "4x^{2}+2xy-3y^{2}", + "834ca86336162deb.png": "{(\\theta^{r})}^{4}", + "834ed1cf536b9e9c.png": "(\\alpha,\\beta,id)", + "8350ccfb445c07d2.png": "(\\begin{matrix}N\\\\ n_{A}\\end{matrix})=\\frac{N!}{n_{A}!n_{B}!}", + "835132bc57f5d820.png": "-a_{+}^{*}", + "8352b246da8b36d2.png": "[\\begin{matrix}4\\\\ 1\\\\ 8\\end{matrix}]", + "835712ad083227e9.png": "C(T)^{*}", + "835867a44d1af2c4.png": "[\\hat{Y},\\hat{I}_{\\pm}]=0", + "835b6d934037f846.png": "|x|\\le1,|y|\\le1", + "835ddb9334565249.png": "\\tilde{h}[n]", + "8362c202f87e8430.png": "Q_{\\chi^{3}}", + "83641282d51b989a.png": "a_{ij}=I(f_{i};f_{j})", + "83670f4015f4d090.png": "R=Z_{p}[x]/\\langle f\\rangle", + "836e96f37d440c4d.png": "hu", + "83883e4128f37245.png": "\\langle.,.\\rangle", + "838df2460eeee467.png": "\\frac{\\partial^{2}z}{\\partial t^{2}}", + "83904adb7873305f.png": "R_{0,1}=2.405", + "83944399b806835d.png": "[\\begin{matrix}-1\\\\ 1\\end{matrix}]", + "8399a8c1a594cfa4.png": "S=[\\begin{matrix}I&0\\\\ 0&-I\\end{matrix}]", + "839f3ce427280d2b.png": "2^{10/12}=\\sqrt[6]{32}", + "83a2f421444a32fd.png": "D=\\prod_{n=1}^{\\infty}Z/2Z", + "83a92b7cfd250050.png": "(\\begin{matrix}1&1\\\\ -a&-c\\end{matrix})", + "83afdafbf8675bc2.png": "f=f_{0}(1+\\frac{v}{c})", + "83b16d5a56fd2dc0.png": "n=\\frac{i-r}{||i-r||}", + "83b2d391d3928771.png": "cos\\Phi_{r}\\rightarrow\\sqrt{\\frac{r}{2M}}", + "83b62ab09b440259.png": "\\{\\begin{matrix}3\\\\ 3\\end{matrix}\\}", + "83c481da46494526.png": "K((T_{n}))", + "83c6ff3f549fd817.png": "A=(\\begin{matrix}a&b\\\\ c&d\\\\ \\end{matrix})", + "83ca06ba7ee443e5.png": "1:\\sqrt{\\varphi}:\\varphi", + "83ca8171d2ee5827.png": "-\\frac{3}{2}\\pi0", + "86841887d026bddd.png": "\\sqrt[3]{x}=\\sqrt[3]{r}exp(\\frac{1}{3}i\\theta)", + "868c270034210d3f.png": "E>V^{1+\\epsilon}", + "869325542a73b144.png": "\\hat{f}(I)", + "86961e640d1993a4.png": "w=\\sqrt{1-\\frac{U}{E}}", + "86a1780bd9bb33d6.png": "(\\begin{matrix}p\\\\ n\\end{matrix})", + "86a5959afb623c61.png": "g(x)=\\int_{0}^{x}f(t)dt", + "86a6cfa751fa6288.png": "D(f)\\mapsto M[f^{-1}]", + "86affd56129c5424.png": "I\\frac{d^{2}\\theta}{dt^{2}}=N", + "86b2bb60b52c21de.png": "K_{k}(\\tilde{M})", + "86b3cfcaa736a853.png": "\\hat{f}(k,y)=C(k)F(k,y)", + "86b3dc532c648574.png": "\\mathbb{Q}:X\\notin\\mathbb{N}", + "86b5adb9464108da.png": "-\\frac{p\\dot{r}}{r^{2}}=-\\epsilon sin\\theta\\dot{\\theta}", + "86b66ecb6df1a2e4.png": "\\hat{e}_{z}", + "86b9c89fd0191b9f.png": "w_{z}^{\\psi}", + "86bb0e7c0b2bb66f.png": "\\sqrt{X}", + "86bfd94229311625.png": "X", + "86cdb5ca54a302fd.png": "\\int\\frac{dQ}{T}=0", + "86ce0dfd478c52eb.png": "\\{\\begin{matrix}5\\\\ 5/2\\end{matrix}\\}", + "86ce7c86fcbf233e.png": "\\frac{\\omega_{1}}{\\omega_{2}}\\notin\\mathbb{R}", + "86ce9d4b4357c12e.png": "F(x)=1-\\alpha e^{x\\Theta}1", + "86d04eeaf75544ba.png": "(\\begin{matrix}n\\\\ m\\end{matrix})", + "86d9529a3e8628d5.png": "\\overline{Q}=0", + "86d9924b3f673de0.png": "f^{*}(x)=e^{\\frac{xf^{\\prime}(x)}{f(x)}}", + "86dbe2ebca324ad1.png": "m=\\gamma^{0}\\hat{H}_{0}+\\gamma^{j}p_{j}", + "86ddcb9cabed7cfe.png": "\\sqrt{\\varphi}", + "86e1af2a43ce8d5d.png": "\\underline{T}(t)=\\frac{d\\gamma}{dt}", + "86e5fb9dccaeb032.png": "lim_{y\\rightarrow0}g^{\\prime}(y)=-\\infty", + "86efb1b2c17e3780.png": "Odd((\\phi-1)*2^{w})", + "86f2dd56973d40c2.png": "\\sqrt{t}", + "86f3369ab047d45d.png": "dim\\hat{R}=dimR", + "86f410cf2fa0426e.png": "\\Delta_{r}G>0", + "86f4bbb60ee88387.png": "Kx_{i}=\\lambda_{i}Mx_{i}(1)", + "86f5a8ad50e57047.png": "\\alpha=1/\\sqrt{\\beta_{c}}", + "86fab94965182ff8.png": "\\frac{d^{2}u}{dt^{2}}=\\frac{\\Omega^{2}}{4}\\frac{d^{2}u}{d\\xi^{2}}(2)", + "86fb3cee64b99033.png": "U_{sp}(s^{*}(p),p)<0", + "8700f88add649641.png": "\\omega_{1}\\propto\\vec{d}\\cdot\\vec{E}\\hbar", + "8701ae5551a98cd9.png": "\\frac{dC_{U}}{dC_{W}}", + "8702072b42445d0d.png": "\\int Fdx", + "87083f051831f5bd.png": "\\nu=0,\\pm1,\\pm3,\\pm4", + "870ec23dd06cb6ea.png": "0\\le[f]", + "871614111c904a17.png": "y_{1i}-y_{0i}=\\beta_{i}", + "871a53ef0a3d636b.png": "\\sigma|_{[v_{0},...,v_{q}]}", + "871ca91e3837a3f1.png": "K_{-}=Ran(A-i)^{\\perp}", + "871d614e05cb57dd.png": "(\\begin{matrix}0&1\\\\ 0&0\\end{matrix})", + "871def4569bdf7b4.png": "B_{C}\\approx\\frac{1}{T_{M}}", + "87200c0290a6ff71.png": "4^{-N}(\\begin{matrix}2N\\\\ N\\end{matrix})\\approx\\frac{1}{\\sqrt{\\pi N}}", + "8721afb82730155a.png": "\\hat{\\rho}", + "8726aa32137c71a3.png": "\\int_{X}p(x)dx=1", + "872dc1fbb7481fb0.png": "\\overline{H}=G\\cdot exp\\overline{C}", + "873023d161b51217.png": "0=E\\{(\\hat{x}-x)y\\}", + "8731edada640c4e9.png": "\\sum|f(b_{k}^{\\prime})-f(a_{k}^{\\prime})|<\\epsilon", + "8735e880d3fa2c23.png": "(\\begin{matrix}p+q-1\\\\ p-1\\end{matrix})-(\\begin{matrix}p+q-1\\\\ p\\end{matrix})", + "8738d646f6e22f39.png": "(\\begin{matrix}n\\\\ 1\\end{matrix})_{F}=(\\begin{matrix}n\\\\ n-1\\end{matrix})_{F}=F_{n}", + "873c4cff2e6cfe2b.png": "R_{(2,20,0.05)}=3.75", + "87443c104d0a8b57.png": "3^{(\\begin{matrix}n\\\\ 2\\end{matrix})}", + "8747ae86d27ca2e7.png": "\\pi_{i}B(S^{-1}S)", + "87484ad2d7166165.png": "\\int f(x)dx", + "874975f495d5f976.png": "1+\\sqrt{2(1-\\frac{1}{k})}", + "874b859baf2d7b4b.png": "\\hat{w}_{i}^{\\prime}", + "874c39ca70e1eb93.png": "{\\omega^{\\hat{m}}}_{\\hat{n}}", + "874db995a76c20a8.png": "n!=n!!\\times(n-1)!!", + "874fddeeb0f2f5d0.png": "\\int_{-3}^{0}(3)dx", + "8752c4174aaafae1.png": "\\sqrt{2t}", + "8757b7e95f053649.png": "\\lambda=\\sqrt{2}\\sigma", + "8757cae4b7a88342.png": "\\hat{u}_{t}", + "875815d7edd8143e.png": "[\\begin{matrix}x\\\\ y\\end{matrix}]", + "875e5797a90d433b.png": "M\\le n0", + "878c671a6b751c65.png": "E(B)=VF(B)V^{*}", + "878fde4564759a0f.png": "(\\begin{matrix}n-1\\\\ k\\end{matrix})", + "8792c93efa332864.png": "Odd((\\phi-1)*2^{w})", + "8796e108e285a16a.png": "\\frac{dX}{dt}=AX", + "879f0079cf690c3e.png": "\\Delta T(t)=\\Delta T_{0}e^{-t/\\tau}", + "87a32d507765a7d6.png": "\\hat{q}=2^{-1/2}(\\hat{a}^{\\dagger}+\\hat{a})", + "87aaeebf77636d4a.png": "r=\\frac{1}{2}\\sqrt{ab}", + "87ab2b32d21c0c33.png": "\\sqrt{nN}", + "87ac3e4f4f3adf9f.png": "\\frac{d^{k}f}{dx^{k}}(x)=0", + "87af2553698f03b2.png": "\\overline{X}_{1}", + "87b30372bd6e5e0a.png": "(\\begin{matrix}n\\\\ 2k\\end{matrix})", + "87b35ddd4a4b0add.png": "\\frac{\\partial U}{\\partial S}=T", + "87b5de84aa41ff1e.png": "n^{\\underline{k}}=\\frac{n!}{(n-k)!}", + "87ba6053b551a2ee.png": "(S\\cdot X,Y)_{\\sigma}", + "87bc2cfe9654126f.png": "\\Phi(q,\\overline{q})=4loglog|q|^{-2}", + "87bd2770414e2354.png": "\\sum_{k=1}^{\\infty}(\\begin{matrix}\\alpha\\\\ k\\end{matrix})kx^{k-1}", + "87bd9a06293bc1ce.png": "\\overline{w^{\\prime}\\theta_{v}^{\\prime}}", + "87be5be467554ca5.png": "v_{1}=(\\begin{matrix}1\\\\ 0\\end{matrix})", + "87c3d7628795f8f2.png": "(\\begin{matrix}v&0\\cdot\\cdot\\cdot0\\end{matrix})", + "87c4de5f76795851.png": "V^{*}(a\\otimes h)=\\Phi(a)h", + "87c5b2d21f8d9b41.png": "ae", + "87c71902556d9531.png": "\\frac{n}{2\\pi}sin\\frac{2\\pi}{n}", + "87cd5d950ab8c3ec.png": "-1/\\phi", + "87d3b83f2d191b94.png": "\\epsilon=2\\nu\\langle E_{ij}E_{ij}\\rangle", + "87d86d4f915abb12.png": "S=-mc^{2}\\int_{C}d\\tau", + "87d94a7cc4ccdd93.png": "v\\notin C", + "87e0535a692bb089.png": "VM(\\mu,\\overline{R}N\\kappa)", + "87e493840232a873.png": "|\\frac{\\partial S}{\\partial x}|\\ll1", + "87e5eb3c54875a5a.png": "-T\\frac{\\partial^{2}f}{\\partial T^{2}}", + "87e82e6e1ec1d350.png": "\\hat{t}", + "87eee6c462e3afdf.png": "10^{10^{10,000,000}}", + "87eef9e50199d906.png": "(.)^{*}", + "87f534940726475b.png": "n\\ge\\frac{1+\\sqrt{4m}}{2}", + "87fdf1f3f029b467.png": "G=U(1)", + "87fec9dff2dd7ec4.png": "\\int x^{2}d(cosx)", + "88012a4ae36ac3ee.png": "\\tilde{w}", + "8805d52d885940e8.png": "\\overline{P}_{k}=\\frac{1}{2}(1-\\hat{k})", + "8807ad896ed13cab.png": "\\int_{0}^{1}p(x)dx", + "8808872a2d8a4928.png": "\\infty k\\delta(s)\\hat{z}", + "880ad325cf706b05.png": "\\int_{\\Omega}u_{j}u_{j}=1", + "880de232ab52078d.png": "(S,V,\\{N_{j}\\})", + "881275cca1f4cbc3.png": "\\frac{dF}{dL}", + "88131bc0a053098a.png": "14\\sqrt{x}+|15|=|71|", + "8819651ebd48f138.png": "(\\begin{matrix}m\\\\ 2\\end{matrix})", + "881d024f5e0b1e71.png": "f^{\\#}(\\delta_{p}^{v})=\\delta_{f(p)}^{df_{p}(v)}", + "881f559a2e5948e5.png": "\\notin C", + "88281abcdea6a34f.png": "\\beta=\\sqrt{\\frac{m}{r}}", + "8828cf72e7d3a3d4.png": "\\tilde{D}_{8}", + "88299ebe4c86831f.png": "E[\\epsilon_{n}\\epsilon_{i}]=\\sigma_{\\epsilon}^{2}", + "882aa032aa2993c5.png": "\\mu_{ab}^{(c)}(t)=0", + "882c9b83ba6f3aec.png": "\\frac{\\partial^{2}C}{\\partial S^{2}}", + "8833a399dcd6af74.png": "(\\nabla_{X}J)X=0", + "88451251cfebeae7.png": "\\tilde{w}_{i}", + "8846484bf59bcfc2.png": "\\mathbb{Q}:X\\notin\\mathbb{N}", + "8849a8c0876583dd.png": "1-\\frac{10^{3}}{11^{3}}=\\frac{331}{1331}", + "884d80bfc74f9942.png": "Q(\\theta^{(t)}|\\theta^{(t)})", + "8851ee3e3008d1dd.png": "15", + "8857ad151504ec1f.png": "p=\\prod_{i=1}^{n}(1-\\frac{i}{k})", + "885de566012a0683.png": "=\\frac{v_{1}^{2}+v_{2}^{2}}{2v_{1}v_{2}}", + "885f3ddd8b4bc948.png": "(\\begin{matrix}1&4\\\\ 3&-1\\\\ 2&1\\\\ \\end{matrix})", + "88644d9b57a85389.png": "A", + "886dace66ebe54bc.png": "\\tilde{u}=[u,u^{\\prime},u^{\\prime\\prime},...]^{T}", + "887387e5238f038b.png": "e^{W(z)}=z/W(z)", + "887d56f002e2fe8c.png": "D=2w_{0}\\simeq\\frac{4\\lambda}{\\pi\\Theta_{div}}", + "888055c6b633661e.png": "min_{x\\in R}max_{y\\in R}\\{x^{2}-y^{2}\\}", + "888529e00f6e8a5b.png": "OD", + "8885dff08be91819.png": "\\beta=\\omega\\sqrt{LC}", + "88863c00d50d431f.png": "\\Psi(z_{u_{1}}...z_{u_{i}})", + "8888ac88ff936523.png": "\\varphi(-r)=i\\sqrt{r}", + "88ab31d4b53e1228.png": "a_{2,n}=\\sum_{k_{1}=1}^{n}\\sum_{k_{2}=1}^{k_{1}}k_{2}", + "88ac134d0c57e1c6.png": "lim_{t\\rightarrow\\infty}\\overline{x}(t)", + "88b0e26eccd4b0f1.png": "\\overline{H}(y^{n}|x^{n})", + "88b5f213a7296e46.png": "\\sqrt{\\frac{10}{63}}", + "88b80c959f29db51.png": "A=\\int2\\pi R(s)ds", + "88b983ae3078b3eb.png": "\\frac{\\partial f_{k}}{\\partial x_{j}}", + "88bf8431c9f277e6.png": "(\\nabla^{2}+k_{0}^{2}n^{2})\\psi=0", + "88c00065f3699267.png": "{F^{\\epsilon}}^{d}", + "88c00973d498a10b.png": "\\nabla_{t}f(x^{*}(t),t)", + "88cb0991f483e490.png": "Y_{ij}=\\mu_{j}+\\alpha_{i}+\\epsilon_{ij}", + "88ccd4c943964bbe.png": "\\hat{n}_{i}", + "88d7c03f935bf22d.png": "E_{k-1}e^{X_{k}}=Ee^{X_{k}}", + "88da484cff80696b.png": "(8d", + "88dbcb03d29e30a5.png": "4\\times(\\begin{matrix}6\\\\ 2\\end{matrix})", + "88dff2416b6b7ac6.png": "P_{x}[X_{0}=x]=1", + "88e6d1c2006eff04.png": "\\psi=\\tilde{\\psi}", + "88ebb57725cda674.png": "k_{7}^{i}", + "88ebf951bafb6be0.png": "=\\frac{(12)^{2}}{(4)^{1}(2)^{3}}", + "88edf83a8b1ae084.png": "\\tilde{V}_{i}^{b}", + "88f900936796ce83.png": "\\overline{lim}", + "8900828f2824d0de.png": "\\int y(t)dt", + "8905b18f69b9fff2.png": "\\int x\\cdot dx", + "8908b86210ee25f8.png": "s\\in\\alpha,t\\notin\\gamma", + "89094a1b21be4651.png": "\\frac{\\partial}{\\partial y_{1}}=X", + "89096f44198aa2dc.png": "Q=\\int_{R}q|\\psi(r)|^{2}d^{3}r", + "890a2a2895452f55.png": "\\psi_{BL,m}(t)", + "890d2f0c5823a962.png": "[\\begin{matrix}3&4&4\\\\ 4&5\\\\ 6&7\\end{matrix}]", + "890e31d8c8d814f9.png": "\\sum_{k=0}^{n}(\\begin{matrix}n\\\\ k\\end{matrix})^{2}=(\\begin{matrix}2n\\\\ n\\end{matrix})", + "890f71cf816e16bd.png": "2+2\\sqrt{2}", + "8911d6eb60961d52.png": "\\hat{d}(n)", + "8912cd971a4e2544.png": "(1\\pm i)/\\sqrt{2}", + "8913177f364fc596.png": "E_{i}\\frac{x^{i}}{i!}", + "89149f9ddab003e9.png": "q(e", + "8915b3d51722f5fb.png": "R=\\mu_{1}+\\sqrt{S_{1}}X", + "89210e08bed2e1d8.png": "X(\\omega)=tri(\\frac{\\omega}{2\\pi W})", + "8922137aefc69c80.png": "(\\begin{matrix}u&0\\\\ az&u\\end{matrix})", + "89241f2776bdfa25.png": "(10^{n}-1)*7/9", + "89280a64ac0d99d6.png": "[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "892bcb1bff85a019.png": "P^{(k)}=\\sum_{i=1}^{k}U^{(n-i)}", + "892f77868a557e2b.png": "\\{K_{AB},A\\}_{K_{BS}}", + "89321f7e18e33acc.png": "x^{a}lnx=\\frac{lnx}{x^{-a}}", + "89374cf0092fe1cf.png": "q=\\hat{q}", + "8939fdec7a50b862.png": "1.3\\frac{a}{d}\\sqrt{n}", + "8944c3887c1d616b.png": "\\underline{l}", + "8947aceee3e2f48b.png": "k_{x^{b}}", + "8948bfa57f087b4f.png": "(\\epsilon_{i})\\in\\{-1,1\\}^{\\infty}", + "89499e0e3698cacb.png": "\\hat{K}(n)", + "894a5c9db8625384.png": "\\sqrt{u_{x}^{2}+u_{y}^{2}}=c", + "894c1063bdde8894.png": "{M^{\\sigma}}^{\\delta}", + "895c4e3354a4ca5b.png": "2\\sqrt{1-\\frac{x^{2}}{4}}+2", + "89677fb7fc71ef1b.png": "\\frac{\\partial L}{\\partial\\dot{x}}", + "8970428a7e625c53.png": "q<2^{160}", + "897483cd2a370581.png": "\\overline{I}", + "897d2a046b7d7280.png": "(1-G)", + "897e36b1e149d494.png": "C(X,R)", + "8980669922519c75.png": "W=\\int P(V)dV", + "8980ee95dca4dd18.png": "(A-a),B", + "8984286c43fe487d.png": "z_{M}=\\frac{N}{I_{M}}=\\frac{N_{m}}{I_{Mm}}", + "898f3b2e43bec9e2.png": "\\int f^{+}-\\int f^{-}", + "89915fc529b2ad12.png": "\\tilde{w}", + "899996d308d9c6ce.png": "bf(m\\tilde{T})", + "89a5c596c42cf3ac.png": "c", + "89aeebbc10e9270c.png": "\\frac{-1}{ln(1-p)}\\frac{p}{1-p}", + "89b05646b885f0d8.png": "\\partial_{t}L=\\frac{1}{2}\\nabla^{2}L", + "89b3db32777b1ceb.png": "n=\\prod_{i=1}^{r}p_{i}^{k_{i}}", + "89bc8d8b7c379f49.png": "2x-5+\\frac{15}{2x+1}", + "89c31596e1f9fb38.png": "B=\\int_{0}^{1}L(X)dX", + "89c3339a3ebc6313.png": "a,\\tilde{a}", + "89c405859af8bda0.png": "S_{c}=\\frac{Q}{h_{0}-h}", + "89c4d1aecaf9a15e.png": "15*(\\begin{matrix}66\\\\ 8\\end{matrix})", + "89ca0b96584132cf.png": "z=sqrt((-1/3)^{2}-1)", + "89cdb7377a695e3f.png": "(\\pm1/sin\\alpha,0)", + "89d3161b169f2cd6.png": "(H\\eta)_{X}=H\\eta_{X}", + "89d3ea27d03efe06.png": "\\frac{dt}{dr}=2r", + "89d82dd7091df67d.png": "\\tilde{Z}[0]", + "89dcfad05d3ef30a.png": "\\frac{EQ}{EQ^{\\prime}}=\\frac{ES}{ES^{\\prime}}", + "89e01be54c48cce8.png": "\\int e^{x}dx=e^{x}+C", + "89e160ce704ac275.png": "y=(\\begin{matrix}v\\\\ u\\\\ p\\end{matrix})", + "89e4094b5d08b593.png": "\\frac{dV_{r}}{dt}", + "89e4cb4f2d03d226.png": "O(|w_{k}|^{2})", + "89e73580851ba1bb.png": "N_{\\alpha}^{l}", + "89e91ed0848dabd8.png": "t=\\frac{d}{dx}", + "89f0c503c2cba7bc.png": "0\\notin\\Phi", + "89f9c9c5f0ea45cb.png": "\\frac{\\pi}{3\\sqrt{3}}", + "89fc9659f1008bb6.png": "\\hat{3}", + "8a0249f749b0bb90.png": "t=\\frac{d}{v}", + "8a02b5439df0418b.png": "\\varphi_{cb}(a)=a^{b-c}", + "8a0e619fb1951b38.png": "\\Lambda_{(N)}^{2}=C_{KL}N_{K}N_{L}", + "8a0efbca00745300.png": "\\int_{\\Omega}f(x)dx", + "8a1009adadc39781.png": "\\sqrt{x-1}+\\sqrt{x}", + "8a14c9fed2060ec4.png": "K_{h_{\\lambda}}(X_{0},X)", + "8a14caa1f830fd2e.png": "\\frac{dx}{dt}=r+x^{2}", + "8a15821f9dcae67b.png": "\\tilde{Y_{k}}", + "8a16940d86b15074.png": "x\\notin x", + "8a20f72b10cb7d57.png": "Set^{T}", + "8a20fa5bc311e97d.png": "\\simeq-79.0", + "8a2425608cb08e30.png": "sup_{|z|<1}|\\mu(z)|<1.", + "8a24cdd3691a0d1c.png": "\\tilde{K}(p;T)=e^{-Tp^{2}/2}", + "8a2585e82a3ba86e.png": "+j1.14", + "8a297b7dbf760d7d.png": "\\Delta_{2}f_{\\lambda}=(\\lambda^{2}+\\frac{1}{4})f_{\\lambda}", + "8a2d4dd8e97768c0.png": "(\\Omega^{-1}-1)", + "8a35b04acbd67fa9.png": "\\frac{(O_{1}-\\mu)^{2}}{\\sigma^{2}}", + "8a35fb10634efb65.png": "\\varphi", + "8a37bf2141b84065.png": "S=\\sum_{i=1}^{g}n_{i}(\\overline{r_{i}}-\\overline{r})^{2}", + "8a3d0623ccbb773e.png": "\\frac{(PV)}{N}=kT=E_{k}", + "8a4ae5c440349aa5.png": "\\dot{y}=\\frac{dy}{dt}", + "8a4fdf3d61841e78.png": "f\\sim f_{0}+t(f_{1}-f_{0})", + "8a5095db1eeb4a0b.png": "(\\begin{matrix}1&N\\\\ 1&1\\end{matrix})", + "8a53c90a5785475b.png": "J_{c}\\propto T_{c}^{\\alpha+1}", + "8a5500012a93a957.png": "A=4\\pi r^{2}=\\pi d^{2}", + "8a5569c1125a23ec.png": "\\hat{m}_{-}", + "8a597bb1fc61be98.png": "\\Psi_{H}(x_{i},\\vec{k}_{\\perp},\\lambda_{i})", + "8a5b887df7ca3315.png": "\\{|g,n\\rangle,|e,n\\rangle\\}", + "8a5cf81b1099015e.png": "x=[A]y", + "8a609f535c9e43c3.png": "G=H-TS_{int}", + "8a651407385ba0fd.png": "\\hat{x}_{1}", + "8a65a47468a61568.png": "\\hat{B}_{i}", + "8a6fc58e39afdfde.png": "(\\hat{b})", + "8a70899097c234d3.png": "\\tilde{O}(log^{5}q)", + "8a808a0701cf9505.png": "\\overline{C}(8)", + "8a865090b05b0e8d.png": "3^{(\\begin{matrix}n\\\\ 2\\end{matrix})}", + "8a8ede1362baabd0.png": "P(X=x)", + "8a924c1f0fb5fc94.png": "V=_{def}\\{x|set(x)\\}", + "8a94b4781c58e430.png": "1/\\sqrt{2}(\\pm1,\\pm1,0)", + "8a95b9b7489bdbb1.png": "E(k)=\\frac{\\hbar^{2}k^{2}}{2m^{*}}", + "8a9994164058cbc2.png": "\\{x_{n}=cos(n)\\}_{n\\ge1}", + "8a9caf3eba2010ba.png": "\\sum_{j=0}^{n}(-1)^{j}(\\begin{matrix}n\\\\ j\\end{matrix})P(j)=0", + "8aa04602eba82de0.png": "\\mu_{i}\\nu_{j}>0", + "8aa97fa39378a3f9.png": "J_{0}(u_{n}r)", + "8aaa49e70564c93c.png": "2(\\sqrt{xy}-\\frac{x+y}{2})", + "8aab04df42f89eb0.png": "\\frac{n^{2}-3n+4}{2}", + "8ab12836965d6897.png": "T_{m}\\mapsto(T_{n})^{n/m}", + "8ab5722a62b8716d.png": "\\int e^{x}cosxdx", + "8ab83d0bc622394c.png": "Z^{0}\\rightarrow\\overline{b}b", + "8abe7cf4af43cb0a.png": "I_{C}=C\\frac{dV_{in}}{dt}", + "8abed432807dfa0c.png": "\\omega\\in X^{-1}((u,v])", + "8acad3e378a1b8cb.png": "30<\\epsilon_{r}<50", + "8acd238aca335986.png": "\\partial^{2}f/\\partial x^{2}", + "8acde10f3da7ca91.png": "R/P_{i}^{a_{i}}", + "8ad13493f2c40b3c.png": "\\frac{-e^{-ikr}}{4\\pi r}", + "8ad4dcab45343547.png": "\\overline{m_{1}}", + "8ad514fa38583873.png": "(\\sqrt{1-x^{2}},-x)", + "8ad8fd34caa6720a.png": "F_{D}=\\frac{3\\pi\\eta Vd}{C_{c}}", + "8adaad922d4a62de.png": "[A,\\overline{Q}]=\\frac{1}{2}\\overline{Q}", + "8adedb67b291bff2.png": "(\\begin{matrix}p+q\\\\ q\\end{matrix})", + "8ae48fbbec6ec1f9.png": "L=\\mathbb{Q}(\\sqrt{d})", + "8af17d0e4ff315d4.png": "\\hat{Z_{b}}", + "8af1885debfb22bc.png": "G^{\\prime}=(V,E_{L}^{\\prime},s,t)", + "8af35876f65222a3.png": "\\tilde{n}", + "8af612c5bab0bda7.png": "\\hat{g}(f)", + "8afb3fce88adbea3.png": "f^{\\prime}(\\overline{x})", + "8afb9b8f4637ca5e.png": "1:\\frac{1+\\sqrt{5}}{2}", + "8afd3c043338ee46.png": "\\sum_{j=0}^{m-1}(d+1-k_{j})", + "8afdf0fcf0ebfad0.png": "\\frac{d^{n}Y}{dx^{n}}", + "8b00c4b0d01a98e2.png": "\\sqrt{-b}", + "8b02751d1781d8d3.png": "v=v^{i}(x)\\partial/\\partial x^{i}", + "8b05193031639e3d.png": "+j1.14", + "8b1c6ab3a76763dd.png": "c\\notin A", + "8b1c97eaf37215eb.png": "\\int_{0}^{x}1dt=x", + "8b217f6f72fe2b73.png": "|1-\\lambda R(\\underline{k},\\omega)|<1", + "8b27fc8364e4c7e7.png": "3(x+1)=3x+3", + "8b2afe789a5b4a8a.png": "\\int\\sqrt{1+1/x^{2}}dx", + "8b2c8f7ac1bd5d2c.png": "\\langle x,y|x^{2}=y^{3}\\rangle", + "8b2e3dcdb54e15d4.png": "\\lambda=\\frac{h}{mv}\\sqrt{1-\\frac{v^{2}}{c^{2}}}", + "8b3165ba39679299.png": "F(a)=\\frac{xa^{2}}{2}", + "8b31d3e15c6a1570.png": "\\sqrt[n]{x}=exp(\\frac{1}{n}lnx)", + "8b33c20ac8efdb88.png": "(\\begin{matrix}1&0\\\\ -\\frac{1}{f}&1\\end{matrix})", + "8b35d2a9d3467e7f.png": "b=[\\begin{matrix}11\\\\ 13\\end{matrix}]", + "8b39097bf7c78f1a.png": "|\\omega_{i}|=q^{1/2}", + "8b3bb722c72dde2b.png": "\\int f(x,y)dx", + "8b3e40f82adf6426.png": "rect(\\frac{t-u}{\\Delta_{t}})", + "8b42148da068b687.png": "\\int sin(cos(x))dx", + "8b45d2250c1e684f.png": "=(10^{1.0})^{(3/2)}", + "8b491c9446414ed7.png": "u:=m(S\\otimes1)R^{21}", + "8b4b20a9713a45b7.png": "\\tilde{v}_{ij}", + "8b59286d87ca4172.png": "[\\begin{matrix}2&2&4\\\\ 3&5\\\\ 6&6\\end{matrix}]", + "8b5bc06f4699530a.png": "\\varphi_{i}(x)=(x,i)", + "8b5c6bce71de52d7.png": "A^{?}=A+1", + "8b658364fe291e04.png": "f(z_{0}(1-\\epsilon))", + "8b6c4b81d7b89ebf.png": "(\\begin{matrix}n\\\\ 2\\end{matrix})p", + "8b72bded61eaecb9.png": "U((n+1)\\Delta t)", + "8b779820e43d9a6a.png": "\\frac{dI}{d\\alpha}=-\\pi", + "8b7882d7283fffce.png": "(\\begin{matrix}p\\\\ 1\\end{matrix})", + "8b7f64bb6b7a5980.png": "(\\alpha,\\beta,id)", + "8b816ba8470afe33.png": "G_{n}(x_{1},...,,x_{n})", + "8b86fbac28282d07.png": "T(R)=T_{eff}", + "8b97477080ac3660.png": "2^{m},1,2^{m}", + "8b9756e97c234767.png": "2\\frac{d+1}{\\pi}E(\\frac{2\\sqrt{d}}{d+1})", + "8b9db092a604cbd1.png": "\\int_{b}^{a}|f(x)|dx", + "8ba420589854fb6c.png": "\\eta_{c}=(4/3)\\pi r^{3}N/L^{3}", + "8bc4f7b8fe26571d.png": "\\dot{\\gamma}=\\frac{V}{H}", + "8bcbc6cfb6a707d3.png": "\\tilde{S}_{i}", + "8bd4fbfd750611e2.png": "\\hat{F}(i)", + "8bdda13d856d22ad.png": "\\frac{dF}{dL}", + "8bde84c160c7a56a.png": "(a\\times b)mod9", + "8be3a971cb46025c.png": "\\tilde{\\mu}", + "8be535a672310597.png": "F[X,Y]/(X^{2}-Y^{2})", + "8be60096cde877e8.png": "2gq^{1/2}=2g\\sqrt{q}", + "8be62946232f1653.png": "A+H_{2}O\\rightarrow B", + "8be735886f5b7d76.png": "\\tilde{H}_{\\infty}(W|E)\\ge m", + "8be7569272380579.png": "\\frac{dF}{dx}+2xF=1", + "8be887fa1e98d8e6.png": "a\\times b=-I(a\\wedge b)", + "8bf7315b72ed801b.png": "\\frac{1}{x}\\times\\frac{1}{y}=\\frac{1}{xy}", + "8bf945f965e80752.png": "{(\\nu^{\\phi})}^{\\alpha}", + "8bfe046f5de40c76.png": "\\tilde{x}_{0}\\in\\tilde{M}", + "8c0016f821483d17.png": "\\hat{X_{a}}", + "8c0196f8be15f62e.png": "\\tilde{x}^{2}", + "8c04c39aae6537eb.png": "s\\{\\begin{matrix}5\\\\ 3\\end{matrix}\\}", + "8c09df2497ad190f.png": "\\hat{S}(n)", + "8c0aca38fcfbf443.png": "\\frac{\\partial\\eta}{\\partial y}>0", + "8c0f2f7130679abe.png": "\\hat{e}(s_{0})", + "8c0f9f0aa6933524.png": "E_{i}\\frac{x^{i}}{i!}", + "8c10464dd13dd664.png": "-\\frac{dN}{dt}=\\lambda N", + "8c1084f6bc26befa.png": "\\dot{p}(0)=-m\\omega^{2}x_{0}", + "8c1121061f3b3417.png": "\\{\\begin{matrix}3\\\\ 5\\end{matrix}\\}", + "8c1596b079cdfea2.png": "q_{y=0}=1-\\hat{y}", + "8c180e2d6e1d9240.png": "t_{i}=min(t_{i}^{U},L)", + "8c187b589ddc0fb1.png": "[\\begin{matrix}1&1\\\\ 0&1\\end{matrix}]", + "8c1a6efc6a1b97ae.png": "a_{1},a_{2},...,a_{n}\\in Z", + "8c1e4a1056f99b65.png": "\\hat{u}", + "8c1e50addabcd4c0.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "8c1e73179f2c65c6.png": "D(P_{max})=0", + "8c20ecb0369b70d0.png": "A^{k}=\\Sigma_{i=1}^{k}u_{i}\\sigma_{i}v_{i}^{\\top}", + "8c2361cf198a89e4.png": "\\gamma=i\\underline{k}^{*}", + "8c243878dd915a16.png": "\\hat{e}(s_{0})", + "8c2f2a8e185de6fc.png": "\\frac{\\partial H(x)}{\\partial x}B(x)", + "8c3054f0a6fd0d8d.png": "(Z_{1}/X_{1},Z_{1}/Y_{1})", + "8c309537ad4b2d5c.png": "\\omega=\\frac{d\\theta}{dt}", + "8c3388879746c7d4.png": "P\\cdot R\\cdot[1-T]/n", + "8c3ab173a93ea83b.png": "f(x)\\in B_{\\epsilon}(f(a))", + "8c3c5e9f4963a21e.png": "(\\begin{matrix}0&0\\\\ 0&1\\end{matrix})", + "8c471f0681b305dc.png": "\\int_{C}x^{2}dx", + "8c47af8ee896e620.png": "\\frac{\\partial v_{i}}{\\partial x_{i}}=0", + "8c4cccc8ab75e339.png": "m_{i}^{2}=p_{i}^{+}p_{i}^{-}-\\vec{p}_{\\perp i}^{2}", + "8c517864db90c724.png": "1+\\sqrt{366}\\approx20.13", + "8c51c3417df5a926.png": "\\sqrt{-0}=-0", + "8c5a8ac94eb6a350.png": "I(\\theta)=p_{i}(\\theta)q_{i}(\\theta)", + "8c62bce64b2ed269.png": "\\int_{-\\infty}^{\\infty}", + "8c679895ee9c67cf.png": "so(1,1)\\cong R", + "8c6af27fa7622c16.png": "\\frac{dF}{dx}", + "8c6cdea59aa6dd1d.png": "v_{it},i=1,...,d", + "8c6f7731ce5a408e.png": "\\int_{a}^{b}", + "8c7981d1b90495cd.png": "\\tilde{B}_{6}", + "8c7a1fb5c2f00eae.png": "\\Delta A=\\overline{D}", + "8c869dd9e511b2ad.png": "[\\begin{matrix}-1&1\\\\ 0&0\\end{matrix}]", + "8c897fef1f52c4e9.png": "\\frac{\\partial f}{\\partial y}(X,Y)=0", + "8c8b5dec7c0006d0.png": "f(x)=\\prod_{i<4}(x-x_{i})", + "8c9542f7ed031e04.png": "\\frac{\\partial C}{\\partial S}", + "8c97c6ef2ac3538c.png": "\\frac{\\partial Y}{\\partial K}", + "8c97f6de182d6c29.png": "b\\simeq\\frac{a^{2}-x}{2a}", + "8c9ef6f4afcf1f79.png": "[\\gamma^{\\mu},\\gamma^{\\nu}]_{+}=2g^{\\mu\\nu}", + "8ca11b7aebae012d.png": "T=\\frac{\\partial U}{\\partial S}", + "8ca316bc87644545.png": "\\hat{d}", + "8ca6a65a3cad8cc1.png": "d_{1,0}^{1}=\\frac{-sin\\theta}{\\sqrt{2}}", + "8caada13d612ad49.png": "\\frac{\\partial C}{\\partial t}", + "8cb007e37de59a91.png": "\\lambda^{-1}R_{x}^{-1}(n-1)", + "8cb0746fec4e0a84.png": "A=l^{2}+l\\sqrt{l^{2}+(2h)^{2}}", + "8cb0b1e2ef0767a2.png": "[a*]p\\equiv p\\wedge[a][a*]p", + "8cbbbf5a7c69963a.png": "[*,*]", + "8cbc459d860ce589.png": "C_{D}=\\frac{D}{\\frac{1}{2}\\rho AW^{2}}", + "8cc084477adfd298.png": "f=2^{\\sqrt{lgn}}", + "8cc34f9409442e9a.png": "1,2,3,5,8,13,...", + "8cc81e40ef16b3f6.png": "y(t)=\\int_{0}^{1}w(t,\\xi)d\\xi", + "8cca96b13adba2f4.png": "\\int dx=0", + "8ccb66fb47b4a440.png": "\\tilde{x}\\in F", + "8ccf1f45d343167e.png": "\\frac{d^{2}y}{dt^{2}}", + "8cde361dc0ad510d.png": "\\tilde{O}(log^{3}n))", + "8ce67d43c033324a.png": "(\\begin{matrix}2n\\\\ n\\end{matrix})", + "8ce7b876e175cbcb.png": ":\\hat{b}_{1}^{\\dagger}\\hat{b}_{2}\\hat{b}_{3}:=\\hat{b}_{1}^{\\dagger}\\hat{b}_{2}\\hat{b}_{3}", + "8ce7db372fc80fce.png": "\\int VdP", + "8cf2dce4450de161.png": "f_{t}=\\frac{\\sigma_{t}^{2}}{p_{g}q_{g}}", + "8cf4a112c0cf2230.png": "{R^{2}}_{323}=\\frac{-1+g^{2}}{r^{2}g^{2}}", + "8cf4e9e2474aa863.png": "\\alpha\\notin\\omega^{G}", + "8cfac7787ed379d2.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "8d0110247284b538.png": "\\omega_{\\mu}^{1}", + "8d05b6437e83c50d.png": "det[\\begin{matrix}1&-1\\\\ 1&2\\end{matrix}]=3\\ne0", + "8d0752b77a67e9ce.png": "u_{i}=v_{0}+w\\alpha^{i}R_{i}", + "8d0aa93063740de2.png": "S_{\\sqrt{3}}", + "8d26e153b4bf8e74.png": "\\beta=O(1/m)", + "8d2779817a0a2834.png": "0=E\\{(\\hat{x}-x)y\\}", + "8d2943079d10f998.png": "\\vec{t_{2}}\\langle s^{\\prime\\prime}\\rangle=\\vec{t_{2}}\\langle s^{\\prime}\\rangle", + "8d2e0fcd875513f5.png": "\\chi_{0.50}^{2}", + "8d2ec55b39a5a87b.png": "(R^{3})^{*}", + "8d359cb14a1c8ab0.png": "f_{\\beta}(t)=e^{-t^{\\beta(t)}}", + "8d371d5085ff93a1.png": "dS=\\frac{dQ}{T}", + "8d3ca960bc53a2a7.png": "\\psi_{1}\\equiv-\\frac{Ua^{3}}{4r^{2}}sin\\theta", + "8d46bb6b946989bd.png": "Q\\notin z", + "8d4ed5db3d3d9702.png": "\\frac{c}{(b-c)}=\\frac{a}{b}", + "8d55e6b2ea113180.png": "C=(\\begin{matrix}1&i\\\\ i&1\\end{matrix})", + "8d57651c9a9bcce8.png": "A^{k}(e_{1})", + "8d585ff101791281.png": "\\hat{\\zeta}", + "8d5a154a7cf0125d.png": "\\{1/n\\}_{n\\in N}", + "8d5f4537c5cff6fe.png": "sys^{2}\\le\\frac{2}{\\sqrt{3}}\\cdot area", + "8d5f74d237db2de5.png": "D_{xx}D_{yy}-D_{xy}^{2}", + "8d5f8e7020df7d75.png": "\\tau_{\\alpha}^{p}", + "8d6f8c0860b32e6d.png": "\\rho_{N_{1},N_{2}}=\\rho_{\\epsilon_{1},\\epsilon_{2}}", + "8d739cb8da99af75.png": "\\sqrt{\\phi}", + "8d78af5049e995bd.png": "\\frac{d\\rho}{dr}=-\\frac{\\rho(r)g(r)}{\\Phi(r)}", + "8d78fb216a629bc5.png": "cos(\\omega_{0}n)u[n]", + "8d7f8e06f1253019.png": "k=AT^{n}e^{-E_{a}/(RT)}", + "8d9beb1255283caf.png": "F_{X}^{-1}(u)", + "8da02971370878ad.png": "f_{P}:[l]\\mapsto[m]", + "8da70bf843a72f84.png": "s\\notin\\alpha,t\\notin\\gamma", + "8da7fd4e05b73cb3.png": "R_{ji}=N_{j}B_{ji}\\rho(\\nu)", + "8dac1d31949bc8f8.png": "f(x)-a^{2}(x)", + "8daf67f4935f76dc.png": "(\\begin{matrix}x&y\\\\ -y&x\\end{matrix})", + "8db603f524ca07db.png": "\\underline{P}(Cl_{1}^{\\le})=\\{x_{1},x_{5}\\}", + "8db810056562aa47.png": "v_{1}^{\\prime}=v_{1}-v_{0}", + "8dbba110082ec9df.png": "\\infty k\\delta(s)\\hat{z}", + "8dbee35db7256079.png": "x_{2}=b+\\sqrt{b^{2}-c}", + "8dc69449fe54b3b4.png": "H^{rot}=\\frac{1}{2}I\\omega^{2}=\\frac{L^{2}}{2I}", + "8dc8b90e4e871991.png": "\\overline{f}=\\hat{f}", + "8dc8c4ed55327b11.png": "||\\hat{y}||_{\\infty}\\le5in\\phi p^{1/m}\\}", + "8dcc3f8051ce0706.png": "(A+UCV)X=I", + "8dccf50caaf64561.png": "\\frac{d}{dx}(ln|x|)=\\frac{1}{x}", + "8dcf2b1910b68d72.png": "(\\begin{matrix}n\\\\ m\\end{matrix})", + "8dd01e76a28fce47.png": "(\\hat{b})", + "8dd7310016b09d18.png": "r=r(r,\\theta,t)=r\\hat{e}_{r}", + "8de26e41d7ec86ab.png": "W=\\alpha M\\tilde{Q^{c}}\\tilde{Q}", + "8df8a25e0aca9c07.png": "R_{i}=i,C_{i}=0.01i", + "8df951762ab96946.png": "\\overline{\\psi}=\\sum_{i}\\psi_{i}b^{i}", + "8dfe679b753ea941.png": "\\langle W,R,\\{D_{i}\\}_{i\\in I},\\Vdash\\rangle", + "8e00f1dff3eaf898.png": "\\tilde{y}=\\tilde{w}=h(\\tilde{X})-\\tilde{Y}", + "8e02032a35bf1d57.png": "P", + "8e0245165f93162d.png": "\\tilde{A}_{4}", + "8e03b65c18d2f11c.png": "d_{\\hat{K}}", + "8e090b54c34db763.png": "\\chi^{T}(A+I-J/C)\\chi", + "8e0a592665dd239f.png": "\\tilde{u}(x)", + "8e0a6921c4d46904.png": "\\int_{0}^{r}4\\pi u^{2}du", + "8e0da6841f6558de.png": "\\frac{1}{2}(z+1)", + "8e113a27822f4dc6.png": "X:=X+\\langle m_{i},\\hat{s}_{j}\\rangle", + "8e11b668d37effda.png": "4log_{2}n-4", + "8e1af94875deb5af.png": "\\Delta\\vec{F}=A\\Delta\\vec{p}", + "8e1cb2942383f5cd.png": "\\sqrt{2}+1", + "8e244c0981607855.png": "\\sqrt{R}", + "8e27128023de18f8.png": "\\int_{V}JdV=0", + "8e34b57f0794df43.png": "\\tilde{p}=\\frac{r}{r+k}", + "8e37d81726c7e706.png": "\\frac{df}{dz}=f", + "8e3abe0271f321b8.png": "|+\\rangle", + "8e3febd593748c80.png": "\\frac{1}{2}\\hbar\\omega_{q}", + "8e4537d144842089.png": "Inat(2+1)(2+1)", + "8e4c8d7c655d295b.png": "F_{X,Y}(x,y)", + "8e4ea40ad0d0b46d.png": "\\lambda_{g}^{m}", + "8e4f9debdbdd5cce.png": "(i\\cdot n)\\hat{f}(n)", + "8e533b94dfa1d641.png": "\\int_{1}^{3}(27-x^{3})dx", + "8e53531042cf0669.png": "E:=B^{G_{K}}", + "8e546b122ae998a8.png": "(1-C)(1+C)", + "8e634743f9e323d9.png": "\\frac{3}{5}(N_{p}+N_{n})^{2/3}", + "8e65e06c52a8fbed.png": "\\tilde{r}", + "8e6777e27b8604a0.png": "a(m)=\\alpha m+\\beta m^{3}", + "8e67c561fa7c6345.png": "(\\begin{matrix}1&1\\\\ -a&-c\\end{matrix})", + "8e6e8ef4ea19da60.png": "L=-\\tilde{F}\\dot{v}^{2}+2\\dot{v}\\dot{r}", + "8e7905b9f2b15642.png": "E[y]=\\mu=g^{-1}(\\eta)", + "8e79c7f93ffaf771.png": "\\prod_{i=n-r+1}^{n}i", + "8e8059b29ae355db.png": "\\sum_{b\\in B}l_{b}b\\mapsto\\sum_{b\\in B}l_{b}^{\\sigma}b", + "8e82bde4383d92ae.png": "\\hat{S}_{n}", + "8e8440adde9a7df7.png": "\\tilde{A}_{2}", + "8e882a4ecff304a0.png": "p(x)=\\prod_{i=1}^{m}p_{i}(x)", + "8e8e3c50f197656c.png": "Rv_{i}=\\tilde{\\lambda}_{i}v_{i}", + "8e8f584333d670a3.png": "(2^{r}+1)|(2^{k}+1)", + "8e968491a8825bad.png": "(b_{n}<0)", + "8e9d4579156de570.png": "f^{\\prime}(z)=\\frac{-e^{\\frac{1}{z}}}{z^{2}}", + "8eb7dc1e15d1eab8.png": "\\Delta_{0}logf=-Kf^{2}", + "8ebe3ce041ef1170.png": "\\tilde{E}^{a}", + "8ebeb56b36a024dc.png": "q^{-1}+O(q)", + "8ec4b637d857795e.png": "S^{\\prime\\prime}0", + "9031c143b99ee0fa.png": "v=\\sqrt{\\frac{T}{\\rho}}", + "9035267a876cc3cf.png": "\\alpha\\approx\\frac{at_{0}\\Delta_{SO}}{\\Delta_{BG}}", + "903587ee3df89cb7.png": "R=\\mu_{1}+\\sqrt{S_{1}}X", + "9038fc82edeb4dda.png": "(\\lambda x)^{*}=\\overline{\\lambda}x^{*}", + "903c1e4c12516fc8.png": "\\chi(F(n))=P(n)", + "903d093034e0b527.png": "\\pi^{2}\\approx227/23", + "90424dc32b34b9b6.png": "3(x+1)=3x+3", + "904799d1c1b95770.png": "\\overline{X}\\sim N(\\mu,\\sigma^{2}/n)", + "9047b55e021a4da8.png": "G\\overline{t}", + "904dfd5f36c93c43.png": "R=Z_{p}[x]/\\langle f\\rangle", + "9051d733442e9d8d.png": "\\tilde{t}_{j}", + "9053f5c47a8cbdaf.png": "\\int_{0}^{a}sinxdx", + "905979528630db3d.png": "\\frac{d^{3}}{dx^{3}}[x^{4}]=24x", + "905e1a07f278e0b0.png": "\\psi(\\epsilon_{\\Omega+1}+1)", + "905e9481f8e09339.png": "(+\\alpha,-\\alpha)", + "905f58bcbcde0479.png": "\\int_{0}^{T}wx(t)dt", + "906194e9b7f7ac0a.png": "s\\{\\begin{matrix}p\\\\ q\\end{matrix}\\}", + "9063049753f37e5e.png": "b_{n}=(-1)^{a_{n}}", + "90719b2cbdaba1d1.png": "\\Sigma_{12}\\Sigma_{22}^{-1}(a-\\mu_{2})", + "9074c559bb672460.png": "x\\in\\mathbb{R}^{n}", + "9078496ec31a29c7.png": "|pp^{\\prime}|\\le(2/s)|pq|", + "9084421c457ca5a7.png": "\\int dV|\\Psi|^{2}=N", + "9088d3402daf70a5.png": "\\underline{x}^{-k}", + "90897f43776512ec.png": "X=[\\begin{matrix}w+ix\\\\ y+iz\\end{matrix}]", + "9089fde17aa395a9.png": "v=\\sqrt{\\frac{2\\mu_{0}^{2}}{3\\lambda}}", + "908c96ed89ee7214.png": "|E(F_{q})|=q", + "90916eda8f97c586.png": "r(0)=r_{0}\\in R^{2N}", + "9096c1bd7c47eabe.png": "\\tilde{A}_{5}", + "90a0f5a40b6203de.png": "O(n^{4k-3})", + "90a996c0789a6e6c.png": "C_{\\alpha\\dot{\\alpha}}", + "90b69de1906f55b2.png": "\\overline{u^{\\prime}v^{\\prime}}", + "90bae819f398428e.png": "(x_{0}+1,y_{0})", + "90be23ecf4d784b3.png": "I_{S}[f_{S}]", + "90c1b43378a08bd9.png": "\\frac{d}{dt}f(\\gamma(t))|_{t=0}", + "90cb8ffe271689ac.png": "m=\\frac{y_{end}-y_{start}}{x_{end}-x_{start}}", + "90cc65ca07a101fa.png": "\\int_{-2}^{6}\\frac{dx}{x}", + "90d0bc8b417ce170.png": "e^{\\delta G}=\\prod_{evenl}e^{\\delta G^{[l]}}", + "90d44e01d946a468.png": "\\{\\begin{matrix}3\\\\ 5\\end{matrix}\\}", + "90d581b3599be99c.png": "P_{m}(C(Z))", + "90d80ce0c3f0bdc9.png": "\\sqrt{q}", + "90d8a0346f67e1ab.png": "\\Delta x^{\\prime}=\\Delta x/\\gamma", + "90daf8b4a3b1b4e5.png": "\\chi(\\tilde{M})=k\\cdot\\chi(M).", + "90eba2f8247c55a1.png": "[\\begin{matrix}1&1\\\\ 0&1\\end{matrix}]", + "90ef5c38f3b3e992.png": "(A^{T}A)^{-1}=Q", + "90f0f8c728169b32.png": "N=10^{a-bM}", + "90f208c88b2c3829.png": "\\hat{D_{B}}", + "90f30307a23d808e.png": "|n(x_{0}^{\\mu})\\rangle", + "90f8a062c342d42c.png": "h=2\\frac{dA}{dt}", + "90f934411df76df3.png": "\\Pi_{f}=1-e^{-BR}", + "90fa948413b3a1e9.png": "Rg(x):=g(-x)", + "90fb1de4236c3cc5.png": "g(n)=\\prod_{k=1}^{n}f(k)", + "90fc6669722fcae1.png": "\\frac{\\partial x}{\\partial u}", + "90fee3da18ef41c4.png": "\\hat{6}", + "91024025cf34e7c2.png": "[\\begin{matrix}1&0&-1\\\\ 0&0&0\\\\ -1&0&1\\end{matrix}]", + "910746f4e25c9ddc.png": "-1^{\\sqrt{2}}", + "9109a2fcfffbeee6.png": "QTcB=\\frac{QT}{\\sqrt{RR}}", + "910ef311f01e35d0.png": "V=\\frac{1}{2}(x_{1}^{2}+x_{2}^{2})", + "9110ad93858755df.png": ">z>", + "91171ab175c380ea.png": "\\int PdV+\\int VdP", + "911bbb78f26e2bf9.png": "(e^{\\pi})^{i}=-1", + "912005459f1fbc02.png": "\\frac{16}{64}=\\frac{16/}{6/4}=\\frac{1}{4}", + "9121eb64fdec6c75.png": "[\\begin{matrix}4&6\\\\ 3&5\\end{matrix}]", + "9122342576e285c3.png": "\\int_{0}^{1}f(x)v(x)dx", + "9125cce34d3816de.png": "\\hat{\\zeta}", + "9126dfc43779063a.png": "\\overline{n}_{4}", + "912a847e01a8a081.png": "|C_{G}(g)|", + "912fef89fa9dc12c.png": "\\frac{df}{dz}=g", + "913101b6a29a25d4.png": "p_{1}=p(x_{0}+\\Delta x)", + "9131e07a1af4d4bf.png": "\\tilde{E}^{a}", + "913471917719e558.png": "\\overline{X}_{2}", + "91372379bc1e2e20.png": "\\tilde{n}_{i}", + "91378725dbfd82f9.png": "\\int e^{-x^{2}}dx", + "913955796a1496bc.png": "(\\begin{matrix}14\\\\ 5\\end{matrix})=2002", + "913b12ef7027c4aa.png": "\\sigma^{z}=(\\begin{matrix}1&0\\\\ 0&-1\\end{matrix})", + "913d6945a42f77e0.png": "\\tilde{H}", + "914022e6521aeb22.png": "(\\begin{matrix}a&b\\\\ b&c\\end{matrix})", + "9144a5a2dd8f5514.png": "\\sum_{n=1}^{\\infty}n^{-\\frac{s}{2}}\\frac{s^{n}}{(-2)^{n}}", + "9145dae27ff7e18e.png": "\\int_{0}^{t_{1}}E(t)dt", + "9145f9a7f54682b4.png": "\\int x^{3}e^{x^{2}}dx", + "9147ce65562d340d.png": "\\frac{dx}{dt}=r\\pm x^{2}", + "914a0bb4a282f3c5.png": "\\hat{4}", + "914b4781337a9d74.png": "E[\\epsilon|X]=0", + "915414618b5f131a.png": "-e_{k}\\frac{1}{kh}asin\\theta", + "9156819fc6985dac.png": "\\int udu", + "9159d153c790d773.png": "C^{\\prime}\\supseteq C(\\alpha)", + "915a6c48f03b5bfc.png": "\\overline{S_{n}}=a\\mathbb{I}\\{S_{n}>a\\}", + "915e38950e3535e5.png": "\\hat{Z}", + "9162976af779fb3f.png": "(x+y+z)^{2}=1", + "9165672ac8e3e9fa.png": "\\tilde{h}(E)", + "91658021c1db13c9.png": "(\\begin{matrix}X\\\\ k\\end{matrix})", + "9166afd0396503df.png": "0,0,1,-1,0,\\cdot\\cdot\\cdot,0", + "916bff6c2e7419c2.png": "B_{\\rho}^{\\eta}", + "916cf461f377880a.png": "M_{J}\\sim\\rho^{\\frac{3}{2}(\\gamma-\\frac{4}{3})}", + "916f7a99626d747f.png": "\\tilde{z}", + "916f9d23b923686e.png": "[\\begin{matrix}1&2\\\\ 2&4\\\\ \\end{matrix}]\\sim[\\begin{matrix}1&2\\\\ 0&0\\\\ \\end{matrix}]", + "9170a1ff4a38ff28.png": "f(t,n)=\\sum_{i=0}^{n}(\\begin{matrix}t\\\\ i\\end{matrix})", + "9170a8aa7a4f8ff3.png": "\\frac{\\partial f_{k}}{\\partial x_{j}}", + "9170e5b64d364ac6.png": "(\\begin{matrix}2&0&0\\\\ 0&6&0\\\\ 0&0&12\\end{matrix})", + "917607e3042fc977.png": "[\\begin{matrix}2&2&4\\\\ 3&5\\end{matrix}]", + "917a19751f318b41.png": "\\frac{d[A]}{dt}=-k_{1}[A]", + "917b5296a12d435d.png": "\\kappa_{s}=\\kappa(T_{s})", + "9187ca356e48022a.png": "[\\begin{matrix}x\\\\ x^{2}\\end{matrix}]", + "91899d8d66f359ab.png": "\\frac{a}{b+\\frac{c}{n}}\\rightarrow\\frac{a}{b}", + "9189d3c333ab4951.png": "e^{(\\frac{-\\Delta E}{kT})}", + "918c9848fea560d7.png": "\\phi_{0}=[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "918d81493b57039b.png": "\\nu_{0}=\\frac{a}{2\\pi}\\sqrt{2D_{e}/m}", + "918e70d36d4bc841.png": "r(u):=0.2", + "91981d2617c432ea.png": "f^{\\prime\\prime}<4", + "91a2911b16e8d345.png": "K_{2}^{M}(Q_{p})", + "91a99f2f0e7d6da7.png": "\\tilde{\\phi}(xU)=\\phi(x)", + "91abca2d4929cdc9.png": "(\\begin{matrix}13\\\\ 10\\end{matrix})=(\\begin{matrix}13\\\\ 3\\end{matrix})=286", + "91af077e41adfcc5.png": "\\zeta_{K}(s)=\\sum_{a}\\frac{1}{(Na)^{s}}", + "91b47af532371b17.png": "y=\\frac{1}{2}laea_{y}(\\frac{\\lambda}{2},\\varphi)", + "91b7a0b5e0ffecf4.png": "\\frac{\\partial C}{\\partial r}", + "91b998c9df1d8f39.png": "\\int_{0}^{t}", + "91c2d4806e7bb592.png": "x^{n}-1=\\prod_{m|n}\\Phi_{m}(x)", + "91cca7b5999419ec.png": "2,3,5,11,17,41", + "91d011d3b928b93c.png": "g(2\\omega,2\\omega_{0f},\\Gamma)", + "91d7ca6ba25e465c.png": "T=\\frac{\\pi}{\\sqrt{I}}", + "91d98ee7d58856a7.png": "U=(\\begin{matrix}0&1\\\\ 1&0\\end{matrix})", + "91da7626d6b23285.png": "\\{v_{1},v_{2}\\},\\{v_{2},v_{3}\\}", + "91dbb94aefbfbc0a.png": "\\partial_{\\mu}\\gamma_{\\mu-}=0", + "91e0be2a2d541523.png": "\\hat{F}_{ab}^{i}\\dot{\\gamma}^{a}\\dot{\\gamma}^{b}", + "91e357627fab8d1c.png": "\\lambda_{w}(t)=w^{|t|}t", + "91e46fdaf3df5980.png": "Hg_{1}^{-1},...,Hg_{n}^{-1}", + "91e8214c2bbc4b70.png": "f_{*}(L_{X})", + "91ead3d9b0407453.png": "O((n+r)log(n))", + "91ecece178be2ad4.png": "\\tilde{K}(p;T)=e^{-Tp^{2}/2}", + "91f0f24bd3d7f2fe.png": "\\pi_{1}(SO(2))\\cong Z", + "91f18749546d47bb.png": "a(t)=\\frac{d}{dt}v(t)", + "91f653928213e905.png": "Z=\\frac{X-E[X]}{\\sigma(X)}", + "920a982cefc294b4.png": "A\\rightarrow B/C\\_D", + "920cd156882174c5.png": "|x-\\sum_{n=0}^{N}x_{n}|\\rightarrow0", + "920ed6aa29031eaf.png": "O(mn+n^{2}logn)", + "921283da364e068f.png": "\\langle\\overline{z}\\rangle=e^{i\\mu-\\gamma}", + "92128b892c2cab50.png": "|\\overline{VT}|", + "9213666b6c55844e.png": "\\mu=-e\\varphi+\\epsilon_{F}", + "9213db6680de7b4b.png": "k_{x^{b}}", + "92177a0ec12f35cf.png": "L>>(x+a/2)", + "921870c95cd6f26d.png": "[,,]", + "921b65723c6eb1e5.png": "[\\begin{matrix}A&0\\\\ 0&B\\end{matrix}]", + "921d84ccaf4f49fe.png": "rel_{i}\\in\\{0,1\\}", + "921fd2e8ffba8afd.png": "\\overline{X}=\\frac{1}{n}\\sum_{i=1}^{n}X_{i}", + "92252b1b3ac2d87d.png": "\\int x(t)dt|_{t=z}", + "922abca034619c07.png": "\\frac{ds}{dt}=0", + "922b2a134633cf61.png": "C\\rightarrow C^{*},z\\mapsto e^{z}", + "922d39ca35790dc5.png": "|\\Psi\\rangle=a|\\psi\\rangle+b|\\phi\\rangle", + "9233972ec39353cb.png": "Pr(R_{i}<\\underline{R})", + "9235cbde602e9154.png": "(A[[X]],\\cdot)", + "92417c3d2e486bd3.png": "\\tau:E_{p,0}^{2}\\rightarrow E_{0,p-1}^{2}", + "924528ff511aa357.png": "f(\\infty)=\\sqrt{A^{2}+B^{2}}", + "924b8d69a3275b27.png": "P(t)=e^{tQ}", + "924d7333d678326f.png": "A", + "92537cf13e8a6ed4.png": "(\\frac{16}{27})^{\\frac{1}{3}}\\approx0.840", + "925949d5c1593180.png": "[\\begin{matrix}1&2\\\\ 1&1\\end{matrix}]", + "925f071a9fbd8e2e.png": "1\\le g^{(2)}(0)\\le\\infty", + "925f41c3034765b0.png": "\\frac{\\partial c}{\\partial z}", + "926c0f108aa6c1e1.png": "\\{\\begin{matrix}3\\\\ 5/2\\end{matrix}\\}", + "926da3be22cd1137.png": "\\gamma_{m}^{j}", + "927c7f463edc6e12.png": "12\\sqrt{25+10\\sqrt{5}}", + "927f6a4525a629d1.png": "P_{total}=\\sum_{i=1}^{n}p_{i}", + "928995483451c850.png": "r=g^{e}y(modp)", + "928a1b0b7e36f1d9.png": "(\\frac{N}{2}\\times\\frac{N}{2})", + "928ce98fe2e05f8b.png": "\\sigma_{k}=\\sqrt{\\lambda}", + "928e3d5c5fe11d8f.png": "\\overline{\\psi}=\\sum_{i}\\psi_{i}b^{i}", + "929e9d52cac02a5f.png": "\\Pi(t)=e^{it\\sqrt{D}}.", + "92a063169ebb04d2.png": "\\tilde{x}_{0}\\in\\tilde{M}", + "92a406f4fa6ce691.png": "v=\\sqrt{\\frac{3RT}{M}}", + "92a5ab90d2f2f676.png": "\\frac{1}{p^{k}},\\frac{1}{q^{l}},\\frac{1}{r^{m}}", + "92ac5dbb7addd5b4.png": "H^{i}(V,Z_{l})\\otimes Q_{l}", + "92b19eb085c07f34.png": "[\\begin{matrix}cos(\\phi)&-sin(\\phi)\\\\ sin(\\phi)&cos(\\phi)\\end{matrix}]", + "92b6d0776bb76095.png": "g=\\prod_{i\\in I}(X-\\alpha_{i})", + "92b7187e8488b98d.png": "i=1-\\frac{n-1}{n}\\alpha", + "92b78c4b7b9042a9.png": "\\tilde{h}[n]", + "92ba22ce377a939c.png": "L=K[X]/(f(X))", + "92bf7cab0d487416.png": "\\Delta\\alpha=\\frac{1}{k}\\frac{\\partial\\phi(x)}{\\partial x}", + "92c0ee570cb67bcb.png": "\\hat{p}", + "92cda0f03716dae5.png": "\\int fg=f(x)\\int g", + "92cf11c0785f0f3d.png": "\\beta=O(1/m)", + "92d4cfc7f5b56e9a.png": "B_{\\tilde{\\nu}}", + "92d8270f6966514a.png": "\\int dy=\\int93xdx", + "92e2fa93e9414910.png": "\\tilde{v}_{r}^{p_{i}},\\tilde{\\omega}_{r}^{B}", + "92e6b9c977556062.png": "\\hat{y}_{t}", + "92e788b6e28e8a36.png": "[\\begin{matrix}3/2&0\\\\ 0&2/3\\end{matrix}]", + "92e9641e29814f7e.png": "\\langle N_{i}|i<\\omega\\rangle", + "92f684bbf39ff188.png": "y=\\int_{0}^{2}xdx", + "92fb728827999fdd.png": "\\underline{P}X=\\{O_{1},O_{2}\\}\\cup\\{O_{4}\\}", + "930357e14a538556.png": "I_{P}=\\frac{V_{P}}{|Z|}", + "93047daec032d18c.png": "\\int_{a}^{b}f(x)d_{h}x", + "93064db010f701ad.png": "\\int_{\\Omega}u_{j}u_{j}=1", + "9308279e9c2716f7.png": "0<\\mu<\\frac{1}{\\sigma^{2}}", + "930ddc12d0c1a69b.png": "\\frac{dG}{dr}=0", + "93177abac9c5dad3.png": "\\frac{\\partial z}{\\partial x}=3", + "9322ef22eb12762a.png": "|\\mu|(\\Omega)", + "9323039e436d0c7c.png": "a^{1/n}\\rightarrow1", + "9324a928300e44a0.png": "0.75\\overline{0}", + "9331d00d2067622d.png": "=\\frac{e}{\\sqrt{\\alpha}}", + "9333cf820eb3406c.png": "\\hat{U}_{q}", + "933ce2ebcdb71661.png": "y=(\\begin{matrix}v\\\\ u\\\\ s\\end{matrix})", + "93424a9079173e1f.png": "\\sqrt{17}", + "9347025dda210e9f.png": "max_{c\\in C}\\{w_{C}(c)\\}", + "93472aa7214bee51.png": "(1,1)_{0}", + "934ad36e3d45240c.png": "\\lambda E=R_{n}-G-H", + "934da4cd3c46b90f.png": "\\frac{h-h^{\\prime}}{\\lambda}=\\frac{D}{\\lambda}=N", + "93500f82df878543.png": "Pm\\overline{3}n", + "9351d3d3e7a77692.png": "\\bigcup_{i}B_{i}\\supseteq\\bigcup_{i}A_{i}=R", + "93556d2d7f109966.png": "(\\begin{matrix}x\\\\ n\\end{matrix})", + "935ae9e3708d95e5.png": "\\int x^{2}e^{x^{2}}dx", + "9363c20b3677db6c.png": "A_{(0,0,1)}(x)=x^{2}", + "9364922ce22690f6.png": "||Df^{-n}v||\\le c\\lambda^{n}||v||", + "936547aaed50b2f0.png": "\\sqrt{\\frac{1}{126}}", + "93664899e533446f.png": "(1,1,1,1,1,1,1,1)", + "9368b50828f91125.png": "(\\begin{matrix}A&B\\\\ C&D\\end{matrix})", + "9370b259264d642b.png": "\\tilde{A}_{3}", + "9374a02b1b4d6881.png": "S_{gen}^{\\prime}=\\frac{Q_{2}^{\\prime}-Q_{1}^{\\prime}}{T_{surr}}", + "9375c0ccb39369bd.png": "log_{2}(6^{5})", + "9378d62ebf0095c5.png": "\\int xe^{2x}dx", + "9378f78ccb3174f0.png": "\\alpha\\in A^{1}(k)\\subset P^{1}(k)", + "937dc56cd35915d3.png": "(x+y+z)^{2}=1", + "9383cadb0a677fe4.png": "\\sum_{k=1}^{n}F_{k}^{2}=F_{n}*F_{n+1}", + "93842430dd447db6.png": "x^{*}\\in X^{*}\\\\ \\{0\\}", + "938a21f5ccb78b10.png": "\\tilde{X}_{N}", + "938a847d08e1410e.png": "\\frac{dy}{dx}=\\frac{x}{y}", + "938ca2b2349f4d70.png": "\\{(-1)^{\\pi}\\}", + "938ecadf3572039e.png": "q=\\frac{\\partial\\psi}{\\partial n}", + "939e9ee63bc69cfa.png": "(\\pm\\sqrt{2},-1)", + "93a097866ff3fe88.png": "\\Delta h=f\\frac{u^{2}L}{gR}", + "93a14755e2f67ddd.png": "t_{4}^{\\prime}=\\frac{t_{4}\\cdot\\frac{v}{h^{4}}r_{4}}{\\sqrt{1\\cdot\\frac{v^{4}}{h^{4}}}}", + "93a5324ed4a1d5f4.png": "x_{1}/(x_{1}-x_{2})", + "93aee25ce872a7fb.png": "Th_{\\Pi_{2}^{0}}(N)", + "93b03440a36b97c5.png": "(\\begin{matrix}n+x-1\\\\ n\\end{matrix})", + "93b43f20fafab7a2.png": "\\frac{\\partial u}{\\partial t}=0", + "93b5405771a682d8.png": "(A-B)\\sqrt{g}=1.", + "93b5d20ed61ce9a0.png": "c\\sqrt{2}", + "93b61cdc0e1051d8.png": "c=\\sqrt{n}", + "93b88995a4a037fb.png": "Y_{0}\\approx1/\\sqrt{S}", + "93b8acaf5b9dc610.png": "n+(-\\infty)=-\\infty", + "93c1b36ee06a6de0.png": "\\{-2,-1,1,2\\}", + "93c23f04ee3a3bd6.png": "c_{w}=(\\frac{\\lambda_{1}-\\lambda_{2}}{\\lambda_{1}+\\lambda_{2}})^{2}", + "93c4b21f8fdd6694.png": "\\Delta v=V_{exh}ln(\\frac{m_{0}}{m_{1}})", + "93c817ecf7c7f65a.png": "\\frac{dX}{dt}=AX", + "93c88fbd95da9ed4.png": "D=N-K+1", + "93cab4e306f9da2e.png": "2\\sqrt{n}", + "93d3e735f1a7d862.png": "(x-1)=\\frac{1}{1+x}", + "93d9e154f24e8159.png": "\\chi^{2}>\\chi_{k-1,\\alpha}^{2}", + "93dc2b8647da2ae2.png": "r=b_{0}b_{1}b_{2}...", + "93dda23a1f6a4367.png": "\\frac{dv}{dr}", + "93decac2b4c6a12b.png": "\\Delta(\\overline{OP_{i}P_{j}})", + "93e02930859b0c04.png": "\\tilde{B}_{6}", + "93e2aaab28f0b85f.png": "e_{q}(z)e_{1/q}(-z)=1", + "93eae6efc33c69ff.png": "u(x,t)=ce^{-|x-ct|}", + "93ec02515f4ed2d1.png": "\\frac{K_{i}}{K_{d}}=\\omega_{0}^{2}", + "93ed932121aed3cf.png": "{j^{\\lambda}}^{y}", + "93f4c5d9827cbed4.png": "U=\\int f(v)E(v)dv", + "93f7f2c2dff2a243.png": "H_{n}(M,M\\backslash\\{p\\};Z)", + "93fe94ea7f669700.png": "P(T|F)=\\frac{P(T)}{P(F)}", + "93fea6cb8cae1743.png": "f_{0}=\\frac{1}{2\\pi\\sqrt{LC}}", + "93ff1479a28a1d0d.png": "\\approx1.3\\times10^{154}", + "93ff87edfa2381a1.png": "(w/(P.\\sqrt{T}", + "9404853120b4abcd.png": "[\\begin{matrix}4&6\\\\ 3&5\\end{matrix}]", + "94085fff4508577f.png": "\\int d^{D}x\\sqrt{-g}G", + "940db56a3d083d4b.png": "\\delta=\\delta_{S}=1+\\sqrt{2}", + "940e437ae827c25e.png": "(\\begin{matrix}N+I-1\\\\ I-1\\end{matrix})", + "9412364a05c73d6d.png": "g(\\theta)=(1+cos\\theta)", + "94125f6454ccb44c.png": "v=[\\begin{matrix}0\\\\ 1\\end{matrix}]", + "9412a54386e08330.png": "\\frac{dy}{dx}", + "941c4544ad202b4d.png": "\\int(\\int f(r)dr)dv", + "942a5539146106dd.png": "Q=-k\\frac{dT}{dz}", + "942cc8830b52eb8b.png": "\\chi_{imp}=\\frac{C}{T+\\theta}", + "9434e45771d8fff2.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "94356062b22dffa5.png": "rect(.)", + "943ba4f84b30c82b.png": "\\frac{\\partial g}{\\partial x}", + "943ea5f5c29b8af3.png": "x=v\\sqrt{\\frac{h}{2g}}", + "944289e8670bc01d.png": "\\langle\\langle\\sigma_{A}(\\sigma_{B}-\\sigma_{B}^{\\prime})\\rangle\\rangle", + "94441bcb44a32a2d.png": "(\\begin{matrix}a&b\\\\ c&1-a\\end{matrix})", + "9444590b2ea33260.png": "\\int_{a}^{b}f(x)dx", + "944f095ded347461.png": "(\\begin{matrix}\\pm\\sqrt{N}\\\\ 1\\end{matrix})", + "945a847346872ff6.png": "x", + "946162db648cc5ea.png": "33.\\overline{3}", + "9462130ab88e4f48.png": "PB-C=\\sqrt{\\gamma}Q", + "946a7aa59e9b5464.png": "\\nu=\\frac{\\partial V}{\\partial\\sigma}", + "946a97b7b4700d87.png": "\\mu=e^{\\int p(x)dx}", + "94700f48cd7bdffc.png": "\\frac{d\\phi}{dx}", + "9474b4bd9f83f25f.png": "G=\\pi_{1}(Ff)", + "9474bf297d3a56d6.png": "sys^{2}\\le\\frac{\\pi}{2}\\cdot area", + "94756f434591bedc.png": "k\\approx aF^{b}(T_{2lm})^{c}", + "9479cfb672435038.png": "I(X;Y)\\le H(X)", + "947ab4d6a86abe0b.png": "\\sum_{i}p_{i}|\\psi_{i}\\rangle\\langle\\psi_{i}|", + "947bf51d5a2b9ec8.png": "\\prod p_{i}^{t_{i}-1}", + "948a0d7890f8a80e.png": "O(\\sqrt{|V|}\\cdot|E|)", + "948b8a6707f08966.png": "\\hat{\\varphi}=(-sin\\varphi,cos\\varphi)", + "948c1870da7a6faa.png": "(t,x^{2},...,x^{n})", + "94911abca9ecf49b.png": "L=n_{l}-n_{\\overline{l}}", + "949522848103d04c.png": "R_{crit}=\\frac{\\pi M}{\\sqrt{k-1}}", + "949681cbea9f0b02.png": "[e_{i}^{\\prime}]=[L][e_{i}]", + "949b23a609ebf7cb.png": "A=[\\begin{matrix}1&0&0\\\\ 0&0.6&0.8\\end{matrix}]", + "949dd4d4ed75a6a9.png": "4-2\\sqrt{3}", + "94a02107e8225375.png": "A_{4}=S(b^{-1})M", + "94a050845fca590a.png": "-ih\\frac{\\partial}{\\partial x}", + "94a62720636056e1.png": "E(X)=\\int_{\\Omega}XdP", + "94a645d1e04c3088.png": "(\\alpha K+\\beta L)", + "94a68d34642ba80c.png": "\\frac{\\partial^{2}y}{\\partial r^{2}}=0", + "94a8edbcec6a0f78.png": "\\frac{dy}{ds}=1", + "94adf2c83cf7112a.png": "W_{r}^{\\omega}", + "94b03038498461a6.png": "V=|a\\cdot(b\\times c)|", + "94b0dac08049f9e1.png": "(\\begin{matrix}7\\\\ 2\\end{matrix})=6\\times\\frac{7}{2}=21", + "94b2d633bf0bc6c1.png": "A^{f}=\\sqrt{I_{0}}", + "94b959fad13e3064.png": "\\tilde{x}(t)", + "94be33fc1e90ba5c.png": "(\\begin{matrix}n\\\\ 1\\end{matrix})_{F}=(\\begin{matrix}n\\\\ n-1\\end{matrix})_{F}=F_{n}", + "94c2194207284aaa.png": "u=\\int u^{\\prime}dx", + "94c4b442b7d92fdf.png": "\\int\\frac{du}{u}", + "94c5761bc1d0ae22.png": "\\Delta_{LB}=\\frac{1}{f^{2}}\\Delta_{0}", + "94c9d214272278af.png": "U=(\\begin{matrix}0&1\\\\ 1&0\\end{matrix})", + "94db34aec798710a.png": "v_{1}=[\\begin{matrix}1\\\\ 1\\\\ 0\\\\ 1\\end{matrix}]", + "94e02c0974041e26.png": "(\\alpha+1)\\frac{\\sigma_{0}}{E}=0.002", + "94eb3e3700bd0a8e.png": "I=\\int e^{x}cos(x)dx", + "94eb5b75c93283eb.png": "0=f^{k}(y)=x", + "94ef4d337810b0ee.png": "(\\begin{matrix}a&b/2\\\\ b/2&c\\end{matrix})", + "94f615bc73ddbd4d.png": "sup_{|z|<1}|\\mu(z)|<1.", + "95006bacd6c8574a.png": "\\mu=\\frac{1}{n}\\sum_{v\\in V}f(v)", + "950aeb15555e3161.png": "\\frac{dF}{dL}", + "95146f3f7124311d.png": "J_{l}^{\\delta}", + "9516b61bd7b634d3.png": "L_{1}^{loc}(R^{n})", + "951794cf31dd2e9d.png": "\\overline{X}=\\frac{X_{1}+\\cdot\\cdot\\cdot+X_{n}}{n}", + "951bf0d476d650f4.png": "\\hat{O}^{\\prime}", + "951ea076ca940c8a.png": "\\int\\frac{dx}{S}=\\frac{2S}{a}", + "951fd41633f25ee4.png": "\\overline{y}_{x}", + "9524c217ebe317d7.png": "I^{0,q}\\rightarrow I^{1,q}\\rightarrow\\cdot\\cdot\\cdot", + "9527a9cfddd71df1.png": "[-1,1]^{2}", + "952fa6329f908aff.png": "\\tilde{x}\\sim F(\\tilde{x}|\\theta)", + "952fbd2f2ea1fa6f.png": "w_{1,1}...w_{n,1}", + "95308718b828e859.png": "S=\\sqrt[3]{\\frac{K_{sp}}{4}}", + "953724bd73fbb113.png": "\\hat{H}=\\hat{H}(\\hat{P})", + "953dbb1c9715c96e.png": "\\{\\begin{matrix}8\\\\ 8\\end{matrix}\\}", + "95405d8b17fcbb80.png": "[\\begin{matrix}-\\alpha-1\\\\ -\\beta\\end{matrix}]", + "95407a85d4edb5d2.png": "(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "9544940e72687b26.png": "B=\\int_{0}^{b}e^{x}dx", + "954b5424009f9ef7.png": "\\tilde{6}", + "954db07e21556e9d.png": "e^{1/2}=\\sqrt{e}", + "954f97f74d426764.png": "\\tilde{O}(n)", + "954fc826aa83e105.png": "\\int_{1}^{5}2xdx", + "9550328409172a81.png": "v_{y}\\sqrt{v_{x}^{2}+v_{y}^{2}}", + "95508226ef87423d.png": "\\hat{X}_{i}", + "95547b5f9026c3e1.png": "[\\begin{matrix}w^{1}\\\\ \\vdots\\\\ w^{k}\\end{matrix}]", + "955766b4a4930542.png": "18-22\\sqrt{3}", + "955a0822e2eddb48.png": "\\sum_{i=0}^{4}(\\begin{matrix}8\\\\ 2i\\end{matrix})(\\begin{matrix}28\\\\ 16-i\\end{matrix})", + "955c723e788aefca.png": "\\hat{b}_{i}", + "955ed14dc306b1ec.png": "-S", + "9564b9649f4ef231.png": "S_{n+1}=\\delta_{M,D}(S_{n})", + "95653c020a9533e2.png": "\\alpha_{i},\\alpha_{j},\\beta", + "9565db185f4e462f.png": "\\Phi^{t}(x_{0})=e^{tA}x_{0}", + "9567126c9871530b.png": "/b:=*b^{-1}", + "956c5a638279361d.png": "\\sqrt{\\eta}", + "956e346b0303b625.png": "2(\\begin{matrix}n\\\\ j\\end{matrix})", + "957797dff1209ce0.png": "1.15m*c^{2}-mc^{2}", + "957b1a3d23945ae9.png": "y(t)=\\int_{0}^{t}dy(r)", + "957c85166067f62a.png": "\\beta=\\frac{\\partial f}{\\partial y}", + "957ddf6ce683bf1a.png": "\\prod p_{i}^{t_{i}-1}", + "957de2138256c3f1.png": "(\\{\\infty\\}\\times K),\\infty\\notin K", + "9580236af7329f6c.png": "\\overline{X}_{n}=(X_{n1},...,X_{nk})", + "9581fdda167e24f4.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=0", + "9582e1fb862ad89b.png": "z_{M}=\\frac{N}{I_{M}}=\\frac{N_{m}}{I_{Mm}}", + "959385c4cf6f740e.png": "(\\begin{matrix}n\\\\ k_{1},...,k_{r}\\end{matrix})", + "95a0aa943145e272.png": "\\tilde{H}_{\\infty}(W|E)\\ge m", + "95a7a399ceafffef.png": "\\alpha_{z}(a):=f(z)", + "95b5c4ab3d8c831f.png": "\\tau_{g}^{\\delta}", + "95b5c8aae3451bcf.png": "126", + "95b9d4a37a176aba.png": "s^{2}=\\frac{1}{\\sum1/\\sigma_{i}^{2}}", + "95bd2c6d54a5e8ac.png": "f_{c}=1-\\frac{1}{\\frac{\\langle k^{2}\\rangle}{\\langle k\\rangle}-1}", + "95cc341041555980.png": "E[(X-\\mu_{X})^{2}]", + "95ce613d8c04e131.png": "E=-Blv", + "95d0ae1c86f5f116.png": "\\forall x\\in V,(x,x)\\notin E", + "95d1ecb9ec0a8d67.png": "\\dot{y}=\\frac{1}{\\mu}x", + "95d525c36fe1e2c5.png": "\\tilde{x}", + "95d5547650169200.png": "|\\begin{matrix}a&b\\\\ c&d\\end{matrix}|", + "95dbe27b454371e4.png": "f\\in S^{\\prime}(R^{d})", + "95e00634339e88de.png": "(s,\\pi_{v},r_{i,v},\\psi_{v})", + "95e60ab3e1c9fb02.png": "\\frac{\\partial\\theta_{e}}{\\partial z}>0", + "95eb8c53415679a3.png": "(\\begin{matrix}2n-2\\\\ n-2\\end{matrix})", + "95ecdfc20bc08ff2.png": "u_{2}=[\\begin{matrix}1\\\\ -1\\end{matrix}]", + "95f1a2f216ca8161.png": "A=\\frac{1}{2}(b+d)a", + "95fd154ef47bbb2f.png": "\\int_{E}\\varphi<\\infty", + "95fd2395fcb361b0.png": "\\tilde{D}_{n}", + "95fd75c5aae7851a.png": "C", + "95fda951ca5d0ab7.png": "M=(M_{i,j})\\in R^{(n)}", + "9602497f9b35c40c.png": "\\vec{v}=-\\frac{\\epsilon_{o}\\epsilon_{r}\\zeta\\vec{E}}{\\mu}", + "96030090e9bf53d0.png": "\\tilde{d}=1", + "96081ddaf01a29be.png": "(x\\times d)\\cdot m=|m|^{2}", + "9608f2b1097c34e5.png": "s=\\frac{1}{2}(a+b+2c)", + "960ad3a55592661d.png": "S=-mc\\int ds", + "960b4691816f7d51.png": "\\tilde{b}_{ij}", + "9611a972d30a1671.png": "\\frac{df}{dx}", + "961646f60b5c1c5e.png": "\\int_{0}^{x}(cos(Nt)-1)dt", + "96198f5e4fb22add.png": "\\int vds", + "961dd02e11ed987e.png": "\\int_{-2}^{2}\\frac{dx}{x}=0", + "9623244abc3b745f.png": "W_{1-2}=\\int PdV", + "96266a45028b6bd1.png": "y^{\\prime}(t)=\\alpha+\\frac{vy(t)}{c+vt}", + "962c002b6b56d7dd.png": "\\Phi=\\frac{1+\\sqrt{5}}{2}", + "96346571dc398509.png": "L_{v}", + "9635443739064ee7.png": "\\frac{dC_{U}}{dC_{W}}", + "9636e1989f07e5c1.png": "\\frac{dr}{dt_{r}}", + "963af220cf5c502a.png": "\\hat{S}^{2}", + "9642551b271ebc5e.png": "\\sigma=\\sqrt{\\sigma_{i}^{2}+\\sigma_{j}^{2}}", + "9644d4a3f160c5f6.png": "\\tilde{M}=M//G", + "96538df8c88ed4b9.png": "\\{v_{1},v_{2}\\},\\{v_{2},v_{3}\\}", + "965494c35c4cc990.png": "A_{i}^{\\prime}\\in A^{\\prime}", + "965bce3706791bdf.png": "C^{g}\\cong R^{2g}", + "96608985108b5b33.png": "-x", + "9663aa5a9e2d2274.png": "\\oint dS=\\oint\\frac{dQ}{T}=0", + "9667dc6c8b017c68.png": "\\partial_{t}u=\\Delta u+\\xi", + "96680dbb0540e97b.png": "P=\\int_{K}\\rho(k)dk", + "966ba12c00785404.png": "\\{|f_{k_{0}}^{i}\\rangle,|f_{k_{1}}^{i}\\rangle\\}", + "966f3e000970a932.png": "\\frac{\\sqrt{3}}{4}a^{2}", + "966feaf2b6cbafc2.png": "min||w^{(i+1)}-w^{(i)}||", + "96739b06247be318.png": "Q_{j,x}=\\int y_{i}dA", + "9673c2026a068cb1.png": "(V_{a,b}:b\\in B)", + "96789e539ba3fa86.png": "U(r_{j}-r_{l}/\\sqrt{n})", + "967a6d7ae2d3bfa8.png": "1/\\sqrt{N}", + "967e309fe834a446.png": "C_{R}=\\sqrt{\\frac{h}{H}}", + "9682ca3b4a5b9bf2.png": "S=\\frac{\\partial M}{\\partial logt}", + "96831b72f3bdd236.png": "D_{KL}^{(e)}(P||Q)", + "96853246534234e6.png": "C(T)^{*}", + "96909635d2ba2b6d.png": "\\prod_{d|n}f(d)", + "9694d0a10eec5417.png": "(\\begin{matrix}2n\\\\ n+1\\end{matrix})=\\frac{n}{n+1}(\\begin{matrix}2n\\\\ n\\end{matrix})", + "969b78dc70c365e7.png": "\\tilde{W}_{t}=W_{t}-[W,X]_{t}", + "969d5871849c2fe3.png": "[A_{n}]", + "969d75615d905f96.png": "\\int e^{-x^{2}}dx", + "96a150ea00f6fdfc.png": "f(x,y,z)=x^{5}y^{2}z^{3}", + "96a5ab209a93cf19.png": "E[\\hat{\\sigma}^{2}]=\\frac{n-1}{n}\\sigma^{2}", + "96a992607d252544.png": "\\int_{d}^{\\infty}e^{f(x)}dx", + "96aad5c338615e51.png": "\\tilde{\\delta}_{ijk}", + "96ac8cf38c9f6c4d.png": "\\tilde{X}", + "96bae0699f2a7d62.png": "\\nu_{e}", + "96baf7d2da03cf50.png": "\\hat{G}(z)", + "96bb07b898837bf9.png": "\\int_{0}^{t}B_{s}^{2}dB_{s}", + "96be3c389b654256.png": "", + "96c1d6325d2753b9.png": "w\\sim N(0,\\alpha^{-1}I)", + "96c8363094d25ee2.png": "\\hat{G}_{T}", + "96d87e3c5c9a3358.png": "(\\begin{matrix}8\\\\ 1\\end{matrix})", + "96d8be62c7e82b0e.png": "\\sqrt{x^{2}-1}\\ne x-\\sqrt{1}", + "96db4ddc641054a5.png": "c_{k-1,0}=0", + "96e39ed470c6dfd9.png": "lim\\frac{x}{y}=\\frac{limx}{limy}", + "96e4114d62f33ea2.png": "P_{[i,\\epsilon]}=\\frac{m_{[i,\\epsilon]}}{M_{\\epsilon}}=", + "96e79fd0e032d9e4.png": "e^{-(\\frac{x-m}{s})^{-\\alpha}}", + "96e9ff72869e5b97.png": "\\delta\\int d\\tau=0", + "96ebe107382e6d89.png": "\\phi:M\\rightarrow\\prod_{i\\in I}R", + "96ee2451008f6571.png": "\\tau_{\\tilde{H}}(\\tilde{G})=\\tau_{H}(G)", + "96eeb420bd0a06f0.png": "\\Delta f=\\frac{\\partial^{2}f}{\\partial x^{2}}+\\frac{\\partial^{2}f}{\\partial y^{2}}", + "96efcfe99038418d.png": "\\sqrt{i}", + "96fb76b34b8abcee.png": "\\frac{d^{2}x}{dt^{2}}", + "96fcde154abc9cc9.png": "k_{x^{b}}", + "96fe006989939555.png": "2^{5}3^{4}", + "97006585d5ccd675.png": "v=\\sqrt{\\frac{T}{\\mu}}", + "97014ce4dbfbf8fb.png": "(\\begin{matrix}0&1\\\\ 0&0\\end{matrix})", + "970633f7201be7a4.png": "\\lfloor(Q-x_{0}-1)/r\\rfloor", + "970ff03d9e897e51.png": "w_{d=1...M,w=1...N_{d}}", + "972123c897bf44c7.png": "(d\\varphi_{x})_{a}^{b}=\\frac{\\partial\\hat{\\varphi}^{b}}{\\partial u^{a}}", + "972a54a412582793.png": "(\\int f)^{3}", + "972dfcd516aa2020.png": "\\gamma(t)=(t,f(t))", + "9734401b39367e6b.png": "p/=\\gamma^{\\mu}p_{\\mu}", + "9749c956866e9e8b.png": "(a_{n})_{n\\in N}^{(k)}", + "9749d6266dab22f5.png": "\\int_{A}(g-f)d\\mu=0", + "974d0fa83affba41.png": "t=t_{0},r=r_{0},\\theta=0", + "974e02e4c75ecd02.png": "\\sqrt{-1}", + "974e2058e877fe2d.png": "(X_{b}^{*},Y_{b}^{*};Z)", + "9750e9f8bca219cf.png": "P_{max}=\\frac{1}{4}p_{max}Q_{max}", + "975233dbad373450.png": "Sh=\\frac{K_{c}L}{D}", + "97551ea9ec7b2493.png": "\\{\\frac{\\partial}{\\partial x^{1}},...,\\frac{\\partial}{\\partial x^{n}}\\}", + "9758344a8bdf0776.png": "\\tilde{B}_{k}(x)", + "975de8823d0a16de.png": "h_{J}\\leftarrow\\hat{h}", + "97634b990d8bb2c5.png": "A=\\int_{0}^{1}dAds", + "97640061bca8bfc5.png": "\\frac{dE_{2}}{dE_{1}}=-1", + "9764f25707fae074.png": "D:\\phi\\mapsto\\frac{1}{i}\\phi^{\\prime}", + "97666f1261f99f84.png": "-\\int E\\cdot dl", + "9766c7dd2adf4370.png": "\\frac{\\partial p}{\\partial y}=0", + "9766e0df1b7bc001.png": "[\\begin{matrix}A&B\\\\ B&C\\\\ \\end{matrix}]", + "976aa033aa9b4414.png": "A_{\\epsilon}^{n}(X,Y)", + "976bcf4629642e06.png": "f_{c}=\\frac{1-\\alpha}{2\\pi\\alpha\\Delta_{T}}", + "977191661eeaa52f.png": "\\tilde{x}\\sim F(\\tilde{x}|\\theta)", + "97743cd4efa4fac8.png": "a^{2}+b^{2}+c^{2}>\\frac{d^{2}}{3}", + "97752e6fcf743816.png": "V_{rect}=[\\begin{matrix}T1&0\\\\ 0&T2\\end{matrix}]", + "9777dc59ab67d9d4.png": "0=\\frac{3x-1}{2\\sqrt{x}}", + "977945c1295e9238.png": "q_{i}=2p_{i}(1-p_{i})", + "977cfc465b3dc60c.png": "\\hat{X}^{n}", + "977e03416d68570a.png": "(1-2t(n-1))", + "977e6bd767f9c202.png": "\\prod_{i\\in I}U_{i}", + "9780ce02b2731cc1.png": "b^{(t_{j})}", + "97829861b1240105.png": "1(2^{1}/1!!)\\pi^{0}", + "978903099d3075cb.png": "(\\begin{matrix}9\\\\ 6\\end{matrix})", + "9789baf58ad70c16.png": "G^{(y_{\\tau})}", + "978a5468f594eff3.png": "lim", + "9791421960420ded.png": "N_{i}=(\\begin{matrix}8\\\\ i\\end{matrix})i^{12}", + "979aa4f20fa27087.png": "1/x=o(1)", + "97a46a9fb2e59df2.png": "(0,-\\frac{J_{3}sini}{J_{2}2p})", + "97a73b04ccc9206c.png": "(i\\hbar\\partial/-mc)\\psi=0", + "97b495d377de758d.png": "\\sqrt{10}(4\\rho^{4}-3\\rho^{2})cos2\\theta", + "97c4cdc7d80dc072.png": "\\tilde{u}_{i}", + "97c6e4f596a70f11.png": "\\alpha\\in A^{1}(k)\\subset P^{1}(k)", + "97ca3e92c5d66324.png": "4\\epsilon_{n,rms}", + "97cb2b875972b06b.png": "K_{+}\\subset K_{+0}", + "97d1388a88af7faf.png": "W=\\int_{C}Fds", + "97d6af3dda5f6de4.png": "\\sqrt{\\frac{20}{63}}", + "97d70ad589619250.png": "z^{X}=\\prod_{x\\in X}z_{x}", + "97d9907a3d681631.png": "||x||>\\gamma_{2}", + "97e1804eff1299c7.png": "\\langle\\pm2i,Z_{4}\\rangle", + "97e6838f0837d367.png": "Q:2^{X}\\longrightarrow2^{R^{n}}", + "97ef5643ee005b59.png": "V=\\frac{4\\pi}{3}{D_{C}}^{3}", + "97f37ef367c34108.png": "W(A_{n})=S_{n+1}", + "97f670457544e843.png": "\\sum_{i=0}^{4}(\\begin{matrix}8\\\\ 2i\\end{matrix})(\\begin{matrix}28\\\\ 16-i\\end{matrix})", + "97fed3c195726c0f.png": "R=[\\begin{matrix}W&X\\\\ Y&Z\\end{matrix}]", + "980ab36d1df0a785.png": "C^{\\rho_{\\mu}}", + "98150acbbe13d7c5.png": "\\langle a_{i}^{\\prime},b_{j}^{\\prime}\\rangle", + "9817af5d74d58254.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=\\prod_{p}p^{b(p,n,k)}", + "981c2229bcc4cdee.png": "I_{2}=\\int f(\\theta)d^{3}x", + "981dd81e3075a884.png": "\\frac{\\pi}{2}(i-1)\\le v_{i}<\\frac{\\pi}{2}i", + "981f8a4f28c24971.png": "\\frac{\\partial\\omega}{\\partial k}", + "98208ac1ddb24189.png": "[\\begin{matrix}1&2\\\\ 2&4\\\\ \\end{matrix}]\\sim[\\begin{matrix}1&2\\\\ 0&0\\\\ \\end{matrix}]", + "982278aac6a68c81.png": "P_{f}(N)", + "982b8769ee35cf1e.png": "\\chi:V^{C}\\rightarrow\\overline{V^{C}}", + "9830d8e96cbfc49f.png": "[\\begin{matrix}1&1\\\\ 0&1\\end{matrix}]", + "98345946a81d2432.png": "(x,v=u\\cdot Mg(x))", + "9835b6fc79aab6a6.png": "-1^{\\sqrt{2}}", + "983decd6bc20b44f.png": "\\hat{f}(5)", + "9843c4cb6a8fd8d5.png": "x(v)+x(v^{\\prime})", + "9848db928be5a18e.png": "C_{n}", + "984b9c87dd955ab8.png": "H^{s/2}(R^{n})", + "98538ee3b83e0707.png": "\\frac{df}{dx}", + "985d86712e451fd9.png": "(\\begin{matrix}n-1\\\\ i\\end{matrix})", + "9863fe12a4f1a2bf.png": "\\underline{P}X=\\emptyset", + "986d577d698edb19.png": "\\prod{A_{i}}^{\\prime}", + "9872127281dec32a.png": "\\overline{x}_{i}", + "98747b7a0c854bd7.png": "\\frac{\\partial\\phi}{\\partial x^{\\mu}}", + "987a471912e044d9.png": "(\\begin{matrix}u&&-v\\\\ v&&u\\end{matrix})", + "987aca46c466c0f2.png": "=(1003-x)^{2}", + "9886860816fb2e76.png": "\\tilde{E}_{i}^{a}", + "98921a3cc8f07d2c.png": "x\\notin U", + "989773b5be93f62b.png": "S=\\int_{a}^{b}x^{x}dx", + "989c56e0302135aa.png": "P=\\{P_{\\theta}|\\theta\\in\\Theta\\}", + "989e2c2418222909.png": "X_{j}\\sim lnN(\\mu_{j},\\sigma_{j}^{2})", + "989e2e6b8a95aa8d.png": "\\int dV\\rho=q_{2}", + "98a36979d87fc572.png": "lim_{t\\rightarrow\\infty}\\overline{x}(t)", + "98a3c826a2b5df41.png": "5n^{2}-4n;n>0", + "98a600642eb6f7f6.png": "E[P^{(k)}]=-k\\alpha", + "98a85701464f3679.png": "2+2\\sqrt{2}", + "98a8c5df5b6e3d9f.png": "(\\frac{\\partial H}{\\partial T})_{p}=C_{p}", + "98afa2c537e2cc77.png": "M_{0}=\\Phi^{-1}(0)", + "98b132cd76403b48.png": "P", + "98b8c5fdbdca7cba.png": "\\tilde{c}(\\Pi)=(-1)^{k-l}c(\\Pi)", + "98baa7db0f9f13ed.png": "\\sqrt{5}", + "98bd93c5832a256f.png": "O((n/\\sqrt{\\epsilon})logn)", + "98c1bc1c7e638eb0.png": "(\\begin{matrix}k\\\\ t\\end{matrix})", + "98c668edff579371.png": "1-\\frac{2}{4}=0.5=50\\%", + "98cb2a5261923308.png": "\\sum_{y\\in A}|\\langle x,y\\rangle|^{2}\\le||x||^{2}", + "98d0e8cd01c331ae.png": "\\int sin^{3}xdx", + "98d79beb3ddee3da.png": "r^{\\prime2}+(r\\theta^{\\prime})^{2}=1", + "98dd68c641ac1e4e.png": "\\hat{h}_{L}", + "98df5d2572ad8050.png": "g_{0}=1_{\\Omega^{\\prime}\\\\ U^{\\prime}}g", + "98e3160d98cd23e5.png": "P=V(LE)-wL", + "98e62e171d057890.png": "2*10^{-2}m/s^{2}", + "98e9a22273e9c59b.png": "r=a\\frac{sin(\\theta+\\theta_{0})}{sin\\theta_{0}}", + "98eceb7fc73097ab.png": "\\int\\frac{dy}{dx}dx", + "98ff341ae006f382.png": "A_{i}\\subseteq A_{i+1}", + "990173615d5ae71d.png": "\\vec{b}=(b_{0},...,b_{L-1})", + "9901925a19359ef1.png": "B(z)=1+zB(z)^{2}", + "990d7c456e11045a.png": "R_{\\mu\\nu}=\\frac{\\Lambda}{\\frac{D}{2}-1}g_{\\mu\\nu}", + "990e731c33017980.png": "2\\notin Y", + "99181ad0ef4bc57e.png": "E=\\int vidt", + "991fcb2fbb7ec2f1.png": "\\frac{dN}{dt}", + "9921e3a798387f6a.png": "f_{i}(x^{1})\\le f_{i}(x^{2})", + "9926d073858a667f.png": "I_{C}=C\\frac{dV_{in}}{dt}", + "992b71ec4ee48177.png": "3", + "9937e44f1d2da859.png": "q=\\frac{\\partial\\psi}{\\partial n}", + "9944a1d3ab23a7dd.png": "N=1+\\prod_{p\\in S}p", + "9945e95bcce44546.png": "\\int\\sqrt{1+1/x}dx", + "9947b10cfe6af87a.png": "J_{1}(x)=x/2\\sqrt{2}", + "9949d57c38cfe5a3.png": "\\varphi\\vee\\psi", + "994f3201889f4e0e.png": "\\sqrt{3}", + "99542dbc4ba58b68.png": "\\tilde{f}=|\\frac{\\tilde{d}}{2}|", + "99563a64e5251d45.png": "|pp^{\\prime}|\\le(2/s)|pq|", + "9957041fbf0216ba.png": "\\nu=\\frac{\\partial V}{\\partial\\sigma}", + "995cd1e44f7cc653.png": "z_{i=1...N},x_{i=1...N}:", + "99602fd8f0687e5d.png": "\\frac{d}{dt}(\\frac{\\partial L_{1}}{\\partial\\dot{\\alpha}})=\\frac{\\partial L_{1}}{\\partial\\alpha}", + "99630ddab4d4c29f.png": "{(1+{(\\frac{x}{b})}^{-a})}^{-p}", + "9965f4a8a752c055.png": "\\int_{a}^{x}f(t)dt=0", + "996b5e703c4d4917.png": "\\prod B_{i}", + "996d6196c96e6ef5.png": "a\\in Z^{-}", + "9977eb40d6d1eadc.png": "\\underline{x}^{-k}", + "997e1af84809bb2b.png": "f(z)=\\frac{1}{(z^{2}+1)^{2}}", + "997e44c165ebfaf9.png": "sup_{|z|<1}|\\mu(z)|<1.", + "9987e072d7da093b.png": "(\\begin{matrix}n\\\\ t\\end{matrix})", + "9988131b96d3236e.png": "M\\in M_{k}\\cup M_{k+1}", + "998b2272b39bfad4.png": "L=\\int_{S_{o}}^{S}nds", + "998d85ef3b465abf.png": "g_{00}=1+\\frac{2\\varphi}{c^{2}}", + "998f678ce2a3cd9b.png": "\\tilde{B}_{k}(x)", + "999765147fb0284f.png": "\\int_{X}f(x)dx", + "999b0c60b45bd2ee.png": "\\sum_{k=1}^{\\infty}(\\frac{1}{k^{3}})", + "999b9608036095ea.png": "s\\notin T", + "999c1739b12e3e65.png": "G=\\int_{0}^{T}S(t)x(t)dt", + "99a75ddaa2e604d0.png": "12\\sqrt{25+10\\sqrt{5}}", + "99b0166f19c07983.png": "\\iint f(x,y)dxdy", + "99b8d8859823ddd5.png": "(\\begin{matrix}-1\\\\ 0\\end{matrix})=1", + "99bea285c8ff5f73.png": "x_{n+1}=x_{n}^{2}modM", + "99bfdb635dec0bc7.png": "h(z)=h_{1}(z)(z-c)", + "99cb5c6cd64c9748.png": "A\\overline{D}", + "99cd4ae36492732e.png": "\\tilde{f}_{0}:X\\rightarrow E", + "99ce1910afcffa6f.png": "\\Pi_{i=1}^{n}(X_{i}+1)", + "99d23f802da1194e.png": "(A-\\lambda I)^{k_{1}-1}", + "99d6b466e3f7aca3.png": "Ff\\in L^{1}(R^{n})", + "99d9f553a3fcb6cf.png": "r=d(x/(y-x))", + "99dd81b291d964f6.png": "\\Omega:=O(F)", + "99e4d59aa1e93721.png": "r^{(\\delta_{\\rho})}", + "99e4dda048bc3cc8.png": "\\tilde{C}", + "99ec07e100b681b2.png": "l_{OB}\\cdot l_{OD}=k^{2}", + "99eda0adc57f2a9b.png": "\\tilde{X}^{n}", + "99f1a8f73b6a934c.png": "4\\sigma/\\sqrt{n}=W", + "99f3b148c238b80e.png": "\\Psi=\\frac{E^{*}h^{\\prime}}{\\sigma_{0}}>\\frac{2}{3}", + "99f84560f0128940.png": "\\tilde{a}", + "99ff554b744e23b9.png": "(\\begin{matrix}5\\\\ 1\\end{matrix})=1\\times\\frac{5}{1}=5", + "9a0c41dbf774af74.png": "\\prod_{x}f(x)", + "9a0c4c8495672732.png": "\\Phi=e^{B+i\\omega}\\Omega", + "9a0d0b83dedeedbd.png": "f^{*}=\\prod_{k=1}^{n}(X-\\alpha_{k}^{*})", + "9a10c3e6c83e9e31.png": "e_{m+1}=\\sum_{i=1}^{m}c_{i}e_{i}", + "9a1270cc6e887be1.png": "(\\begin{matrix}1&0\\\\ 0&\\frac{n_{1}}{n_{2}}\\end{matrix})", + "9a13d65b87a72780.png": "C_{1}=C_{2}=C>0", + "9a14b8fd7fa19518.png": "L_{f,P}\\le R\\le U_{f,P}", + "9a1508863a3affde.png": "\\{P_{\\alpha}[\\cdot]\\}", + "9a18755ad5376f03.png": "\\frac{dN}{dT}", + "9a18bf0997a1bcf7.png": "-{\\alpha_{o}}^{\\prime}x_{i}", + "9a19033d78b47eac.png": "60", + "9a1d38c2750d7fc1.png": "S^{*}=\\frac{S-S_{B}}{S_{T}-S_{B}}", + "9a1e9dd6b09e3f60.png": "H_{k}\\equiv\\frac{2K_{u}V}{\\mu}", + "9a23a1e53be589df.png": "\\epsilon\\sim exp(1)\\cdot q_{sig}\\cdot\\epsilon^{\\prime}", + "9a28929fa62c5bca.png": "t=\\frac{d}{dx}", + "9a2a50c8c6c50195.png": "\\tilde{A}_{7}", + "9a2f8edea4dc946a.png": "\\int_{E}f(t)d\\mu(t)", + "9a33583c71a6408d.png": "\\int_{a}^{b}f(x)dx", + "9a34508c6107498e.png": "\\omega_{a}=\\frac{me^{4}}{(4\\pi\\epsilon_{0})^{2}\\hbar^{3}}", + "9a34e9b1518df0b9.png": "(8d)^{d}\\cdot15^{d\\cdot2^{2d+1}}", + "9a46a26a185237a1.png": "\\kappa_{d}=R_{d}/c_{pd}", + "9a470328b1a4113c.png": "\\hat{g}(f)", + "9a48df47af48ba89.png": "max|x_{i}-m|", + "9a49f4e6167cf223.png": "\\frac{df}{dz}=f", + "9a5091301ce84522.png": "Df=0", + "9a5180fdf17f56f5.png": "\\prod_{k=1}^{n}k", + "9a54bcafe4b75ca8.png": "\\vec{n}_{0}=\\frac{\\vec{n}}{|\\vec{n}|}", + "9a642518277cf2ad.png": "-u^{\\prime\\prime}=f", + "9a64d0219d8876db.png": "1019(4.163\\%)", + "9a68a994ce9933cd.png": "\\vec{b}=(b_{0},...,b_{L-1})", + "9a6b07f3df948724.png": "P(t)=e^{tQ}", + "9a6d0f28a58a04b4.png": "\\frac{\\delta}{2\\pi}\\lambda=2dsin\\theta", + "9a6de0f72bc21458.png": "\\alpha\\le\\zeta_{1}=\\phi_{2}(1)", + "9a723520aae79309.png": "X_{n}=M^{n}X_{0}", + "9a73160798847629.png": "\\tilde{r}_{E}", + "9a7528041e219c28.png": "M_{ij}=\\int v_{i}v_{j}dx", + "9a759d94d5a71662.png": "\\omega^{2}=\\omega_{p}^{2}+k^{2}c^{2}", + "9a7d34a71068a71f.png": "x\\dot{=}0\\rightarrow x\\dot{=}0", + "9a7e490bedd418cb.png": "\\vec{u}=(u_{1},...,u_{s})", + "9a7ec86a8cbd4c71.png": "T_{e}\\gg T_{i}=T_{gas}", + "9a7f5e90f6d5f5d5.png": "\\{\\begin{matrix}3\\\\ 5/2\\end{matrix}\\}", + "9a7fe72a03699423.png": "G^{i}=[G^{i-1}]_{\\delta\\sigma}", + "9a8fb338bb849d06.png": "I:C\\rightarrow C[E]", + "9a900a0c653757f1.png": "\\hat{R}_{m}", + "9a94a23a80cfbaca.png": "K_{+}\\subset K_{+0}", + "9aa2950e322dd098.png": "y=\\sqrt{Ax^{2}+B}", + "9aa57eba87c6e75e.png": "\\langle x,0\\rangle=\\langle0,x\\rangle=0", + "9aa80dd6f7c98d46.png": "Z=\\sum_{j}g_{j}\\cdot e^{-\\beta E_{j}}", + "9aaa9a57e17cc19d.png": "x(\\underline{n})", + "9aab1eeaa89c7d61.png": "{R^{2}}_{323}=\\frac{-1+g^{2}}{r^{2}g^{2}}", + "9aacda4710099280.png": "(\\begin{matrix}0&-1\\\\ 1&0\\end{matrix})", + "9aaf6bf4af4bcb11.png": "(\\begin{matrix}13\\\\ 4\\end{matrix})", + "9aaf763c7c8fd6e5.png": "I^{i+j+1}", + "9ab105329b5a6a6a.png": "T_{h,i}-T_{c,i}", + "9ab1289a5eaeac89.png": "\\dot{w}=\\frac{\\partial w}{\\partial x}", + "9ab3e8925ab487d3.png": "(\\hat{K}+\\lambda nI)^{-1}", + "9ab7cc05b9caa795.png": "\\tilde{\\rho}", + "9abd6ebf754c4424.png": "\\hat{H}=\\hat{H}(\\hat{P})", + "9abe0fda0a363a0b.png": "H_{*}^{?}", + "9ac51e7f496fc837.png": "|1\\rangle=(\\begin{matrix}0\\\\ 1\\end{matrix})", + "9ac5f4643bb515b7.png": "s\\{\\begin{matrix}8\\\\ 3\\end{matrix}\\}", + "9ac62b8b5c21ebc6.png": "(\\frac{d}{dt})^{2}x", + "9ac9404068724a28.png": "E=\\sum_{i=1}^{n}\\dot{q}_{i}\\frac{\\partial L}{\\partial\\dot{q}_{i}}-L", + "9acb32f589c85be1.png": "S\\subsetneq\\underline{m}", + "9ace62804d532661.png": "7=(3-\\sqrt{2})(3+\\sqrt{2})", + "9acfdde838762be7.png": "\\overline{A}=X", + "9acffd5ee638252f.png": "L_{j}=inf_{k\\ge j}M_{k}^{1/k}", + "9ad44f07e9531df6.png": "\\frac{dR}{dP}=0", + "9ad455ce126d99ed.png": "\\frac{dy}{dx}=xy", + "9ad842e9ca9e3414.png": "g:=k\\oplus m", + "9ae0a1d25b517ffb.png": "PB-C=\\sqrt{\\gamma}Q", + "9ae55ed5f4fdc5ef.png": "e^{1/2}=\\sqrt{e}", + "9ae5891872b8c30d.png": "E_{Y}(E_{X|Y}(X|Y))", + "9af27994f64d9864.png": "a\\notin w", + "9af5cf219df68fd6.png": "\\tilde{A}_{6}", + "9af5fa969f72159d.png": "\\frac{\\partial^{2}\\phi}{\\partial x^{j}\\partial x^{j}}=4\\pi G\\rho", + "9af73b8bb7ca9931.png": "\\tilde{C}", + "9af792c895271e59.png": "\\mu=\\frac{N}{2}+1", + "9afae633b335fd42.png": "\\frac{1}{2}[X(z)+X^{*}(z^{*})]", + "9afd30889d09cab9.png": "\\frac{d}{d\\epsilon}C(\\phi^{\\epsilon})|_{\\epsilon=0}=0", + "9afd7598454fe1cc.png": "V=(\\begin{matrix}0&1\\\\ 1&0\\end{matrix})", + "9affa6118e781261.png": 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"[\\begin{matrix}lnx\\\\ x\\end{matrix}]", + "9b64b75fb141ddf2.png": "(0,0,0,1)", + "9b675c143476c5e9.png": "J(x)\\in(X_{\\beta}^{\\prime})_{\\beta}^{\\prime}", + "9b6760e6936f3bd2.png": "\\Sigma_{f}(r,E^{\\prime},t)", + "9b711752fa21319c.png": "||.||_{1}=||.||_{\\infty}", + "9b77a837109747f8.png": "\\tilde{\\nu}=\\tilde{\\nu}_{vib}\\pm BJ(J+1)", + "9b7a856bc2e80445.png": "\\tilde{O}(log^{4}q)", + "9b859aeb2d7dc132.png": "\\lceil\\chi_{c}(G)\\rceil=\\chi(G)", + "9b88b97858fa33c2.png": "3^{\\frac{\\pi+e}{4}}", + "9b93d2a9c908d71d.png": "y(t)=\\int_{0}^{t}dy(r)", + "9b959002eb3afc68.png": "\\overline{n}_{4}", + "9b96179b21672704.png": "\\frac{\\partial}{\\partial x}", + "9b96921ec5b4b2e1.png": "(\\begin{matrix}n-p\\\\ k-i\\end{matrix})(\\begin{matrix}p\\\\ i\\end{matrix})/(\\begin{matrix}n\\\\ k\\end{matrix})", + "9b98781796b8197e.png": "\\Omega_{0},\\cdot\\cdot\\cdot,\\Omega_{2T}", + "9b9deff9418ffac3.png": "\\vec{V}\\cdot\\nabla\\psi=0", + "9ba5b0d52c0fff1f.png": 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1\\end{matrix})", + "9bf1ef99102b8544.png": "E[\\hat{y}]", + "9bf7c2480397c3a4.png": "(\\pi_{n}(t);n=1...N)", + "9bfc4089d648e584.png": "(\\begin{matrix}n-p\\\\ k-i\\end{matrix})(\\begin{matrix}p\\\\ i\\end{matrix})/(\\begin{matrix}n\\\\ k\\end{matrix})", + "9c086577dae437e5.png": "\\prod_{i=1}^{k}p_{i}^{(n_{i}+1)}", + "9c0a60c1df3af482.png": "0=E\\{(\\hat{x}-x)y\\}", + "9c0dc7613c66c5ca.png": "f=\\sqrt{h^{2}+(a+b)^{2}}", + "9c10f24bfa659f5e.png": "ss\\{\\begin{matrix}2\\\\ 2\\end{matrix}\\}", + "9c1831d434d18634.png": "F=S\\int udt", + "9c1950dcae2e039b.png": "Pr(max_{i>1}v_{i}0", + "9c1dbfc6aa16412d.png": "n", + "9c37d0b54841b537.png": "l_{0}=[L_{0}:L_{1}:L_{2}]", + "9c39c6de3bdab95f.png": "\\frac{d}{dx}", + "9c46665b33dfa66a.png": "\\hat{\\alpha}=\\delta/\\sqrt{1-\\delta^{2}}", + "9c46cd5b011aaef6.png": "\\frac{dI}{d\\alpha}=-\\pi", + "9c494dc44266acd9.png": "X=v_{M}/(\\sqrt{2}\\sigma)", + "9c4d2bbbab61b5f3.png": "\\gamma_{total}=\\gamma_{1-l}+\\gamma_{l-2}", + "9c4d6ae50ef1ed1d.png": "4x+3y=17", + "9c5343622bf225e0.png": "J_{-}=J_{x}-iJ_{y}", + "9c5aecfc421153db.png": "cos\\nu=\\frac{d_{1}-d_{2}}{2a}", + "9c6726e9b5149c9d.png": "a(x-r_{1})(x-r_{2})", + "9c6a00dff258205b.png": "Y_{t}=\\int_{0}^{t}H_{s}dX_{s}", + "9c7527887087b5e8.png": "\\hat{g}(f)", + "9c7a97f1958e5353.png": "\\frac{d}{dx}7", + "9c7be2e3c6438c04.png": "\\int vdp", + "9c80604ff5a75621.png": "log_{4}(8)=\\frac{3}{2}", + "9c87cbf04a714d21.png": "d=|(I_{t}-\\mu_{t})|", + "9c8c47afd5af0ed0.png": "\\tilde{n}", + "9c8c499769fe6fd4.png": "\\int_{\\Omega}u_{j}u_{j}=1", + "9c8cfc1a73956020.png": "-\\int E\\cdot dl", + "9c935529e8e59e6a.png": "(\\begin{matrix}9\\\\ 4\\end{matrix})", + "9c9610e8b09c6ee8.png": "\\int cos(x^{2})dx", + "9c97d7965743fb12.png": "\\bigcup_{i}F_{i}(\\lambda)=I(\\lambda)", + "9c9a4c27bc35b70f.png": "x_{n+1}o+0.0005329", + "9d3bc89817c497c9.png": "\\tilde{E}_{7}", + "9d3bfdb727e282bd.png": "[\\begin{matrix}-1&0\\\\ 0&1\\end{matrix}]", + "9d4a409dab2a6ff6.png": 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"9dac4d9cfbd92283.png": "\\frac{1}{q}=\\frac{1}{R}-j\\frac{\\lambda}{\\pi w^{2}}", + "9dad1e4bacef1c74.png": "(\\begin{matrix}n+2\\\\ 2\\end{matrix})-2n-1", + "9dae7e1b062cc166.png": "c=\\frac{d}{t}", + "9daffe68275261f3.png": "S_{G}^{j}(k)=\\frac{d_{G}^{j}(k)}{k}", + "9db54e3d23dff33c.png": "4\\times(\\begin{matrix}6\\\\ 2\\end{matrix})", + "9db7538e341ca6d8.png": "\\frac{1}{n^{3}-n}", + "9dba932cbe431945.png": "|f_{n}(x)|\\le g(x)", + "9dbbe77227e52358.png": "x^{\\underline{n}}", + "9dbe84d42beb8ab8.png": "\\int_{0}^{360}", + "9dc79576efd4b3ae.png": "C_{x}\\rightarrow C^{\\infty}(S_{i})_{x}", + "9dccaf3f6c52d21a.png": "f_{\\xi}(x)=\\langle\\xi|\\pi(x)\\xi\\rangle", + "9dcf92b14ff15408.png": "\\hat{p}=1", + "9dd05487a4c275db.png": "T_{n}n!=n^{n-2}n!", + "9dd11c1c87e73aa0.png": "(\\begin{matrix}1&1\\\\ -a&-c\\end{matrix})", + "9dd1d2ebe73c8d6a.png": "C_{0...m_{j}...0}", + "9dd3333940a497be.png": "\\langle Ff,\\varphi\\rangle:=\\langle f,F\\varphi\\rangle", + "9de33257e61f94af.png": "\\hat{u}_{R}", + "9de7c63b10484488.png": "P\\cdot P=(mc)^{2}", + "9df134ca76703279.png": "||\\sum_{j}T_{j}||\\le\\sqrt{AB}", + "9df2261d6c860681.png": "|\\langle q|p\\rangle|^{2}=\\frac{1}{2\\pi\\hbar}", + "9df51e6a8554a825.png": "sin_{i}c1", + "9e706223ae77d009.png": "\\hat{u}_{R}", + "9e76adc99fd74eb7.png": "\\int_{0}^{L}ds", + "9e7cf94531f896a1.png": "E_{1}=Ae^{i(kx-\\omega t)}z", + "9e7f125280dc59cf.png": "H[w_{1},...,w_{n}]|J|", + "9e7ff002851b37e0.png": "\\tilde{\\Omega}", + "9e8574e94a15ff25.png": "r(\\underline{x},t)", + "9e8d9b20a3d5f83e.png": "f(x)=\\prod_{i=1}^{n}x_{i}", + "9e909307a9ab22d5.png": "[\\begin{matrix}k-1\\\\ -\\frac{1}{\\theta}\\end{matrix}]", + "9e9281a1c3c65fae.png": "\\varphi_{tt}-\\varphi_{xx}+\\varphi=0", + "9e93de52634d41f7.png": "a<_{s}ce(ab)<_{s}b", + "9e9f0fc1b52b8efb.png": "a=\\frac{4r}{\\sqrt{3}}", + "9ea16531916fd782.png": "(\\begin{matrix}k\\\\ r\\end{matrix})=0", + "9ea1dd7280648fb7.png": "\\tilde{V}", + "9ea6cc1f661a6d90.png": "\\hat{k}", + "9eaa3f24cf75e52c.png": "v\\rightarrow(-1)^{l(v)}", + "9eafff727e49fb02.png": "2\\le a\\le\\frac{(b+1)}{2}", + "9eb5cdce2524d62b.png": "K_{k}(\\tilde{M})", + "9ebb2dc94eace6d5.png": "\\frac{\\partial}{\\partial z}f(\\overline{z},z)", + "9ebfe51289e5aa8a.png": "j^{\\underline{m}}", + "9ec661b917b71866.png": "exp(-\\frac{t^{\\prime}-t}{t_{0}})", + "9ed843fd26527f3c.png": "\\tilde{A}_{4}", + "9ede30f06102a643.png": "\\Gamma_{R}=1-\\frac{6\\sum d_{i}^{2}}{n^{3}-n}", + "9ee741bedf92b9e4.png": "abc", + "9eef893d00cf816c.png": "\\nabla_{(\\alpha}K_{\\beta\\gamma)}=0", + "9ef814d7b8c63456.png": "\\underline{\\psi\\vee\\varphi}", + "9ef9ed6785dcd0ad.png": "\\hat{\\mu}_{i}", + "9efa73c7cd071a9b.png": "lim_{p\\rightarrow-\\infty}a_{p}=-\\infty", + "9efbf46bb51e41d8.png": "[f(\\theta_{i-1}),f(\\theta_{i})]", + "9eff5b2ba3b79b03.png": "d_{i}|d_{i+1}", + "9f0d89a14be63a2d.png": "N_{L/K}(L^{\\times})", + "9f0e8a09308e5aa8.png": "\\hat{u}_{k}", + "9f0e936d23328018.png": "d=(1/2)b_{2}", + "9f137c324fcea2fe.png": "E[uu^{\\prime}]=\\sigma^{2}I_{n}", + "9f20b993899ebfff.png": "(\\begin{matrix}n-1\\\\ t-1\\end{matrix})=r(\\begin{matrix}k-1\\\\ t-1\\end{matrix})", + "9f239345871f1d50.png": "\\langle\\frac{F}{||F||},\\frac{T}{||T||}\\rangle", + "9f2398122575e592.png": "\\frac{\\partial^{2}u^{2}}{\\partial x^{2}}", + "9f25873bbb061a2d.png": "c=\\sqrt{n}", + "9f266e8b1ba47ea1.png": "O(n^{c}),00", + "a02e4200a08cb9e7.png": "C^{\\varphi_{\\mu}}", + "a033c42c5183d9f1.png": "\\frac{1}{y}\\frac{dy}{dx}=ln2", + "a03b0e4e0059b2d3.png": "s\\{\\begin{matrix}2\\\\ 6\\end{matrix}\\}", + "a0450af35b187c98.png": "|z|^{n}<\\epsilon", + "a049ae4c756e2504.png": "\\frac{d^{2}u}{dt^{2}}=\\frac{\\Omega^{2}}{4}\\frac{d^{2}u}{d\\xi^{2}}(2)", + "a049b9938a529a51.png": "|\\varphi(s)|0", + "a05826cd0835f5fe.png": "1-\\frac{10^{3}}{11^{3}}=\\frac{331}{1331}", + "a065374b15a17b6e.png": "\\varphi=\\frac{d\\varphi}{dz}=0", + "a0684eaf9b814c18.png": "a\\frac{x^{n}-1}{x-1}=p", + "a0686f6a313fb86f.png": "j(\\{y\\in V_{\\alpha}|\\phi_{3}\\})", + "a068d4ffc92b28e4.png": "\\int f^{+}", + "a06d746f3ed8a822.png": "\\int_{0}^{L}ds", + "a06dc2d1c2097598.png": "(\\begin{matrix}2\\\\ 4\\end{matrix})", + "a07344f7264f6c48.png": "F(z)=F^{\\prime}(z)F^{\\prime\\prime}(z)", + "a07b9e22c28fd71b.png": "\\int_{-1}^{1}x^{-1}dx", + "a07bcdd2040ad648.png": "\\sqrt{m}", + "a07cd5ef1a8d8c34.png": "c=\\sqrt{n}", + "a08379889538b2b0.png": "2^{-r_{2}}\\sqrt{|\\Delta_{K}|}", + "a08389e82b9e88b3.png": "s=\\int\\frac{dt}{r(t)}", + "a08415262bfeb8b2.png": "\\tilde{L}_{i}", + "a094b10389357e09.png": "\\Gamma", + "a094dc2026e05f20.png": "G(y)=\\int_{0}^{y}g(z)dz", + "a098802291c0a79e.png": "\\mathbb{Q}:X\\notin\\mathbb{N}", + "a0a982ad1d04316b.png": "\\int xcosxdx", + "a0a99269786c2dbb.png": "\\int_{\\gamma}f(z)dz", + "a0aab38fc307983f.png": "-\\sqrt{\\frac{1}{70}}", + "a0ad6f9c5fd87cdb.png": "f:(-2,+\\infty)\\rightarrow R", + "a0aeea5f1e28e2ef.png": "y+2^{4}/y=17", + "a0b5d133448a2084.png": "\\frac{df}{f}=\\frac{dn}{(n-1)}=\\frac{1}{n}", + "a0b9a1edeceba539.png": "\\int\\frac{xdx}{r}=r", + "a0bd00b15d2967ba.png": "\\Delta(\\hat{\\Psi}^{\\otimes m},\\Psi_{id}^{\\otimes n})", + "a0c0460b76c71bd0.png": "n_{sp}=\\sum y_{i}", + "a0c3ea66d82c0383.png": "h=\\frac{\\sqrt{3}}{2}a", + "a0c81e909fd62e56.png": "\\gamma_{u^{x}}", + "a0c974edb61d3666.png": "\\hat{K}_{G}", + "a0d1d18bed9e9d05.png": "\\hat{q}", + "a0d21a34c43a7b63.png": "BI=j_{1}F_{L}", + "a0d51141057d055e.png": "\\int f(x)d\\alpha(x)", + "a0d721842cbbb804.png": "\\Lambda", + "a0db1d40178920ae.png": "2g+r-1", + "a0db905baecde166.png": "(\\begin{matrix}8\\\\ 4\\end{matrix})", + "a0e0999e37ea5915.png": "\\frac{\\partial u}{\\partial x}+\\frac{\\partial(-v)}{\\partial y}=0", + "a0ea93bc50292327.png": "\\lfloor log_{k}n\\rfloor+1(n>0)", + "a0ec15ec5b61c0b2.png": "S_{1}", + "a0f4a5bfbd95e97d.png": "\\{\\begin{matrix}3\\\\ 3\\end{matrix}\\}", + "a0f4c9e87847812a.png": "\\frac{dX}{dt}=AX", + "a0f70de518a9685a.png": "var(T)=\\frac{2n(\\sigma^{2})^{2}}{(n+2)^{2}}", + "a0ff27b917c563c4.png": "\\frac{1}{N}=\\frac{1}{\\sqrt{N}\\sqrt{N}}", + "a10435870dc7eace.png": "R_{1}R_{3}=\\frac{R_{a}R_{b}^{2}R_{c}}{R_{T}^{2}}", + "a104c029441b8bb8.png": "K(t)=logE[e^{tX}]", + "a1076e75f2246dfb.png": "K^{*-}", + "a111929639c4a6cc.png": "B_{e}=\\overline{B}(R_{e})", + "a1160ede435ce4c0.png": "[x_{0},...,x_{n}]f", + "a11a9b40fc6bdbdf.png": "(U_{\\alpha})_{\\alpha\\in A_{n}}", + "a11abd6cbc8f9e57.png": "\\frac{dM}{dt}", + "a11b5a63c2c35204.png": "\\overline{AH}", + "a125022efdf34376.png": "\\gamma_{\\mu}a/\\gamma^{\\mu}=-2a/", + "a1266828cbe142bc.png": "\\{[n,n+1]:n\\in Z\\}", + "a1291ece163e14f9.png": "H^{s/2}(R^{n})", + "a1336fc7385876a5.png": "[g,g]", + "a133e3e3af0ad203.png": "y=f(x_{1},x_{2},...)", + "a135d89c3de53859.png": "\\frac{\\sum_{i=1}^{K}\\lambda_{i}}{\\sum_{i=1}^{N}\\lambda_{i}}\\ge\\alpha", + "a136a312cc5e96a4.png": "\\beta=(g_{im}\\cdot1)/n", + "a13a8178821c11a2.png": "f(x)-a^{2}(x)", + "a13bf76d8ab3629b.png": "0.05H_{s}", + "a13cffa3b503948b.png": "\\int_{0}^{\\infty}f(x)dx", + "a13dba75e9d6d5ed.png": "F_{t,T}=S_{t}e^{r(T-t)}", + "a140870a69e474f7.png": "L_{v}=-g\\overline{\\psi}\\gamma^{\\mu}\\psi A_{\\mu}", + "a14326dd27368160.png": "T=\\frac{m\\overline{v^{2}}}{3k_{B}}", + "a144d76f81796c5f.png": "(\\begin{matrix}Z\\\\ I\\end{matrix})", + "a14bb5c3464001cf.png": "\\int x^{k}d\\mu(x)=m_{k}", + "a14c2dfc868030f7.png": "a:=(a_{0},a_{1},...,a_{n-1})", + "a158d06efa7fff66.png": "\\hat{F}(i)", + "a15ae7d0b3cd215b.png": "i_{c}^{z}", + "a15c193ce799011b.png": "\\hat{a}\\hat{U}|\\alpha\\rangle", + "a15fb31dfe457627.png": "D_{j}=-i\\frac{\\partial}{\\partial x_{j}}", + "a16068bd88859bbe.png": "(\\begin{matrix}1&0\\\\ -\\frac{1}{f}&1\\end{matrix})", + "a167c59cc0ae25f4.png": "(\\begin{matrix}p\\\\ k\\end{matrix})", + "a16ba5106011b459.png": "N=[\\begin{matrix}1&2\\\\ 2&1\\end{matrix}]", + "a16c59f14b12eb29.png": "x^{p^{2}},y^{p}\\in G^{\\prime}", + "a1709fc2d4cc04a4.png": "x^{10}+x^{7}+1", + "a1722de6453801ec.png": "\\sum_{m=-l}^{l}", + "a173c2721924efd0.png": "\\int_{-r}^{r}|y-s|dx", + "a174e71c9bf68faa.png": "(-1,0)", + "a17e6539f1608c70.png": "E\\rightarrow\\hat{E}^{+}", + "a17f50c28519b202.png": "\\overline{K}_{n}", + "a180402e05ee504f.png": "\\hat{T}_{f}", + "a18b6b31e03b24ac.png": "\\underline{S}", + "a18d19f71067ceaa.png": "KU_{*}BU(n)", + "a18e0efcaedca85b.png": "\\sum_{j}\\beta_{j}^{2}", + "a1909940921ed91e.png": "t\\{\\begin{matrix}5\\\\ 3\\end{matrix}\\}", + "a190fe74563866e1.png": "M=(\\begin{matrix}n\\\\ 2\\end{matrix})p", + "a199c8800cc148a0.png": "(\\begin{matrix}n-1\\\\ x-1\\end{matrix})", + "a19b3e20b567befd.png": "Q_{A}=10^{R_{A}/400}", + "a1a6348e84c9ff2e.png": "\\frac{1}{min_{i}h_{c}(O)-t_{i}}", + "a1aabca7669f3ad8.png": "\\sum_{n=0}^{N-1}Ae^{i\\varphi_{n}}=0", + "a1ab81d885e17543.png": "\\int f^{+}-\\int f^{-}", + "a1adeecc99c641da.png": "\\int sin^{2}xcos^{2}xdx", + "a1badbb8754c09f1.png": "\\sqrt{T}", + "a1c253f85b587804.png": "\\hat{w}", + "a1c6f5b9155ec0e7.png": "(\\tau_{1}^{-1},...,\\tau_{g}^{-1})", + "a1cb5e3c9f983be2.png": "\\sqrt{u_{x}^{2}+u_{y}^{2}}=c", + "a1d5f23269c4a995.png": "lim_{x\\rightarrow90}\\frac{sin(90-x)}{cosx}", + "a1d75a137792870e.png": "\\sqrt{64}", + "a1d9d4b9cdb9d6f0.png": "\\frac{1}{P_{syn}}=\\frac{1}{P_{1}}-\\frac{1}{P_{2}}", + "a1de4ccdab4579bd.png": "b=1+\\frac{0.477}{Pr}", + "a1dfee50bc53eaa5.png": "\\int u^{1/2}du", + "a1e45cebbccec933.png": "\\hat{\\mu}_{i}", + "a1e94834af4718aa.png": "(P,M)\\rightarrow^{*}M^{\\prime}", + "a1eb178ee5b2c4d3.png": "\\int dy-2y=\\int-dx", + "a1ef2daa6e3dcd6f.png": "\\sum_{i,j}a_{ij}(x)c_{i}\\overline{c_{j}}\\ge0", + "a1f0e6060cd5bbd9.png": "\\frac{\\partial Y}{\\partial\\beta}=Y_{\\beta}", + "a1f2231b75530f7e.png": "I\\models(a,b):R", + "a1f44b8e40a27a2d.png": "(I+1)(2I+1)", + "a1fb924c04c9b91d.png": "\\sqrt{3}a", + "a1ff40f50de7492e.png": "w_{-}=\\frac{c}{n}-v", + "a202c42668d440c2.png": "E[X_{\\tau}]\\ge E[X_{0}]", + "a207670054317321.png": "\\prod n_{i}", + "a212660d0894b519.png": "(q+1)-\\frac{q}{d}", + "a21b75ee2037157f.png": "\\frac{d^{2}y}{dx^{2}}+\\pi^{2}y=f(x)", + "a21db6695339356a.png": "H=21/4-7", + "a220e92d0e69c4ad.png": "P^{(k)}=\\sum_{i=1}^{k}U^{(n-i)}", + "a223bb02b2aa3c5a.png": "\\rho>2b/2D", + "a2269097652417e6.png": "0\\notin\\mathbb{N}", + "a226bed8c8a60158.png": "\\prod_{p^{k}|n}f(p^{k})", + "a22816cd0bcded59.png": "\\frac{1}{2}v^{2}=U(x)", + "a22b853b7d9aa749.png": "x=\\prod_{i}p_{i}^{e_{i}}", + "a22ec74538a44331.png": "ind(D)=\\prod_{i=1}^{r}p_{i}^{m_{i}}", + "a23b3b3580b10055.png": "K\\in C^{1}(R^{n}\\backslash\\{0\\})", + "a23c364b61228bd4.png": "\\frac{dt}{ds}=1", + "a23f43a0093e045c.png": "W=\\int P(V)dV", + "a24030525a0cebc8.png": "(\\begin{matrix}n+x-1\\\\ n\\end{matrix})", + "a24294150b445964.png": "La=\\frac{Re^{2}}{We}", + "a2457cef4d6d2a8c.png": "Y\\in R^{L_{1}\\times L_{2}\\times...L_{O}}", + "a2468e36ee5cb1a9.png": "W=N!/\\prod_{i}N_{i}!", + "a2493172a05ba49a.png": "f(x):=\\int_{0}^{x}\\omega", + "a24c4a623913acff.png": "D=2w_{0}\\simeq\\frac{4\\lambda}{\\pi\\Theta_{div}}", + "a24d7979b51ff410.png": "\\int_{a}^{b}f(x)dx", + "a24da63fb77e4f6b.png": "\\sum_{d|k}p_{n,d}=q_{n,k}", + "a257c7328ed56080.png": "a\\in A_{0}\\bigcap A_{1}", + "a25a6d6a8de3e8fd.png": "r\\dot{r}=-\\frac{\\kappa}{2}r^{2}", + "a25bd127231c5989.png": "I_{x}=I_{y}=\\pi r^{3}t", + "a261395ae3727584.png": "\\overline{p}-p=\\gamma\\nabla\\cdot\\hat{n}", + "a2629c764cc7b812.png": "E=\\gamma_{(u)}m_{0}c^{2}", + "a26324efe6d2a9cb.png": "2(\\mu,\\alpha_{i})/(\\alpha_{i},\\alpha_{i})", + "a264346b810e2e93.png": "\\{\\Omega_{x}^{(k)}\\}_{k=1}^{K}", + "a2688f755e2ea97a.png": "P(N(\\mu,\\sigma^{2}))", + "a27473cab2769c95.png": "3(16-8\\sqrt{2})r^{2}", + "a274d0affdba1dec.png": "\\overline{Y}=X", + "a277b471fbe2c37f.png": "\\{|2\\alpha\\rangle,|-2\\alpha\\rangle\\}", + "a2897e1ea491cadb.png": "G", + "a290d47ece87ba07.png": "=B_{ik}B_{jl}\\overline{T_{kl}}", + "a292536102a061ef.png": "r=\\{\\begin{matrix}p\\\\ 2\\end{matrix}\\}", + "a2933ed23d44035f.png": "1^{1}\\cdot2^{2}\\cdot3^{3}", + "a295769f899ed883.png": "\\frac{p}{q}\\cdot\\pi^{2m}", + "a298b09be529bf07.png": "\\chi(F(n))=P(n)", + "a29da6ea6597cb93.png": "V(x)=-\\int w(x)dx", + "a2a574fdefe092bd.png": "L\\subseteq\\bigcup_{q=2}^{\\infty}V_{n,q}", + "a2a5a0957d393b63.png": "2g+r-1", + "a2a6f5df0a0444d4.png": "\\frac{dx}{dt}=c", + "a2a7fc98ec8d2a9a.png": "(-ln\\hat{G}_{X})>0", + "a2a945369f926ce3.png": "\\frac{1}{c^{2}}u_{tt}=u_{xx}+u_{yy}", + "a2ac708d81dc9c9f.png": "\\overline{x}_{i}", + "a2ad740928415bad.png": "log_{4}(8)=\\frac{3}{2}", + "a2b1ae89a6c1cc38.png": "\\hat{f}(k)", + "a2bd1d9440377e0c.png": "\\int_{a}^{x}f(t)dt=0", + "a2c00a5b275c174a.png": "|x|\\le1,|y|\\le1", + "a2c19ecbd3edf41c.png": "t=\\frac{X_{o}^{2}}{B}+\\frac{X_{o}}{B/A}", + "a2c76fce1e1d0727.png": "M\\int vds", + "a2c81638d4020b3a.png": "\\int ln(3x-5)dx", + "a2cab5a18766be15.png": "||C_{h}f||^{2}\\le||f||^{2}", + "a2cefb5c31367dde.png": "R_{\\eta}^{5}", + "a2d03440ee701ec4.png": "\\hat{f}(3)", + "a2d1cdf9aaa5b058.png": "\\hat{b}_{i}", + "a2d65377a47930d3.png": "\\underline{a}", + "a2db6efb7933a836.png": "y=x^{2}\\iff x=\\sqrt{y}", + "a2dfe707ef71244c.png": "x_{0}\\gamma_{2}", + "a4298fbb0719e33f.png": "y=\\sqrt{x^{2}-|w|^{2}}>0", + "a42de82dd1130ba1.png": "(\\begin{matrix}a&b/2\\\\ b/2&c\\end{matrix})", + "a42f6baad1b75ef6.png": "\\int_{t1}^{t2}Ldt", + "a43076974c2f6c04.png": "deg(f,\\overline{\\Omega},p)\\ne0", + "a4354a7b6e64687a.png": "A=n\\sqrt{\\frac{m}{2\\pi kT}}", + "a4375f8af8137a01.png": "\\tilde{A}_{n}", + "a437cdb27c5c026d.png": "\\lambda^{3}=(\\begin{matrix}1&0&0\\\\ 0&-1&0\\\\ 0&0&0\\end{matrix})", + "a43b90fdc685c461.png": "\\rho^{\\otimes n_{1}},\\rho^{\\otimes n_{2}},...", + "a43d1c09a03c52ad.png": "\\int_{a}^{b}f(x)dv(x)", + "a43d7ea2c1435ba8.png": "(S,\\pi,K_{1},...,K_{n})", + "a440f9c3ff704d3d.png": "M\\int vds", + "a447ac46b9297573.png": "\\hat{\\beta}\\pm2.5se_{\\beta}", + "a4492edb16488759.png": "\\{c_{P}|c_{P}\\ne0\\}", + "a44ba08f7796f83a.png": "z^{X}=\\prod_{x\\in X}z_{x}", + "a452b075bae262bb.png": "(\\begin{matrix}N\\\\ 2\\end{matrix})", + "a453b229aecf090e.png": "g(x)=\\int_{0}^{x}f(t)dt", + "a454c480639296b7.png": "r(0)=r_{0}\\in R^{2N}", + "a454eecd09fe0df0.png": "Q=[\\begin{matrix}0&0\\\\ S^{0}&S\\\\ \\end{matrix}]", + "a4568ad624cfeb9e.png": "N^{O(loglogN)}", + "a458373d8ad07572.png": "R^{n|n}", + "a45a1a8894f4ec1b.png": "C_{XY}^{\\pi}=C_{X|Y}C_{YY}^{\\pi}", + "a45a546ea4803704.png": "\\tilde{z}", + "a4601eed9efe146d.png": "t\\equiv\\sqrt{1-1/\\xi^{2}}", + "a462fe7f305233e7.png": "3/\\tilde{4}", + "a465a082d0fa7ef6.png": "F(x)=\\int f(x)dx", + "a46a2c2cfc108204.png": "(\\begin{matrix}n\\\\ k\\end{matrix})_{q}", + "a46d17c861239c71.png": "\\int_{p}fdx", + "a474c8be2d62be4c.png": "\\Theta=tan^{-1}(m/k)", + "a47ab490430e0c7c.png": "\\{[n,n+1]:n\\in Z\\}", + "a47b20d9fdb923bc.png": "-\\frac{1}{10}\\pi^{2}-ln^{2}\\phi", + "a4857771dcd611de.png": "\\oint F\\cdot dl=0", + "a488d31d3607cfb2.png": "F=\\prod_{i=1}^{m}F_{i}", + "a492223d5cc6444f.png": "F[y]=\\prod y", + "a49e65eacf863e0d.png": "a^{\\prime}=\\frac{dv^{\\prime}}{dt}=a", + "a49f2cf418668b0e.png": "\\tilde{y}=\\tilde{w}=h(\\tilde{X})-\\tilde{Y}", + "a4a2403ce56016a6.png": "\\varphi(x,y)=\\overline{\\varphi(y,x)}", + "a4a72ff67314c332.png": "P^{D}(\\tilde{t}_{i})", + "a4ab4562ea80667e.png": "\\tilde{p}=\\frac{r}{r+k}", + "a4ab5225d34c1c82.png": "\\overline{2}", + "a4acda3964b6439b.png": "k_{\\lambda}e_{i}k_{\\lambda}^{-1}=q^{(\\lambda,\\alpha_{i})}e_{i}", + "a4b121f369c67a3d.png": "lim_{a\\rightarrow\\infty}\\int_{[-a,a]^{n}}f", + "a4b3ca2a3919f095.png": "(O\\underline{A}\\rightarrow\\underline{A})", + "a4b7d16078c1ed03.png": "\\hat{j}", + "a4baefc05275d482.png": "(\\begin{matrix}2&-2\\\\ -2&2\\end{matrix})", + "a4c16ec22ab4292e.png": "AB=(\\begin{matrix}4&6\\\\ 6&2\\end{matrix})", + "a4c47f6f727c753d.png": "r=b_{0}b_{1}b_{2}...", + "a4c62b5df68ecb9e.png": "B=10log_{10}(b)", + "a4cba914e8d36505.png": "\\dot{Y}=\\alpha(v-s)Y", + "a4cd6b8188236e43.png": "\\tilde{Y}^{n}", + "a4d1200de2992de3.png": "\\overline{12}_{24}+\\overline{21}_{24}=\\overline{9}_{24}", + "a4d258a69b71a988.png": "\\Xi_{q}^{z}", + "a4d3e5169f717c86.png": "\\vec{F}\\cdot\\vec{v}\\ne0", + "a4d760c4f8245bef.png": "\\sqrt{2}\\sqrt{2-\\sqrt{2}}", + "a4df056a502107d4.png": "\\alpha\\le\\zeta_{1}=\\phi_{2}(1)", + "a4e53664509c8ca7.png": "\\sqrt{rs}", + "a4e55a862b3c7a54.png": "y=\\int\\frac{dy}{dx}dx", + "a4e65b3a19ce70ef.png": "\\hat{X}^{n}", + "a4e6eff65d884de9.png": "\\forall p\\forall x(x\\notin p)", + "a4f0e513bee4e846.png": "(\\begin{matrix}n\\\\ a\\end{matrix})0)", + "a68fd0fa52c28a90.png": "i\\notin x", + "a691c66bc63fd62d.png": "\\int\\frac{dx}{x}", + "a6989ef8acb6990d.png": "\\gamma_{\\chi}^{\\mu}", + "a69912b90bee46ce.png": "|f_{n}^{\\prime}|>1", + "a6abb8cfaace58b1.png": "n=\\int fd^{3}v", + "a6adffce65eaf0af.png": "\\int_{0}^{\\infty}\\frac{sin^{2}x}{x^{2}}dx=\\frac{\\pi}{2}", + "a6b5abc71562eddb.png": "[\\begin{matrix}x\\\\ x^{2}\\end{matrix}]", + "a6b7c9107dd38c08.png": "\\frac{1}{2}(a+b)c_{0}", + "a6b8f34fae68b00a.png": "11-\\frac{\\sqrt{274}}{2}", + "a6bbc6b4a3fc4fde.png": "\\omega_{N}^{n}=e^{-\\frac{2\\pi i}{N}n}", + "a6bda8135229dfde.png": "\\tilde{E}=E\\times\\mathbb{Z}_{n}", + "a6bdcf80c10726b4.png": "(1)G(x,u,p)=0", + "a6beca9d1b880e73.png": "\\tilde{u}\\in L^{2}(\\mathbb{R}^{n})", + "a6c87b909dd3244d.png": "(\\begin{matrix}n-1\\\\ k\\end{matrix})", + "a6c9634a0058fa94.png": "p_{i}=\\frac{\\partial S}{\\partial q_{i}}", + "a6cf0a1bc226faa1.png": "\\tilde{B}_{7}", + "a6cf1797ab2cfa17.png": "\\%=0", + "a6d0341dec35653b.png": "(\\begin{matrix}n\\\\ k\\end{matrix})+(\\begin{matrix}n\\\\ k-1\\end{matrix})=(\\begin{matrix}n+1\\\\ k\\end{matrix})", + "a6d216e0ebf8c3b3.png": "\\int_{S}\\vec{B}\\cdot d\\vec{S}=const", + "a6d6145c313abac9.png": "S^{n}\\subset R^{n+1}", + "a6db5d4193fcbb3a.png": "\\tilde{V}_{i}^{b}", + "a6de10010653d725.png": "(\\begin{matrix}a&b&b\\end{matrix})", + "a6e912ed9d1e7c86.png": "\\hat{H}=\\hat{H}(\\hat{P})", + "a6f3f5fbabdefe5d.png": "\\hat{\\nu}", + "a6f926836ad6833e.png": "\\int\\Psi\\Psi^{*}dV=N_{s}", + "a6fc9015843cc8a4.png": "[\\begin{matrix}H&H\\\\ H&-H\\end{matrix}]", + "a70753c5c3a766ac.png": "(\\begin{matrix}v&0\\cdot\\cdot\\cdot0\\end{matrix})", + "a70ad28d938019b2.png": "c_{H}\\ge\\frac{T}{\\chi_{T}}(\\frac{\\partial M}{\\partial T})_{H}^{2}", + "a70c43923d307a4c.png": "\\infty k\\delta(s)\\hat{z}", + "a713efd610f3114b.png": "c=\\sqrt{n}", + "a71e52627b5b50ed.png": "\\beta((X_{\\beta}^{\\prime})^{\\prime},X_{\\beta}^{\\prime})", + "a728d50726ad3cea.png": "n=[\\begin{matrix}0&1\\\\ 1&0\\end{matrix}]", + "a72ed80282387aa9.png": "\\frac{n^{log_{a}(b)}}{f(n)}\\in\\Omega(n^{\\epsilon})", + "a73104d7400153e6.png": "(10x+7)dx", + "a7376392beedae87.png": "S=\\int_{0}^{T}E[s(t)^{2}]dt", + "a73d23e4ab1a282f.png": "[2^{\\frac{N}{j+1}},2^{\\frac{N}{j}}-1]", + "a73fa92f862d50e9.png": "\\int_{-\\infty}^{+\\infty}\\frac{1}{2}e^{-|y|}e^{ty}dy", + "a740a318caa395f1.png": "d\\eta_{V}=\\omega_{curl(V)}", + "a741cb986db60c04.png": "\\mathbb{O}", + "a746df851f01b3b2.png": "\\int_{a}^{b}(f(x))^{2}dx", + "a74a97f71ace32f8.png": "\\frac{\\sqrt{\\frac{(d_{1}n)^{d_{1}}d_{7}^{d_{7}}}{(d_{1}n+d_{7})^{d_{1}+d_{7}}}}}{nU(\\frac{d_{1}}{7},\\frac{d_{7}}{7})}", + "a74d1ab192ae4e48.png": "\\int_{t1}^{t2}Ldt", + "a758e59565b92226.png": "\\frac{n\\cdot(n-1)}{2}", + "a7637e1c916ef487.png": "\\vec{r}=[\\begin{matrix}0\\\\ 0\\end{matrix}]", + "a7665543bf2cb3ad.png": "S_{r^{*}}^{\\prime\\prime}(r^{*})<0", + "a76d2c3591a2f9e3.png": "S=\\int_{M}BF", + "a770875faf168333.png": "\\tilde{h}_{u},\\tilde{h}_{d}", + "a77345a353faa465.png": "lim_{t\\rightarrow\\infty}\\overline{x}(t)", + "a77cfdd955e9b33e.png": "\\alpha=-\\frac{log\\frac{\\Upsilon_{\\varsigma_{0}}}{\\Upsilon_{\\varsigma_{2}}}}{log\\frac{\\varsigma_{0}}{\\varsigma_{2}}}", + "a7818c285c5bde68.png": "\\tilde{u}(x)", + "a792ff2f721385f4.png": "\\int_{C}=0", + "a793f179faa687cd.png": "\\overline{P_{e}}=\\sum_{j=1}^{k}p_{j}^{2}", + "a797a010c8f14548.png": "d\\tilde{n}/d\\eta", + "a798362f614f9a6b.png": "J_{0}(u_{n}r)", + "a79d730f6ce6e9d7.png": "\\nu=c|k|/(2\\pi)", + "a7a146eedcd4b878.png": "\\sqrt{\\sum_{i}(x_{i}-\\overline{x})^{2}}", + "a7a78a88bc289f59.png": "e_{\\delta}^{\\alpha}", + "a7a8baae8a02348f.png": "(1|1)", + "a7ab891cc37738fd.png": "(\\begin{matrix}12\\\\ 5\\end{matrix})", + "a7ae6c0a8d8a3177.png": "p_{i}|\\phi_{i}\\rangle", + "a7b1693f52aaabcb.png": "\\tilde{G}_{n}", + "a7b2c3b992b44923.png": "\\frac{dx}{du}du", + "a7b4e65d757ebd65.png": "Gr/Re^{2}\\gg1", + "a7b6eb9d32532766.png": "\\Delta P=f\\frac{L}{R}\\rho u^{2}", + "a7bb9ea434e04237.png": "\\{\\begin{matrix}3,3,3\\\\ 3,3,3\\end{matrix}\\}", + "a7bdc944871f12f5.png": "\\hat{D_{B}}", + "a7c0d72bb0bb76de.png": "x^{2}+\\frac{b}{a}x+\\frac{c}{a}=0", + "a7c27a9cf7276826.png": "F(x)=\\int ln(f(x))dx", + "a7c48282bf4da8da.png": "Y^{T}A_{i}Y\\sim\\sigma^{2}\\chi_{r_{i}}^{2}", + "a7c872a9ec8f9835.png": "1.96x^{2}+19.6x", + "a7ccbaa453dd7543.png": "(x\\otimes y_{1})\\oplus(x\\otimes y_{2})", + "a7d183f2f889b421.png": "\\oint dS=\\oint\\frac{dQ}{T}=0", + "a7daa1bdd7955827.png": "M=[\\begin{matrix}0&1\\\\ -1&0\\end{matrix}]", + "a7e0eea73aca2303.png": "\\{A_{l}\\}", + "a7e2628d2426f2fa.png": "[h_{i},f_{j}]=-c_{ij}f_{j}", + "a7e8bd735afc77a0.png": "\\partial C/\\partial Y_{d}=b", + "a7ecb0635ad2e037.png": "\\overline{X}_{2}", + "a7ed4a344f19679d.png": "S_{s}Z^{2}\\subseteq Z^{2}", + "a7efadac78026bf7.png": "\\underline{AB}", + "a7f055df7a4abf3d.png": "2\\sqrt{2}", + "a7f1648485ccc429.png": "h_{n}=-\\frac{f(x_{n})}{f^{\\prime}(x_{n})}", + "a7f1ac819c109a70.png": "h=\\frac{\\sqrt{3}}{2}a", + "a7f96091ffd1f8c5.png": "\\nabla^{2}\\Phi=4\\pi Gm|\\Psi|^{2}", + "a802377b799dc5ce.png": "\\sqrt{(1-x^{2})^{-1}}", + "a8037d75641b2ac2.png": "O(log|B|)", + "a808b6a36f30612a.png": "n=\\frac{1}{\\sqrt{f}}", + "a8108410ac08e9df.png": "J=-D\\frac{\\partial C}{\\partial x}", + "a813af185bb30475.png": "m\\frac{d^{2}x}{dt^{2}}=f(x)", + "a8166a1bee0f487b.png": "<10^{-6}", + "a81ac7c5dfb9e51d.png": "1-\\int_{t-r}^{t}E(t^{\\prime})dt^{\\prime}", + "a81c06401641bde2.png": "E=Q(\\lambda)", + "a81c7078cedf21e0.png": "4log_{2}n-4", + "a8216ea5b6d4ff4e.png": "2^{c}", + "a823bdd0c5ce7942.png": "\\sqrt{-1}\\partial\\overline{\\partial}g=\\omega", + "a825386cced3117b.png": "\\overline{y}^{n}\\notin q", + "a82629746fade323.png": "\\sqrt{n}/ln(\\sqrt{n})", + "a82de998f63cb231.png": "[\\begin{matrix}-2&-1\\\\ -1&2\\end{matrix}]", + "a82e62316e44a9f2.png": "\\hat{u}_{R}", + "a83311f1dd9ad3be.png": "\\sqrt{J}", + "a8332e71c96ce7c7.png": "C=\\sqrt{2\\pi}", + "a838c4b080618fa9.png": "F(\\underline{x}_{0},\\underline{u})", + "a839677b25b2a4da.png": "\\frac{5}{36}+\\frac{1}{24}\\sqrt{15}", + "a83c0d7f040c1154.png": "\\int_{X}dxf(x)", + "a83d5c14499014a5.png": "\\tilde{K}", + "a83e80ffc69a5b5c.png": "(x,y,w)\\in R_{*}^{3}", + "a8417fd1ad77ec52.png": "S=[\\begin{matrix}I&0\\\\ 0&-I\\end{matrix}]", + "a843de3b0e7025f7.png": "R=q_{1}+(\\frac{q_{2}^{\\prime}}{q_{2}})", + "a846bf7218796010.png": "{v_{1}}^{\\prime}|\\dot{x}+a(t,x,\\dot{x})|", + "a990ca88142bd496.png": "n=\\int fd^{3}p", + "a993cf649ab3d6a4.png": "\\int sin(x)e^{x}dx", + "a99724fc6bce7104.png": "\\tilde{\\psi}(t)", + "a997ac7ee89e55ae.png": "K=r\\times(p-\\frac{qA}{c})", + "a99a8698d2dd9d91.png": "\\mu_{F}=(\\pi_{F}^{T})_{*}\\mu", + "a99b296ce5820fe4.png": "\\frac{\\partial z}{\\partial x}=f^{\\prime}(yz)y\\frac{\\partial z}{\\partial x}", + "a99ea4dae2007546.png": "H=G^{2}-\\frac{p^{\\prime\\prime}(x_{k})}{p(x_{k})}", + "a9a57df2ed20381a.png": "\\int_{a}^{b}[f(x)-g(x)]dx", + "a9a90337c844fe85.png": "k^{2}=\\omega^{2}(\\mu\\epsilon)", + "a9a9f987a4dc6ea6.png": "0\\le N<(\\begin{matrix}n\\\\ k\\end{matrix})", + "a9ad5e9336e6c635.png": "r=\\sqrt{x^{2}+y^{2}}", + "a9ad89fe98b775c7.png": "\\tilde{H}_{2}", + "a9b2703b300715e8.png": "A^{-1}JA=J", + "a9b2ab2a5557eb8d.png": "\\sqrt{\\phi}", + "a9bcbc82a19c3893.png": "\\epsilon_{\\circ}=8.85\\times10^{-12}F/m", + "a9bfa04ddf8c52c6.png": "L(A)\\cap L(B)=\\emptyset", + "a9cafa61e0662dba.png": "O_{R}P", + "a9ccb91de5c9e9b8.png": "X_{n}\\sim N(\\mu,1)", + "a9d1cd404dc4f1a8.png": "\\tilde{\\phi}", + "a9db7e728a3e6078.png": "\\tilde{a}", + "a9dee4d8554c8168.png": "\\hat{I}_{S},\\hat{I}_{B}", + "a9ea8c98ce18cdec.png": "\\Phi=\\frac{1+\\sqrt{5}}{2}", + "a9f52355a3e3308c.png": "((\\begin{matrix}2n-2\\\\ n-1\\end{matrix})/n!)^{2}", + "a9f6584b43c1ae44.png": "a_{8}*b_{7}=r^{2}", + "a9f8bccd82ca4cc8.png": "k_{\\lambda}e_{i}k_{\\lambda}^{-1}=q^{(\\lambda,\\alpha_{i})}e_{i}", + "a9fac638e250ca8f.png": "S_{m}^{2}=m(a+b)+1", + "aa096585603adfe9.png": "(\\begin{matrix}6\\\\ 2\\end{matrix})=15", + "aa0af5a1adc33fc5.png": "\\frac{d^{2}y}{dt^{2}}", + "aa0eb7f61fa80ee1.png": "E=E_{0}-\\int PdV", + "aa1201f18b9ef169.png": "\\{\\Lambda_{m}\\}_{m}", + "aa18ea30249db987.png": "\\prod_{p}(a,b)_{p}=1", + "aa1b77dd7a445c9d.png": "J(t)=y^{k}(t)e_{k}(t)", + "aa1d134ac99b59db.png": "[\\begin{matrix}4\\\\ 1\\\\ 8\\end{matrix}]", + "aa1e95b6b22c9308.png": "\\Psi_{L}(\\eta)=\\Psi_{G}(\\eta)", + "aa21aeb83e9ecaff.png": "F(s)G(s)=H(s)", + "aa21c1d74f887f08.png": "\\neg\\psi", + "aa225f70e39c61b4.png": "\\hat{B}_{i}", + "aa22b46e73e52ffc.png": "\\int_{S}H^{2}dA", + "aa32b605c10d55d3.png": "\\sum_{i=6}^{10}26^{i}10^{16-i}(\\begin{matrix}16\\\\ i\\end{matrix})", + "aa350262cae1902b.png": "\\frac{-1}{log_{2}p}", + "aa360377fd148d9e.png": "\\dot{m}_{out}=K\\cdot C(4)", + "aa3e60649cf13e73.png": "V=L\\frac{\\partial I}{\\partial t}", + "aa53897c7b76efa5.png": "1/\\sqrt{1-(v/c)^{2}}", + "aa53c534c6a7c909.png": "(\\begin{matrix}m-1\\\\ k-1\\end{matrix})/(\\begin{matrix}N\\\\ k\\end{matrix})", + "aa56794e4fa5c953.png": "P=\\int I(x,y)dxdy", + "aa59698c4ec46b84.png": "\\tilde{w}_{i}", + "aa68de5b1fc6c6c6.png": "s_{k}=(w^{T}*x)", + "aa6ec6abb583a5a8.png": "\\hat{r}", + "aa7fbf64d99e7da3.png": "n!:=n\\times(n-1)!", + "aa80bd8f1382904a.png": "(X-k)/\\sqrt{2k}", + "aa8358481f84cabf.png": "\\sqrt{L}", + "aa83b84f0e357d57.png": "\\frac{L(tx)}{L(x)}\\rightarrow1,x\\rightarrow\\infty", + "aa863df1ce6709c5.png": "\\int_{\\Omega}fw>0", + "aa8664d12930bbd2.png": "e^{\\frac{-1}{x^{2}}}", + "aa871ae14b8a221d.png": "P(\\zeta)=e^{i\\omega_{k}\\zeta}", + "aa911a9b136cd9ac.png": "\\int^{c\\in C}F(c,c)", + "aa9207e26ac067fd.png": "A_{k+2}=(2k-\\lambda)A_{k}", + "aa948a5a9bb2f1af.png": "F\\underline{A}", + "aa9c8c3a4532cc12.png": "\\pi-arccos(\\frac{1}{3})", + "aa9caa156e5cfdb1.png": "F=\\phi R_{m}", + "aaa392563218fcdb.png": "R=\\mu_{1}+\\sqrt{S_{1}}X", + "aab211757747deae.png": "\\omega_{\\rho}^{k}", + "aab3e06bcaaf647a.png": "J_{1}(x)=x/2\\sqrt{2}", + "aab42a20fcbead78.png": "m]", + "aab4ecf0c18843b7.png": "\\hat{g}", + "aab673c6fee5814e.png": "(\\begin{matrix}e&0\\\\ 0&1\\end{matrix})", + "aab70bc1cf6f365a.png": "R_{\\mu}=\\frac{2G}{c^{3}}P_{\\mu}", + "aaba04a58dd3ae5c.png": "[\\begin{matrix}1&1\\\\ 0&1\\end{matrix}]", + "aabb5d201853d9ae.png": "|A|<|P(A)|", + "aabde41879d92c6f.png": "a^{2}=g(a,a)\\in R", + "aabe8edeb8aff0c0.png": "\\sigma_{\\overline{X}}^{2}=\\sum_{i=1}^{n}w_{i}^{2}\\sigma_{i}^{2}", + "aaca34085e6627f4.png": "\\int f(x)dx", + "aad4ed0caa8c1c0e.png": "25=\\frac{[2*3*5]^{2}}{[2*3]^{2}}", + "aadb16534b86b115.png": "x^{\\prime}=\\sqrt{\\frac{-z}{x}}", + "aadc48578ec5ec4e.png": "Q_{Hur}=Z[\\eta][i,j,j^{\\prime}]", + "aae28a14ad87ef01.png": "X_{n}=M^{n}X_{0}", + "aafa6264e2704814.png": "\\frac{d^{2}y}{dt^{2}}", + "aafdb6e8c064d51e.png": "E[P^{(k)}]=-k\\alpha", + "aaff39ad000a390c.png": "V^{C}=V^{+}\\oplus V^{-}", + "ab00110433fe1145.png": "\\chi_{\\mu}^{A}(1)\\chi_{\\nu}^{B}(1)", + "ab00c5b970465063.png": "(x,y)\\mapsto x+y\\sqrt{-1}", + "ab061bfe3ea535e0.png": "\\sqrt{\\pi}", + "ab0b5ad21ef1b2ea.png": "(\\begin{matrix}n\\\\ n\\end{matrix})", + "ab1ce3c2ea7553d7.png": "(w/(P.\\sqrt{T}", + "ab1d0b8e3e653893.png": "\\hat{H}_{I}=\\sum_{i}\\hat{S}_{i}\\otimes\\hat{B}_{i}", + "ab2949c7b33e274f.png": "f(\\gamma x)=\\gamma f(x)", + "ab2f3691517134dc.png": "\\int_{0}^{t}B_{s}^{2}ds", + "ab2fbbce7d57b590.png": "\\tilde{y}", + "ab31e752c13053f0.png": "S_{x_{B-l}}=I\\otimes S_{x_{l}}", + "ab362d44af0bb46e.png": "\\hat{U}|\\psi_{i}\\rangle", + "ab3a810f68efc889.png": "[\\begin{matrix}0&1\\\\ 0&1\\end{matrix}]", + "ab3b673f343c584c.png": "K^{*-}", + "ab454c961e808423.png": "L(p;q)=L(p;1,q)", + "ab4e1053d035cb51.png": "\\sigma^{2}=3.5033\\cdot10^{-2}", + "ab50fa96b2fbd3a4.png": "B_{n+1}=\\sum_{k=0}^{n}(\\begin{matrix}n\\\\ k\\end{matrix})B_{k}", + "ab552e70a5e61423.png": "A=\\frac{\\sqrt{3}}{4}a^{2}", + "ab5b76cbcdd9a4f6.png": "K_{2}^{M}(Q_{p})", + "ab5d41b22c1a4374.png": "G^{\\alpha\\gamma}=\\kappa T^{\\alpha\\gamma}", + "ab5eff80020ca35b.png": "\\phi(r,\\theta)=-\\frac{Q}{2\\pi}lnr", + "ab5fb0d7379d328f.png": "4!/(2!2!)=6", + "ab69ce26c09cdaac.png": "|4d,m_{2}\\rangle", + "ab74fe12ee9a7ef2.png": "\\Sigma_{y=0},\\Sigma_{y=1}", + "ab7ef448a3129b4c.png": "X:(\\Omega,F,P)", + "ab87833939701281.png": "(\\hat{x}\\hat{y})^{2}=\\hat{x}\\hat{y}\\hat{x}\\hat{y}", + "ab921b12a9d25744.png": "(\\begin{matrix}X+n-1\\\\ n-1\\end{matrix})", + "ab964760bc428bfe.png": "\\sigma=1/\\sqrt{2\\mu\\omega}", + "ab96c5681dfe35cc.png": "a=[\\begin{matrix}2\\\\ 0\\\\ -1\\\\ 1\\end{matrix}]", + "ab9bcad9ad74a6ab.png": "[K_{i},P_{0}]=-iP_{i}", + "ab9cd1fde954f328.png": "\\tilde{A}_{3}", + "abafb5c50ec95fcb.png": "3^{(\\begin{matrix}n\\\\ 2\\end{matrix})}", + "abb18c8f6ec4db3a.png": "M=\\prod_{n}c_{n}", + "abb633719307513c.png": "\\frac{\\pi}{C\\sqrt{2}}\\frac{1}{\\sqrt{p}}\\sim\\frac{\\sqrt{\\pi}}{2}\\frac{1}{\\sqrt{p}}", + "abb983c124d4941a.png": "\\frac{\\sqrt{2}}{12}", + "abc183a127c23698.png": "g=U(g)\\cdot X(g)", + "abca63ca83dadf4b.png": "Qx=A^{T}\\lambda-c", + "abcd1a450d93971f.png": "p_{3}=(\\frac{m_{1}}{1+m_{1}})^{2}", + "abcea94620ba72cf.png": "C_{n}=C_{2}\\prod_{q|n}\\frac{q-1}{q-2}", + "abd39797f781b642.png": "T>T_{c}=1/(2\\sqrt{log2})", + "abd7d5961cd5dcbe.png": "\\hat{F}=\\frac{i-0.3}{n+0.4}", + "abd8520feef06c61.png": "f=g\\prod_{1}^{k}u^{a_{j}}", + "abdd4f867ca2c16a.png": "1,\\frac{1}{2},\\frac{1}{3},\\frac{1}{4}", + "abde2d9c6b6bac12.png": "1-Q_{1}(\\frac{\\nu}{\\sigma},\\frac{x}{\\sigma})", + "abe5cc8e8514a3e4.png": "\\omega=\\frac{d\\theta}{dt}=\\frac{v}{r}", + "abe9dcad613f261c.png": "P(X=x)", + "abe9fc2005f7d44c.png": "h=E_{m}^{-1}(0)", + "abeaeaf193e2b6ff.png": "(\\begin{matrix}n-p\\\\ k-i\\end{matrix})(\\begin{matrix}p\\\\ i\\end{matrix})/(\\begin{matrix}n\\\\ k\\end{matrix})", + "abeb66116d87a016.png": "\\overline{\\nu_{e}}", + "abf45b766e84fbbd.png": "0+0=1+1=0", + "abf66f631b77e6ab.png": "B_{12}=\\frac{\\pi e^{2}}{m_{e}h\\nu}f_{12}", + "abf800cd71181dbd.png": "sen(\\sigma)(\\varphi)", + "abf8d4dec8127322.png": "\\langle\\psi|E_{A}\\psi\\rangle", + "abfeefd8d63b497d.png": "\\tilde{B}", + "ac0210f9260082bf.png": "[\\begin{matrix}1&0\\\\ 0&0\\end{matrix}]", + "ac047ef2c80c18a1.png": "\\frac{dC}{dt}=0", + "ac0be0c320f52052.png": "u^{\\prime}(t)=\\Delta_{D}u(t)", + "ac12057f333a7f1d.png": "e^{+}e^{-}\\rightarrow\\gamma\\gamma\\gamma\\gamma", + "ac16e7b274cd7a11.png": "n", + "ac18e263db9c37a9.png": "(\\begin{matrix}-1&-1\\\\ 1&0\\end{matrix})", + "ac1cc9c09670fcff.png": "v=\\sqrt{\\frac{ke^{2}}{mr}}", + "ac1f5e5c20483a1b.png": "J_{x,y}\\sim|x-y|^{-2}", + "ac37fa5c1309b5f4.png": "\\Psi_{v}^{\\varphi}", + "ac3acec72d085824.png": "\\langle x-Px,v\\rangle", + "ac3f208eab6294a7.png": "3x+(1-x)", + "ac5249fec7d0024c.png": "(\\overline{K}^{\\prime},|\\cdot|^{\\prime})", + "ac5314b800d658bb.png": "Z_{\\gamma}^{f}", + "ac6716cefea9eb04.png": "C=\\sqrt{2\\pi}", + "ac69e7d143ba819e.png": "g(n)=\\prod_{k=1}^{n}f(k)", + "ac6bc1a91e6e3e1f.png": "\\sum_{i=1}^{n}(2i-1)^{3}", + "ac7049c5dec8b9ba.png": "I_{x}=I_{y}=\\pi r^{3}t", + "ac7081898c20069f.png": "|AC|=|DG|", + "ac778bebc925cf3c.png": "(P,M)\\rightarrow^{*}M^{\\prime}", + "ac79cef4b64d346a.png": "\\hat{r}", + "ac7ab20f54af39d7.png": "\\hat{v}", + "ac8a62d960159653.png": "\\frac{-1-\\sqrt{5}}{2}M_{\\sigma,\\epsilon}", + "ad82dd7813106fe7.png": "\\sum_{I=1}^{L}I=L(L+1)/2", + "ad88b5f8c4fee911.png": "c=r-\\frac{1}{T}ln(\\frac{F}{S})", + "ad8fdf60d9303d83.png": "\\{M_{k}[n]\\}_{k=1}^{K}", + "ad9a27fab9b2e182.png": "(A-\\tilde{\\lambda}_{*}I)", + "ad9b723edb302426.png": "\\tilde{t}_{i}", + "ad9f07bbe9ca7a2e.png": "\\frac{dy}{dx}=1/4", + "ada781fdfcbd45b6.png": "E=Q(X_{1},...,X_{r})", + "ada99a3de196c4bd.png": "x=p-\\frac{y^{2}}{4p}", + "adaab26b01d6e529.png": "m(A)=\\int_{A}Xdn", + "adba33346d5b74b0.png": "\\hat{X}_{i}", + "adc589dba95cf8e3.png": "\\int_{a}^{b}f(x)dv(x)", + "adc78225d32c2807.png": "H^{\\prime}\\cap f(C_{w})", + "adc94ba65e323a19.png": "\\sqrt{2t}", + "adc9ea50fddd2f96.png": "\\sqrt{\\frac{12}{35}}", + "adcabe11be15d181.png": "\\xi_{1}<\\sqrt{2}\\lambda<\\xi_{2}", + "add1669bb4f205c1.png": "\\frac{1}{\\sigma_{i}+n\\lambda}\\sim\\frac{1}{\\sigma_{i}}", + "add8a8b3cf1b7300.png": "|\\psi_{00}\\rangle=|0\\rangle", + "add98b8679c4defd.png": "\\int udu", + "ade32899aa8a3cb7.png": "\\Delta E>=0", + "ade472f6ad6cc9e3.png": "{(\\theta^{r})}^{4}", + "aded6ee9693b020b.png": "\\dot{x}=\\Gamma V(x)", + "adedb36a3246725e.png": "\\frac{d}{dx}\\delta(x-a)", + "adeed898b52cbdea.png": "k_{2}\\ll1,Q=100", + "adef475c8d5aab35.png": "\\hat{w}_{2}", + "adfbc1e7343bebd1.png": "q_{ab}/\\sqrt{q}", + "adfe40fbf16db93f.png": "\\int f(x)d_{h}x", + "adffafafc063ceae.png": "{B^{w}}^{2}", + "ae06a83fd1217eea.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "ae077c1d5ea99d28.png": "(X_{1}:Y_{1}:Z_{1})", + "ae0842fbce28a173.png": "\\tilde{6}/2", + "ae0d76070c4b196a.png": "\\sum_{i=6}^{10}26^{i}10^{16-i}(\\begin{matrix}16\\\\ i\\end{matrix})", + "ae0e8937335fe8e7.png": "\\frac{\\partial\\Psi}{\\partial J}", + "ae1379320d6c89fa.png": "P\\underline{\\vee}Q", + "ae17b8d0c8498889.png": "\\underline{a}_{1},...,\\underline{a}_{r}", + "ae19fb6ee79a4b0c.png": "C_{0}^{\\infty}(U)\\subseteq L^{2}(U)", + "ae1d0cc36a286e5c.png": "V_{1}^{N-1}y", + "ae1e10707a0a3396.png": "S\\in(\\begin{matrix}[n]\\\\ m\\end{matrix})", + "ae27380cf2d562fa.png": "(\\begin{matrix}p+q\\\\ q\\end{matrix})", + "ae2aab0de16be465.png": "(\\begin{matrix}1&\\nu\\\\ 1&1\\end{matrix})", + "ae2afefd6eaade8f.png": "X^{u5}", + "ae305ca110b9052a.png": "S^{0}\\rightarrow S^{n}\\rightarrow RP^{n}", + "ae30d1b094ac4949.png": "\\Phi_{j}^{\\chi}", + "ae356df8117e82cd.png": "\\frac{35\\sqrt{\\pi}}{64}", + "ae38a76c7304058e.png": "Q_{i}[x_{\\alpha}^{j}(t)]=t\\delta_{i}^{j}", + "ae3e8291528f0fb2.png": "FOV_{C}=\\frac{FOV_{P}}{mag}", + "ae46d8e5576d3646.png": "\\tilde{H_{i}}=\\varphi(H_{i})", + "ae4fe21a535568b0.png": "\\frac{U}{U_{v}}\\approx\\frac{m_{0}}{m^{*}}\\frac{m_{0}c^{2}}{E_{G}}", + "ae5dca496e6950f9.png": "(\\begin{matrix}n\\\\ 4\\end{matrix})", + "ae63bfe359d7845c.png": "|\\varphi(s)|=p(N-1)", + "b051dd4bf909f832.png": "I_{2}=\\int f(\\theta)d^{3}x", + "b057469082bcc947.png": "(n+1)p-1\\notin\\mathbb{Z}", + "b059a18e6e53a427.png": "F=S\\frac{(1+i_{f})}{(1+i_{d})}", + "b05ee81fd1a371d5.png": "\\frac{\\partial}{\\partial x_{k}}|x|_{2}=\\frac{x_{k}}{|x|_{2}}", + "b05f0b0b9fed13a2.png": "E(V/m_{0})", + "b061b1718419a2dd.png": "cos^{2}\\theta+sin^{2}\\theta=1", + "b06284b1c0a86077.png": "\\int_{S^{2}}K_{g}=4\\pi", + "b063e424fc3d0e20.png": "(1+\\lambda_{2})", + "b0646fdf345d2baf.png": "I\\approx\\frac{V_{in}}{1/j\\omega C}", + "b06efdb44c1b4923.png": "(1-k)\\psi(k)+ln[\\frac{\\Gamma(k)}{\\lambda}]+k", + "b072ef45d060c4c9.png": "\\mathbb{P}", + "b0756a247ef21662.png": "\\dot{m},P_{D}", + "b077044678cdf4d9.png": "(1-o(1))\\cdot lnn", + "b07ad71567871702.png": "W=\\int V(P)dP", + "b07e17629418531b.png": "\\sqrt{3}", + "b0861b6b5f10e61a.png": "x\\mapsto\\prod_{i=1}^{n}u_{x}(i)", + "b08935084e1ef91f.png": "S_{Fermigas}\\approx\\frac{\\pi^{2}k}{-3e}T/T_{F}", + "b08d67bc7cdf8400.png": "0.3<\\frac{M_{1}}{M_{2}}<20", + "b09385414d63d055.png": "F(a)=\\frac{xa^{2}}{2}", + "b0a20317862a94d6.png": "V", + "b0aacc0f4b54f2c9.png": "v=\\sqrt[2]{\\frac{2Pt}{m}}", + "b0ab3e819322ce72.png": "\\frac{dI}{d\\alpha}=-\\pi", + "b0b16ddddce52d1a.png": "\\int(p(x))^{n}f(x)dx", + "b0d72b462d33ea05.png": "\\frac{3^{11}-1}{3-1}=88573", + "b0d8a2c830c81e0e.png": "V(x)=-\\int w(x)dx", + "b0d97fc1c8f1466e.png": "d=(1/2)b_{2}", + "b0da0813730539bf.png": "(=\\hat{\\beta}\\hat{\\alpha})", + "b0da9ef36db54b56.png": "\\sqrt{u_{x}^{2}+u_{y}^{2}}=c", + "b0df173ba1f006b2.png": "(1\\Rightarrow y)=y", + "b0e2fa577d81df95.png": "\\alpha\\equiv1(modm_{0})", + "b0fa9702a5eb884b.png": "\\frac{dx}{dt}=3", + "b0fbf99d7d9a4fcc.png": "\\{\\phi_{1},\\phi_{2}\\}_{PB}=c", + "b100f7df3d95b1ae.png": "(e^{-\\pi(t-\\tau)^{2}})", + "b10188836983b1bc.png": "\\int x^{2}e^{x^{2}}dx", + "b1041cfc4c5c57c6.png": "s", + "b10a8a739e96b917.png": "g_{0}=1_{\\Omega^{\\prime}\\\\ U^{\\prime}}g", + "b10eb835196a2e5a.png": "A=\\overline{A}+\\frac{1}{c}Ve_{4}", + "b118b3a16d0139f6.png": "\\tilde{\\psi}(\\alpha)=\\psi(\\alpha)", + "b11978a0d78c3637.png": "s,e,e_{v}\\in Z_{q}", + "b11d63157b9a2a62.png": "(\\begin{matrix}c_{k-1}\\\\ k-1\\end{matrix})\\le N-(\\begin{matrix}c_{k}\\\\ k\\end{matrix})", + "b12598bb3a562e0d.png": "\\int x^{2}d(cosx)", + "b12788938dfa6af3.png": "\\hat{u}[n]", + "b12b6f30abb8ae07.png": "\\dot{\\sigma}=C\\dot{\\epsilon},(1)", + "b1302e23f143a5e0.png": "\\sqrt{2}k", + "b139052d6ba176c5.png": "x_{B}\\notin U_{c}", + "b148ce6aa0192b17.png": "|\\sum_{i=1}^{k}x_{i\\cdot d}|>C", + "b149ab19eb4215b9.png": "R_{\\eta}^{5}", + "b14b52f1ac10d174.png": "\\sum\\vec{F}=0", + "b14c2ff5b95a4eaf.png": "E^{\\ominus}(H^{+}/H_{2})(abs)", + "b153023f6e03ca0f.png": "\\tilde{n}(t)", + "b156da1815585e0a.png": "B_{e^{\\tau}}", + "b159ee59e1682f06.png": "\\dot{x}=\\Gamma V(x)", + "b15ad58b69e2523d.png": "\\phi:M\\rightarrow\\prod_{i\\in I}R", + "b15c9515a1b1dd50.png": "2^{(\\begin{matrix}n\\\\ 2\\end{matrix})}", + "b160b9c9daeb1d34.png": "\\underline{k}-\\omega", + "b165e78df21cedbb.png": "(a\\pm\\sqrt{a^{2}-4})/2", + "b16991d0f893ad9c.png": "M_{31}(R)", + "b16c11ad3d337ac8.png": "J_{-}=J_{x}-iJ_{y}", + "b173af2c1514cb90.png": "g", + "b17578d0a34e46ea.png": "\\int\\Psi\\Psi^{*}dV=N_{s}", + "b1761d462328eee8.png": "(\\begin{matrix}n+k\\\\ k\\end{matrix})", + "b17b381b2c2f12d4.png": "a(m):=\\epsilon(a)m", + "b181b68152fb087a.png": "Hom_{D}(X,f(-))", + "b1832efe1ebe3f85.png": "\\prod M_{n_{i}}(D_{i})", + "b185029d5c82cb6b.png": "[-(a/4)^{1/4},0]", + "b18c0d9e9f1c0341.png": "\\overline{G}_{k}(X)", + "b18c37fe17c822a5.png": "\\tilde{D}_{7}", + "b194bd59ed7a8de8.png": "t_{r}^{\\prime}=t-\\frac{1}{c}|r-r^{\\prime}|", + "b195694f581105ef.png": "[\\begin{matrix}1&0\\\\ 0&1\\end{matrix}]", + "b195ad32be0b8994.png": "\\sqrt{G}", + "b19b829029bcca62.png": "H=\\hat{a}^{\\dagger}\\hat{a}+\\frac{1}{2}", + "b19c9876bc1b7383.png": "(i,j=1,2,3)", + "b19e6879641b9fb8.png": "A=\\underline{m}", + "b1a032ac7e760d9f.png": "\\frac{dh}{dt}=0", + "b1a2af0ea2552389.png": "ba^{RC}\\notin O", + "b1a527020d1c57ed.png": "\\prod x_{i}", + "b1a565dbc209ed9e.png": "\\lambda=\\sqrt{2}\\sigma", + "b1a56d9a1b3e3fc7.png": "c=\\int_{a}^{b}f(x)", + "b1a7f923ab3909c2.png": "\\bigcup_{\\alpha\\in A}\\Sigma_{\\alpha}\\subset P", + "b1b2c59c4e4c3660.png": "p(x)=\\tilde{y}", + "b1b48f52d0303753.png": "Spec(\\oplus_{0}^{\\infty}I^{n}/I^{n+1})", + "b1b9b2c714f8967e.png": "\\infty k\\delta(s)\\hat{z}", + "b1bfbb2f6194cdef.png": "g^{(c_{h})}", + "b1c80c1d56984d1f.png": "P", + "b1c86e67c27c9da3.png": "(A\\backslash Y),B,C", + "b1c9f848af6be62d.png": "(A^{*}f)(u)=f(Au)", + "b1cdf6d203e9ef3c.png": "m_{B}/m_{A}B", + "b1ce2b07d42de59c.png": "\\hat{v}_{i}", + "b1cffabddb9e1d90.png": "I_{F}(f)", + "b1d532e1ee3d3890.png": "t", + "b1d6dbce24a232fe.png": "(\\rho,\\rho\\dot{q}_{i},\\rho\\dot{p}_{i})", + "b1d6fc2a4c147945.png": "\\sqrt{\\frac{10}{21}}", + "b1dcbef9647543d2.png": "\\int_{\\partial\\Omega}", + "b1dd18b3901bc32a.png": "\\frac{d(e^{x})}{dx}=e^{x}", + "b1ddb19f61534c3e.png": "\\hat{z}", + "b1e540e608e1f40f.png": "Var(\\epsilon_{j})=\\sigma_{\\epsilon}^{2}", + "b1f4dd2140a5e14c.png": "c_{k-1,0}=0", + "b1f5c2391e5477de.png": "\\omega_{n}=\\frac{\\pi^{2}\\hbar n^{2}}{8L^{2}m}", + "b2014126501cf5eb.png": "\\frac{df}{dz}=g", + "b2090418be702646.png": "\\theta_{min}\\approx\\frac{CD}{AC}=\\frac{\\lambda}{W}", + "b2095d985a9f435f.png": "\\frac{dy}{dx}=0", + "b21656fc8c3983ac.png": "\\tau=(1+\\sqrt{-163})/2", + "b227176a25db38d6.png": "P=(X_{1}:Y_{1}:Z_{1})", + "b22b6d5432bb8222.png": "\\int K=1/6", + "b22e0fbe2229d9d4.png": "\\hat{\\theta}=\\hat{z}", + "b22e201c151d4b70.png": "T^{t}:=S^{1}\\times\\cdot\\cdot\\cdot\\times S^{1}", + "b23c1f2e7f0920a9.png": "|\\langle\\chi|\\psi\\rangle|^{2}=|\\langle\\psi|\\chi\\rangle|^{2}", + "b23e9935f57326b7.png": "\\frac{d}{dx}7", + "b23e9f58e7f1e27b.png": "4(n-2)(n-1)", + "b24320883f936014.png": "[\\begin{matrix}1&0&0\\\\ 0&4&0\\\\ 0&0&-2\\end{matrix}]", + "b243ef3c30bce1ad.png": "\\sum_{k=0}^{n}(\\begin{matrix}n\\\\ k\\end{matrix})^{2}=(\\begin{matrix}2n\\\\ n\\end{matrix})", + "b248e61d46d98662.png": "F(x)=\\int_{x}^{0}f(y)dy", + "b24c92e897ad2804.png": "(Pf)^{\\wedge}=Q\\hat{f}", + "b25077d7f1d03f17.png": "-I=I_{0}sin\\delta", + "b251d937214d4ca8.png": "AB", + "b2544a9fe779f36a.png": "\\tilde{L}=\\sqrt{\\nu}(C-||C\\varphi||)", + "b255d395a608a3d8.png": "\\kappa\\notin\\{\\lambda,\\mu\\}", + "b2590a5d61f7275f.png": "\\tilde{G_{0}}", + "b25c6ed60b8bc6b6.png": "f(\\underline{m})=0", + "b25ceebe3b729efc.png": "L=L_{0}\\sqrt{1-v^{2}/c^{2}}", + "b25ec0451f4badb1.png": "\\partial_{t}L=\\frac{1}{2}\\nabla^{2}L", + "b26b7f5c9017b868.png": "|G(\\chi)|=\\sqrt{N}", + "b26db84e31387581.png": "\\frac{dx}{dt}=r\\pm x^{2}", + "b27a18bc80471595.png": "\\Delta x^{\\prime}=\\Delta x/\\gamma", + "b28253f3072b9207.png": "\\gamma(-1,i)=1", + "b282700a25088f6e.png": "(\\begin{matrix}4\\\\ 7\\end{matrix})", + "b28354aeaf8ca025.png": "T_{e}\\gg T_{i}=T_{gas}", + "b28aac9e18d5bc25.png": "z_{1}=f_{c}(z_{0})=c", + "b28b982ced8c9dc3.png": "M=(\\begin{matrix}-i&i\\\\ exp(it)&exp(-it)\\end{matrix})", + "b28cf21b4aef2454.png": "T_{o}(p_{i,j})=p_{i,j}+t_{o}", + "b297f2572ad7e678.png": "e^{x}\\ge(1+\\frac{x}{n})^{n}", + "b29b7f14fdaf0a9b.png": "4+\\sqrt{2}+\\sqrt{6}", + "b2a198a762805687.png": "Rg(x):=g(-x)", + "b2a42d469bcc471f.png": "k_{\\tau}^{\\psi}", + "b2aeb7f82275825a.png": "\\sqrt{i}", + "b2c0264136dc02ea.png": "\\tilde{H}_{d}", + "b2cab2821be03822.png": "8\\frac{m}{s^{8}}\\frac{(8s)^{8}}{8!}\\approx3329m", + "b2ce21cb56234a24.png": "\\underline{v_{row}}=2", + "b2d0235f458a526c.png": "\\chi_{i^{t}}", + "b2d07b2c097555ff.png": "I=\\int r^{2}dm", + "b2d1722a2113843f.png": "\\lambda\\frac{1}{k_{1}^{2}}\\frac{1}{k_{2}^{2}}\\frac{1}{k_{3}^{2}}\\frac{1}{k_{4}^{2}}", + "b2d892be5219a69e.png": "V_{v}=\\frac{(p_{ct}-p_{cm})}{p_{ct}}", + "b2d986edbe71f658.png": "lim_{T\\rightarrow0}\\Delta S=0", + "b2f003c55cca3296.png": "4+\\sqrt{2}+\\sqrt{6}", + "b2f00aa47853686d.png": "\\overline{y}_{x}", + "b2f1b10dafe72008.png": "1/\\sqrt{2}(\\pm1,\\pm1,0)", + "b3050d88054b6ca0.png": "H(t):=\\int_{0}^{t}h(s)ds", + "b30ff05ee939442d.png": "\\sum_{L}L^{2}4^{-2L}e^{-4\\beta L}", + "b312b780406adbd7.png": "minmax_{i,j}c_{ij}x_{ij}", + "b316db363982ce2b.png": "(\\frac{dt}{dr})^{2}", + "b318d379cc3f8d8f.png": "\\tilde{q}_{i}", + "b31d96df58a79b78.png": "t\\{\\begin{matrix}p\\\\ q\\end{matrix}\\}", + "b3201075252ca368.png": "\\tilde{B}_{2}", + "b32ce4fe38599fbb.png": "\\int_{X}f(x)dx", + "b3314bf86eefe380.png": "f^{\\xi_{m}}", + "b33d79814f94b9c3.png": "D=\\{x^{2}+y^{2}\\le4\\}", + "b33db861d7cd6dc9.png": "V_{i}^{\\prime}=\\sum_{j=1}^{3}a_{ij}V_{j}", + "b3408bf216fbc53f.png": "-4,8(3,7)\\times10^{-8}", + "b342c654687266cf.png": "F^{\\pm}:=\\sum Z^{\\pm}t_{j}", + "b342f2604013169a.png": "(\\begin{matrix}n-1\\\\ r-1\\end{matrix})", + "b3495a7ba765cd9d.png": "C(T)^{*}", + "b34a3d1ab1b45b83.png": "\\chi(F(n))=P(n)", + "b34c40ae942f52ce.png": "m", + "b34c4fc2e8c41064.png": "|a|=\\sqrt{a^{2}}", + "b34cbb4a2967ced5.png": "\\frac{1-x^{-n}}{x^{2}-x}", + "b351284218fa2f70.png": "H=\\int\\rho hdV", + "b351c84b9aba0372.png": "\\hat{y}_{i}", + "b35c6a54f1eedc53.png": "\\hat{S}^{2}", + "b360e5761d2512c5.png": "B_{0}=\\mu_{0}M", + "b3665c431ac72aa1.png": "E\\mapsto\\langle F(E)\\xi|\\xi\\rangle", + "b366631a0bcb8318.png": "\\hat{f}", + "b367b17ecba46d66.png": "a_{(\\nu_{7})}", + "b36c732d2bbbff8b.png": "[\\begin{matrix}E&F\\\\ F&G\\end{matrix}]", + "b36f2681df55280e.png": "a\\hat{b}cd", + "b3718ad5a86d3865.png": "\\frac{dA}{db}=p", + "b37740391de89e26.png": "\\tilde{a}_{1},...,\\tilde{a}_{m/n}", + "b377e3fff7b99c87.png": "K=\\frac{1}{2}Nm\\overline{v^{2}}", + "b37a85c46c3599eb.png": "g^{\\prime}(x)=\\frac{1-lnx}{x^{2}}", + "b37b62d431028ea5.png": "\\psi(R_{1}...R_{n})", + "b37df90007cd5d69.png": "\\sum_{j=0}^{m}(\\begin{matrix}m\\\\ j\\end{matrix})^{2}=(\\begin{matrix}2m\\\\ m\\end{matrix})", + "b37f5726e435d6e2.png": "\\tilde{C}_{2}", + "b3800237ee5ced9e.png": "\\sqrt[n]{|a_{n}|}>1", + "b382af4a9d754b78.png": "\\tilde{BC}_{2}", + "b38ac334afa187a2.png": "(\\begin{matrix}n\\\\ 0\\end{matrix})=1", + "b38b8060ac78e0cb.png": "\\frac{\\partial f}{\\partial x}=y", + "b39650a3ea5798dc.png": "=\\frac{1}{2}I\\omega^{2}", + "b3a18c9016f9e7c0.png": "(\\begin{matrix}1&1\\\\ -a&-c\\end{matrix})", + "b3a5d2260bd49f3b.png": "f_{s}\\sim\\int f_{s+1}", + "b3a759f20d6a07c0.png": "(\\begin{matrix}n+k\\\\ k\\end{matrix})", + "b3b3ce6248583d12.png": "f_{0}=\\pi\\circ\\tilde{f}_{0}", + "b3b7da80aab2425d.png": "F=\\prod_{i=1}^{K}f_{i}", + "b3b9aa878b85cfa2.png": "u", + "b3bab6cde94124ad.png": "Fr=\\sqrt{(\\frac{y_{c}}{y})^{3}}", + "b3bba5bdf9ad913d.png": "[(n:=n+1)*]", + "b3c81f4883d14b4e.png": "E[|T_{j}|]=\\frac{t}{d}", + "b3cc575fe041f7d3.png": "\\frac{dk}{dt}", + "b3cdad41e4472eab.png": "\\frac{40}{3}\\times\\frac{201}{16}", + "b3d115116b537cb5.png": "V_{R}=IR=C\\frac{dV_{C}}{dt}R", + "b3d2c44307176da4.png": "f(.,.)", + "b3d3a3b84ed0b074.png": "-\\frac{d^{2}}{dx^{2}}", + "b3d3af9b08a3c532.png": "\\tau=\\sqrt{t^{2}-x^{2}}", + "b3d532526da12978.png": "x^{i}\\circ f(t)=tv^{i}", + "b3dbbe7c0a092cbb.png": "\\{\\tilde{J}_{k}\\}=\\beta(\\{J_{k}\\})", + "b3de3e7dd15ba64d.png": "C_{ij}=\\frac{r_{i}s_{j}}{x_{i}-y_{j}}", + "b3e52e768ab5f3f3.png": "2^{(\\begin{matrix}n\\\\ 2\\end{matrix})}", + "b3e57564034de892.png": "2^{a}3^{b}\\rho\\ge3", + "b3e6bef51ae43530.png": "b\\overline{z}", + "b3e762d249f9520c.png": "y(x)=\\int g(x)dx", + "b3e7cde57f7cceb4.png": "X_{\\alpha}=\\frac{c-b}{a-b}", + "b3ea8e94a5c95871.png": "\\gamma=(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "b3ec9a6dda53eb32.png": "[\\hat{Y},\\hat{I}_{\\pm}]=0", + "b3f0f40d168fe541.png": "F=S/S_{P}", + "b3f10c2c3d7254f4.png": "\\underline{x}(t)", + "b3f13da11eb1510e.png": "\\hat{W}", + "b3f5fb777cb4f2a1.png": "L,\\overline{k}", + "b3f6bfafc365daf1.png": "(Tx_{n})_{n\\in N}", + "b3f9f6051e3a4b18.png": "(\\begin{matrix}n+1\\\\ k\\end{matrix})", + "b3fe576d9e980741.png": "B=[\\begin{matrix}0&A^{*}\\\\ A&0\\end{matrix}]", + "b3fe8f9a59c3f6b9.png": "\\overline{p(t)}=\\frac{p(t)}{m}", + "b4048aade045921c.png": "\\sqrt{-1}", + "b405d4f37ec939ca.png": "e^{-3\\pi i}=-1", + "b407debbd66b4cf9.png": "\\frac{d^{2}u}{dy^{2}}=\\frac{1}{\\mu}\\frac{dp}{dx}", + "b40f3a949a38bb29.png": "C=[\\begin{matrix}0&1\\\\ 0&0\\end{matrix}]", + "b40f60c66c0812a9.png": "N=\\prod_{l\\in S}l>4\\sqrt{q}", + "b41409bfdce5d46b.png": "D_{192}\\approx\\frac{1}{4}D_{96}", + "b4180fd1dc90b39f.png": "\\hat{B}", + "b41a7c7515df5ee0.png": "(sx_{i},sy_{i})", + "b41c5d67a4794971.png": "\\lceil\\chi_{c}(G)\\rceil=\\chi(G)", + "b427bab18a80c106.png": "w=\\sqrt{1-\\frac{U}{E}}", + "b4297e8f4db5ee06.png": "\\mathbb{B}", + "b42c9b5e241f8981.png": "\\int_{0}^{x}f(x)dx", + "b431a5dbead53812.png": "\\partial_{g}(U|\\Psi_{0}\\rangle)", + "b43a34f3df77c9fe.png": "(I-Q)f(x,\\lambda)=0", + "b43d3d285a198419.png": "[\\begin{matrix}0&1\\\\ 0&0\\end{matrix}]", + "b444b0b1b2f6af14.png": "(\\nabla I)(x;t)", + "b44dc54ee12957d5.png": "F_{2}=XW-YZ", + "b4514b0f1d4a5ba2.png": "c_{i+1}=a_{i}-a_{i+1}", + "b45600f071d5b7f1.png": "\\langle m_{i},\\hat{s}_{j}\\rangle", + "b457c40195384878.png": "(\\begin{matrix}A&B\\\\ C&D\\end{matrix})", + "b46038c19eed53f1.png": "y(x)=\\int g(x)dx", + "b4633433175e4e14.png": "e(x)_{U}=\\chi_{U}(x)", + "b46352267a3f1631.png": "\\frac{13}{52}+\\frac{12}{52}-\\frac{3}{52}=\\frac{11}{26}", + "b463cfd89091e36a.png": "(-1)^{2(j_{i}-m_{i})}=1", + "b46bdfc843cb0408.png": "E_{Y}(E_{X|Y}(X|Y))", + "b4739c9b537780d0.png": "\\{\\begin{matrix}3\\\\ 5/2\\end{matrix}\\}", + "b477de59aa0d2bd3.png": "(\\frac{N}{2}\\times\\frac{N}{2})", + "b4811912513376df.png": "[\\begin{matrix}1&2&1\\\\ -2&-3&1\\\\ 3&5&0\\end{matrix}]", + "b4864b317f0f90bb.png": "\\frac{\\partial^{2}z}{\\partial x^{2}}", + "b48b618a481ce683.png": "\\tau=\\int dt^{\\prime}f^{2}(t^{\\prime})", + "b48dc16219cccce6.png": "-s", + "b49914dd441ce3bf.png": "v=", + "b49cde5a207448c3.png": "\\sqrt{a}\\times\\sqrt{a}=a", + "b49f87703c8c8b5c.png": "X=[\\begin{matrix}w+ix\\\\ y+iz\\end{matrix}]", + "b4a1a285b7e6ff72.png": "\\sqrt{E}", + "b4a288a55e79769d.png": "\\frac{\\partial P(x,t)}{\\partial t}=c\\frac{\\partial^{2}P}{\\partial x^{2}}", + "b4a87d3eb159f10c.png": "y^{+}=\\frac{yu_{\\tau}}{\\nu}", + "b4b1f736deae5999.png": "\\dot{y}=\\frac{1}{c}\\overline{h}(0,y,0)", + "b4b4554d3bdcc784.png": "\\hat{e}_{j}", + "b4bd4ee912e8ea7f.png": "f^{*}", + "b4bee3827f3e4eb0.png": "z_{1}=-1+i", + "b4c037617d6b7077.png": "\\gamma_{c}=b\\frac{\\overline{(w^{\\prime}c^{\\prime})_{s}}}{w_{s}}", + "b4c43f0a8e302e6d.png": "[\\begin{matrix}1&1\\\\ 0&1\\end{matrix}]", + "b4c723fdd22e8667.png": "f_{i}(x^{1})\\le f_{i}(x^{2})", + "b4c7d5e9a60a07f3.png": "2drtan(0.5^{\\circ})", + "b4cc7e2a3818ea69.png": "-N^{2}0", + "b4e3eaf18d59745c.png": "2=1/(1-(1/2))", + "b4e5319c16723684.png": "\\int_{X}p(x)dx=1", + "b4e85ed048a2b144.png": "(\\begin{matrix}N\\\\ M\\end{matrix})", + "b4f75c7b13a29f1f.png": "|Q_{0}|=|Q_{L}|=\\frac{P}{2}", + "b4fae55c8827a5e3.png": "g=k\\oplus p,", + "b505173cf3341153.png": "2(x^{2}+y^{2})=s^{2}", + "b512bcbe50000aa3.png": "b=\\sqrt{c^{2}-a^{2}}", + "b5135046457d1b03.png": "\\mathbb{E}[logX!]=\\overline{logX!}", + "b513fc12113110f3.png": "M\\in M_{k}\\cup M_{k+1}", + "b51989a7820295ec.png": "D_{X}(p+tA)=0", + "b5198cff1797609a.png": "\\int_{E}\\varphi=\\infty", + "b52a1c61c846e8cf.png": "f_{1}=(x,y,0)/norm", + "b52b516ba2135c13.png": "\\tilde{g}_{n}=[\\begin{matrix}g_{n}\\\\ \\gamma_{n}\\end{matrix}]", + "b52d37de601d9a67.png": "cf(\\prod A/D)<\\lambda", + "b5313266f1d0a0b7.png": "(\\begin{matrix}5+1\\\\ 1+1\\end{matrix})=15", + "b53550bcb22bb997.png": "n^{O(d)}", + "b53af2401c263444.png": "\\frac{1}{p^{2s-11}}", + "b53b2a4520551670.png": "\\tilde{\\beta}", + "b53e2f0a4721d4cc.png": "\\tilde{m}", + "b54121bd78cbc6c8.png": "\\frac{1}{r}e^{-m_{W,Z}r}", + "b54288330987a7e4.png": "a\\notin w", + "b542c50719ca6f5f.png": "=\\int u+(-v)dx", + "b542c81d6db40bb3.png": "\\sqrt{f}", + "b54afb7ad55d33c4.png": "\\pi_{0}(B^{+}C)", + "b5520f826a760991.png": "rF=\\underline{0}", + "b555bce43433083d.png": "f_{t}(\\zeta(t))=\\gamma(t)", + "b55666d4bead22e6.png": "\\{a,b,n-2,1\\}", + "b55d0a6667f6577d.png": "\\sqrt{2n}", + "b5631c3e966ddbe3.png": "\\hat{\\pi}", + "b5635e630237bbaf.png": "x=\\sum_{i}v_{i}^{T}xv_{i}", + "b565a1ec01f42f57.png": "U_{q}(gl(1|1))", + "b566dd11c8520db9.png": "\\lambda_{k}^{1/2}", + "b570910d73869dc9.png": "\\overline{4}3m", + "b5735927317bc33e.png": "\\hat{D}=D", + "b57767844ceb76a5.png": "\\Phi:N\\rightarrow P^{(1)}", + "b57c3086621bddff.png": "X_{i+1}\\cup\\beta(X_{i+1})", + "b57de54062741a6c.png": "\\tilde{z}", + "b57ed60913e966c6.png": "N_{A}\\approx6.022\\times10^{23}", + "b57f7f6c71488c01.png": "Df=(Dg)^{-1}", + "b580e8725bf5fd05.png": "\\partial_{t}L=\\frac{1}{2}\\nabla^{2}L", + "b585cf58d869840c.png": "P_{c}=\\frac{N\\hbar\\omega}{cV}=\\frac{N\\hbar k}{V}", + "b58f642059bec423.png": "\\tilde{e}_{i}\\tilde{f}_{i}", + "b590c203d54325c8.png": "\\alpha\\in A^{1}(k)\\subset P^{1}(k)", + "b5989eb76658a09a.png": "A\\underline{\\delta}B", + "b59a80ebb8219862.png": "F[x,y]=\\int_{E}xydt", + "b5a029591602886a.png": "(f-f^{2})\\sigma_{D_{0}}^{2}", + "b5a09e67c1b6f264.png": "L_{j}=inf_{k\\ge j}M_{k}^{1/k}", + "b5a3804c070e24ef.png": "F:M_{n}(K)\\rightarrow K", + "b5a38808cb96c4b8.png": "\\int r^{2}dm", + "b5b0b43a641a6e15.png": "d=(1/2)b_{2}", + "b5bc8df320e03a88.png": "\\prod_{i=1}^{m}Q(\\beta_{i}x)", + "b5c0b05a8717b258.png": "\\hat{\\Gamma},\\Gamma", + "b5c57d5a52a21bf4.png": "Pr[X\\in\\partial B]=0", + "b5caf17ac34a6d6d.png": "(AB)_{p,q}^{ij}", + "b5cb23a02abd456a.png": "X=(X(t),t\\ge0)", + "b5cda95ced550fc1.png": "\\sqrt{V}", + "b5d275eccc67ac7e.png": "D^{(t_{\\gamma})}", + "b5d5eb4a6a5ce6f4.png": "C_{c}=2\\sqrt{\\kappa I}", + "b5d887d9ad9ac2a4.png": "y=\\frac{1}{2}laea_{y}(\\frac{\\lambda}{2},\\varphi)", + "b5dd47f3282de74f.png": "u_{k,j}^{(0)}\\equiv\\partial u_{k}^{(0)}/\\partial x_{j}", + "b5de87a1e8562d84.png": "\\Omega_{x}=E(X^{\\prime}X)", + "b5e196afc0c53745.png": "|\\overline{TU}", + "b5ec2ebdb55db78d.png": "\\tilde{u}_{k}(K)", + "b5ed426e7f47db92.png": "FN_{2}(air)=0.79", + "b5ef78bcabb92b3e.png": "\\int_{S}\\vec{B}\\cdot d\\vec{S}=const", + "b5f17bb0fd6fdc4b.png": "E(\\lambda)=\\chi_{[0,\\lambda]}(T)", + "b5f7e25025f5d71b.png": "\\{\\begin{matrix}3,3,3,3,3,3\\\\ 3\\end{matrix}\\}", + "b5ffcca40ce5e3f5.png": "G:L\\rightarrow R-Mod", + "b6093d0320ea1e13.png": "[\\begin{matrix}S/I&S/I\\\\ 0&S\\end{matrix}]", + "b60d5ca77436aee3.png": "lim_{i\\rightarrow\\infty}c_{i}T_{a,r_{i}\\#}\\mu=\\nu", + "b60f65cbd8976419.png": "\\bigcup_{\\alpha\\in A}\\Sigma_{\\alpha}\\subset P", + "b6152f841de5685d.png": "-\\sqrt{s}", + "b61587fc4589c1cd.png": "\\frac{dE_{r}}{dx}", + "b6167582beb81132.png": "M(x)=e^{\\int P(x)dx}", + "b62088a2902f425a.png": "\\frac{d^{2}y}{d^{2}t}", + "b6237ce783dfa0bb.png": "V_{-}=Be^{\\frac{-1}{RC}t}", + "b62794540a7edb4c.png": "\\partial\\psi(\\theta)/\\partial\\theta", + "b627ebc34c667c56.png": "\\hat{T}_{\\pm2}^{(2)}=\\hat{a}_{\\pm1}\\hat{b}_{\\pm1}", + "b638cf5238858035.png": "\\frac{d\\rho}{dr}=-\\frac{\\rho(r)g(r)}{\\Phi(r)}", + "b6407f27990dfe9d.png": "\\overline{v_{i}}", + "b641c1bbc1615def.png": "P=Clocktick", + "b643d7d8079da5e8.png": "(16^{4x})^{2}", + "b644ad1436941978.png": "\\sum_{k=1}^{\\infty}(\\begin{matrix}\\alpha\\\\ k\\end{matrix})kx^{k-1}", + "b64ab821ccdd3466.png": "(\\begin{matrix}2n-2\\\\ n-2\\end{matrix})", + "b651ed94c7d5b9f4.png": "\\overline{\\Omega}", + "b6565fc7f47fc8e9.png": "(CH_{2}(COOH)_{2})", + "b661323b00a06e1f.png": "=(1003-x)^{2}", + "b666a615a9a5e1c1.png": "a\\sqrt{D}", + "b67024f188d5cb68.png": "W^{1-\\frac{1}{p},p}(\\partial\\Omega)", + "b67b5f3034d387c0.png": "A(i_{U,\\overline{U}})", + "b681726005375b86.png": "f_{s}=\\frac{1}{T}>2f", + "b681fd39a5801d5c.png": "\\Xi_{(\\alpha_{\\sigma})}", + "b689386c0c1db33d.png": "\\prod_{n}(z-c_{n})", + "b68acd13fe4eccb9.png": "\\sqrt[3]{0.125}\\cdot10^{-e^{\\pi i}}", + "b690f0ea003143de.png": "T_{v}^{-1}=T_{-v}", + "b693162a5de5042a.png": "\\oint_{\\partial T}f(z)dz", + "b697567d29a27028.png": "\\frac{V_{o}}{V_{i}}=-\\frac{D}{1-D}", + "b69b9571eaa1f057.png": "R_{g}=\\frac{1}{\\sqrt{6}}\\sqrt{N}a", + "b6a1e2f0061a4c75.png": "\\frac{\\hbar}{ea_{0}^{2}}", + "b6a296f8398db2bc.png": "\\sigma^{2}=3.5033\\cdot10^{-2}", + "b6a873526de24dae.png": "\\bigcup_{x\\in S^{c}}B_{ct}(x)", + "b6b2282142e88dd7.png": "(\\pm\\sqrt{2})^{2}-4=-2<0", + "b6bfd565e5db0041.png": "\\sqrt{x}+O(\\sqrt[4]{x})", + "b6c64bb65fe4d812.png": "k[X][f^{-1}]", + "b6ccf6700843e83c.png": "\\tau=\\sqrt{t^{2}-x^{2}/c^{2}}", + "b6d1316e0cd9fd24.png": "\\sqrt{-1}\\partial\\overline{\\partial}g=\\omega", + "b6d1b217d3f1d9cc.png": "(W;M_{0},M_{1})", + "b6d76fa1c3b55558.png": "c=F^{-T}F^{-1}", + "b6d8c4a0385f8291.png": "O(id^{2}+d^{3})", + "b6daa7396adeab8e.png": "\\Phi_{\\alpha}(A_{\\alpha}^{1},...,A_{\\alpha}^{n})", + "b6dc864e2221814a.png": "\\hat{n}_{b}", + "b6e1da34b44160eb.png": "-2log(p(y|\\hat{\\theta}_{0}))", + "b6e29421b00ef5bb.png": "1,1+x", + "b6e4659f9f892bad.png": "\\sqrt{\\frac{15}{56}}", + "b6e5c810d975d626.png": "J^{\\mu}=c\\overline{\\psi}\\gamma^{\\mu}\\psi", + "b6e896ebb99fba15.png": "d=(1/2)b_{2}", + "b6ebb8429fe5a1a1.png": "[\\begin{matrix}1&1\\\\ -1&1\\end{matrix}]", + "b6f29ca83c5f5d36.png": "L(\\vec{r},\\hat{s},t)", + "b6f3ff06e69c3f07.png": "B=10log_{10}(b)", + "b6f654ab4575d24c.png": "f(x|t)=Tr(x)", + "b6ff460988b141c9.png": "(\\begin{matrix}8\\\\ 4\\end{matrix})", + "b6ff56a165972e8a.png": "sin\\phi=\\frac{(r^{2}-r_{1}r_{2})}{r(r_{1}-r_{2})}", + "b7008b2dee929fec.png": "x^{+}=\\frac{t+x}{\\sqrt{2}}", + "b700d9bdb27aa20e.png": "\\tilde{O}(1)", + "b7082ad515449f60.png": "(\\begin{matrix}p+q+3\\\\ 2\\end{matrix})", + "b70ab535459df392.png": "\\int_{C}=0", + "b70ff0958d87fb06.png": "\\overline{t}(modl)", + "b710f37ba7d99c5e.png": "\\prod_{i=1}^{k}p_{i}^{(n_{i}+1)}", + "b714976c251a7b18.png": "[\\begin{matrix}0\\\\ 0\\end{matrix}]", + "b7157f686158c796.png": "\\omega_{\\rho}^{k}", + "b7161c8f77b916b2.png": "(\\begin{matrix}1&t\\\\ 0&1\\end{matrix})", + "b71ef3fcf1cf976d.png": "J=[\\begin{matrix}0&1\\\\ -1&0\\end{matrix}]", + "b720b3fd051ab3ae.png": "t\\{\\begin{matrix}2\\\\ n\\end{matrix}\\}", + "b7285828a130e8bd.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "b72ccf82f83e9e9b.png": "\\int_{\\infty}^{\\infty}", + "b7305efc6af1fe02.png": "\\frac{dy}{dx}=0", + "b7335ca57c6958b4.png": "X(\\underline{k})", + "b7390ff73d1a4e69.png": "A=4\\pi{R_{p}}^{2}", + "b73951ccce15e9c7.png": "M=m/\\sqrt{1-v^{2}/c^{2}}", + "b73b93f3b636ec9b.png": "\\tilde{E}=E\\times\\mathbb{Z}_{n}", + "b740323f986a7903.png": "s_{\\alpha}:M\\rightarrow T^{*}M", + "b7404b1007328340.png": "r", + "b740fb514e36b832.png": "X_{n}=[\\begin{matrix}x_{n}\\\\ y_{n}\\\\ z_{n}\\end{matrix}]", + "b7418bee6842762e.png": "\\tilde{D}_{8}", + "b7420e24c1f0f219.png": "[\\begin{matrix}0&1\\\\ 0&0\\end{matrix}]", + "b743872171b17618.png": "|\\epsilon_{\\sigma_{1},...,\\sigma_{n}}|", + "b744c7c8aaba8859.png": "O(\\frac{1}{\\epsilon^{d}}logn)", + "b747d0f6f0e18f4c.png": "U_{1}=[\\begin{matrix}1&0\\\\ 0&1\\end{matrix}]", + "b753410312cc1fd4.png": "\\tilde{g}=e^{2\\varphi}g", + "b758dc1d5938dddb.png": "E_{c}=\\frac{|E|^{2}}{8\\pi}", + "b76068e28261fafd.png": "e^{x}\\ge(1+\\frac{x}{n})^{n}", + "b76469ee8ce6c962.png": "(i\\cdot n)\\hat{f}(n)", + "b765317a97d8047e.png": "(\\begin{matrix}k\\\\ 2\\end{matrix})-m", + "b769165d6a6bbaf4.png": "Z_{y^{\\beta}}", + "b76a7f9752414d5a.png": "T[h(x)]-1", + "b76fb5a8d37a1e01.png": "V^{\\prime\\prime}:=\\bigcap_{a\\in A_{0}}V_{a}^{\\prime}", + "b77a6e618f7b04f4.png": "G:L\\rightarrow R-Mod", + "b7831089c8bc4400.png": "[A]_{p}\\subseteq cl(A)", + "b78a405ed485ed4b.png": "-\\sqrt{\\frac{4}{15}}", + "b793ccef06d72fd3.png": "|++\\rangle", + "b79845b440e944da.png": "(\\begin{matrix}5\\\\ 5\\end{matrix})", + "b79dda62238e3c19.png": "\\tilde{v}_{i}", + "b7a90df707dbfbf2.png": "D_{192}\\approx\\frac{1}{4}D_{96}", + "b7aa88e8ab3edc9b.png": "C=\\frac{\\partial P}{\\partial\\rho}", + "b7b2f2fd36c811ae.png": "G(x)=F(a+bx)", + "b7b452bc096bd836.png": "\\beta=\\frac{\\partial f}{\\partial y}", + "b7bac9eea37eb812.png": "E=\\frac{1}{2}(t-y)^{2}", + "b7bd9257657360e4.png": "p", + "b7c038fb50ef3659.png": "min\\{e(u),c_{f}(u,v)\\}", + "b7c1440f9fffb4bc.png": "(\\begin{matrix}3\\\\ 4\\end{matrix})", + "b7c75382ff52249f.png": "\\sqrt{1+[f^{\\prime}(x)]^{2}}", + "b7ce307639fdeb48.png": "-I=I_{0}sin\\delta", + "b7d2925d428f965d.png": "L_{+}", + "b7d87d55c662efdf.png": "\\sqrt{2}a", + "b7de4faaa94aa99b.png": "\\Psi=\\frac{1}{\\sqrt{2}}(\\phi_{1}+\\phi_{2})", + "b7df034043a5d157.png": "V=(\\begin{matrix}1&-1\\\\ 0&1\\end{matrix})", + "b7e2e2159841115f.png": "G(\\vec{R}-\\vec{R}^{\\prime};N)", + "b7e708764fc85ea4.png": "s_{\\lambda}s_{\\mu}=\\sum_{\\nu}c_{\\lambda,\\mu}^{\\nu}s_{\\nu}", + "b7e925811dfdb48e.png": "C_{E_{2}}^{J}=-\\epsilon_{1}^{1}\\epsilon_{2}^{3}/D", + "b7eb57d4ba0bf3f9.png": "[\\begin{matrix}3&1\\\\ 0&3\\end{matrix}]", + "b7f3b4b74d37ba1c.png": "\\prod_{p}(a,b)_{p}=1", + "b7f475d4155f41b1.png": "\\underline{S}_{\\lambda}", + "b7f838e1b8daf5cb.png": "\\{e,k_{1},k_{2}\\}", + "b7fb5399050270f4.png": "(\\begin{matrix}N\\\\ 2\\end{matrix})", + "b809bc002513fe57.png": "\\underline{x}(t)", + "b80c23bbac2b4839.png": "H(\\tilde{x}|\\alpha)", + "b80fbd641ac51b87.png": "Dir(\\alpha/K\\cdot1_{K})", + "b814f62616af972a.png": "\\int_{c(r)}R(z)dz=0", + "b81b5b99a9eb88cd.png": "\\chi_{+}^{-k}=\\delta^{(k-1)}", + "b81d9e4f46f5b34d.png": "\\overline{S}", + "b81f08dd19017492.png": "f=(\\begin{matrix}0&0&V_{s}\\end{matrix})^{T}", + "b82079727064fe01.png": "(\\begin{matrix}r^{-1}&0\\\\ 0&r^{-1}\\end{matrix})", + "b828b5f1ef9b36fe.png": "E_{1}=Ae^{i(kx-\\omega t)}z", + "b82af69b8107934c.png": "\\frac{\\partial F}{\\partial x}=I", + "b82d78e1398f4992.png": "C(\\rho)=\\langle\\rho^{2}\\rangle/\\langle\\rho\\rangle^{2}", + "b82f4528b350129d.png": "T_{1}(A)=", + "b83c89cab6e01750.png": "(\\begin{matrix}n\\\\ 3\\end{matrix})", + "b83e5b3c1d37662b.png": "H(x)=1_{(0,\\infty)}(x)", + "b83ea92b4f983645.png": "\\gamma_{nl}|A|^{2}A", + "b84540ee1d0c71f2.png": "2(N-1)-(R-1)", + "b84888c82124a540.png": "\\Delta E^{tot}=Q+W", + "b852e120b7a7bec7.png": "(\\begin{matrix}2&-2\\\\ -1&2\\end{matrix})", + "b854af34e30db3c1.png": "C(T)^{*}", + "b85542786afe732f.png": "|\\overline{VU}|", + "b85aa52d647acd17.png": "\\int_{X}fd\\mu", + "b85acb8c4ee8081e.png": "(\\begin{matrix}2\\\\ 0\\\\ 19\\end{matrix})", + "b85c98e7cc11969d.png": "P(Y>n)\\le\\frac{E(Y)}{n}", + "b85dab5f5e62b5cd.png": "\\Pi_{i}=\\cup_{o\\in S_{i}}H_{o}", + "b85ed759d1b69aa4.png": "(\\begin{matrix}6\\\\ 4\\end{matrix})", + "b86bebcb3279c85a.png": "x_{0}\\notin\\partial E", + "b8747f9c4e702474.png": "M\\int vds", + "b87632d9b6938214.png": "[\\begin{matrix}x\\\\ x^{2}\\end{matrix}]", + "b8766401be38f482.png": "S=-mc^{2}\\int_{C}d\\tau", + "b884913eb28bf1a7.png": "||u-f||_{p}^{p}", + "b884b2c780d908b7.png": "V_{\\theta}=\\frac{2n}{(n-1)^{2}}", + "b8854e7a32e69bb9.png": "-k\\sum_{i=1}^{\\Omega}P_{i}lnP_{i}", + "b885d7e9cd5eb507.png": "\\tilde{W}_{t}=W_{t}+\\frac{\\mu-r}{\\sigma}t", + "b88612e96d9ad230.png": "\\xi,\\xi_{1},\\xi_{2},\\xi_{3},...", + "b88b82928e8b52d8.png": "(\\begin{matrix}6\\\\ 3\\end{matrix})", + "b88ccde9ff8c8bff.png": "A=16\\pi G^{2}M^{2}/c^{4}", + "b890c8aa3562bd43.png": "X:=\\bigcup_{k=1}^{m}3B_{j_{k}}", + "b8912e06261274b9.png": "logmin(n_{x},n_{y})", + "b89853e73dd55439.png": "(\\begin{matrix}p+q\\\\ p\\end{matrix})", + "b89c77d2f4cb4041.png": "(\\begin{matrix}m+n\\\\ m\\end{matrix})", + "b89ee1c621b48aa4.png": "(\\begin{matrix}n\\\\ c\\end{matrix})", + "b8a2242bdbefd0e2.png": "P^{m}(x,B)\\ge\\nu_{m}(B)", + "b8aaf4c35f10d113.png": "K_{h_{\\lambda}}(X_{0},X)", + "b8abadd2e4592a5b.png": "U=\\int f(v)E(v)dv", + "b8ae9fee45968be1.png": "I(\\theta)=p_{i}(\\theta)q_{i}(\\theta)", + "b8b867b261d0abf5.png": "(\\begin{matrix}d-1\\\\ n\\end{matrix})", + "b8be65261db9146a.png": "p_{i}((x_{j})_{j\\in N})=x_{i}", + "b8c21ecd458e04a4.png": "(\\begin{matrix}p\\\\ r\\end{matrix})", + "b8d00de0eebf608b.png": "\\sum_{n=0}^{\\infty}\\frac{n+1}{2^{n}}", + "b8d1e3a8fbbc91b8.png": "m=(n^{\\prime}-n)", + "b8d2d6abd26dd061.png": "s\\{\\begin{matrix}4\\\\ 4\\end{matrix}\\}", + "b8d2d944868c22f6.png": "\\Psi_{mn}=exp\\frac{-a_{mn}}{T}", + "b8d698a51c1b1f24.png": "(Pf)^{\\wedge}=Q\\hat{f}", + "b8da33469317cbff.png": "Mo=\\frac{We^{3}}{FrRe^{4}}", + "b8df8ad6ac88c0d5.png": "(\\begin{matrix}n\\\\ 2\\end{matrix})", + "b8e3e70712004bcc.png": "4\\overline{)956}", + "b8e939b707d91d00.png": "e^{1/2}=\\sqrt{e}", + "b8ea0ce1cf9519a8.png": "\\int_{0}^{1}f(x)dx=1", + "b8eee1ed9fc38e8f.png": "(\\begin{matrix}-1\\\\ 0\\end{matrix})", + "b90296a59e00dcff.png": "x_{i}=[P^{i}(R)]", + "b90501d5d7741f7e.png": "1-\\frac{2}{4}=0.5=50\\%", + "b90b58ce494b65b2.png": "(\\begin{matrix}x&-y\\\\ y&x\\end{matrix})", + "b90c1e9c13f26583.png": "R_{0}=\\sqrt{x^{2}+y^{2}+z^{2}}", + "b90c943877c2823d.png": "J_{c}\\propto T_{c}^{\\alpha+1}", + "b911c3cc9aec20d5.png": "S_{+}|+\\rangle=0", + "b914d43b1773deb9.png": "modl^{n+1}", + "b91bd2eae2959076.png": "\\sum_{j=0}^{n}(-1)^{j}(\\begin{matrix}n\\\\ j\\end{matrix})P(j)=0", + "b91c1821962cb152.png": "\\tilde{d}_{m}", + "b91dac3256f4af70.png": "\\frac{d}{dx}x", + "b9215d111ce8af2d.png": "H_{n}(Y\\cap Z)=0", + "b92685a7c781bd1b.png": "(A+B)\\sqrt{k}", + "b927b4f9b2708c7f.png": "\\sum_{n=1}^{\\infty}ln(a_{n})", + "b92fde44756c9034.png": "K", + "b93348fb0aa6723e.png": "\\hat{t}", + "b938b2a268ee4a12.png": "\\tilde{\\nu}", + "b939d8b433ae4ccd.png": "\\frac{\\partial\\phi}{\\partial x^{\\mu}}", + "b93d5864c17f3637.png": "\\sqrt{t}", + "b93ef37ad9204099.png": "\\overline{Y_{v}}=P_{\\overline{x}}\\overline{X_{v}}", + "b941407defba3047.png": "\\overline{W}_{t}", + "b94223538d33a228.png": "a=\\frac{2}{ln(10)}", + "b945009455da884d.png": "\\int_{c(r)}R(z)dz=0", + "b94573f0a9c19ae2.png": "x^{i}\\circ f(t)=tv^{i}", + "b946d5bc95bf3949.png": "3(x+1)=3x+3", + "b94d94b8c01ea9a7.png": "\\underline{\\mathbb{Z}}_{X}", + "b94e9189bb411249.png": "(\\frac{1}{2})^{(2\\times2)}=\\frac{1}{16}", + "b9521ddfc8659659.png": "+\\sqrt{2}", + "b95994e27ec0a6dd.png": "u\\notin V^{\\prime},W^{\\prime}", + "b95c1dd799018ada.png": "C_{1}:=\\{z:|z|=r_{1}\\}", + "b95d5d8a7b6bbff3.png": "\\{v_{1},v_{2}\\},\\{v_{2},v_{3}\\}", + "b95e206f14b6c519.png": "A=[\\begin{matrix}1&0&0\\\\ 0&0.6&0.8\\end{matrix}]", + "b961d11c79258918.png": "[w_{a}E(R_{a})]", + "b969c7a7ef459e53.png": "(-\\infty,-1/e]", + "b96a404ebd9beaa4.png": "f(S_{i},S_{1}^{i},...,S_{K}^{i})", + "b96eb8f4282936e8.png": "r+3^{y}>s+3^{x}", + "b96f379ecddda080.png": "\\frac{1}{B(E,0)}=1", + "b970857e5c1c3c2e.png": "f(x_{1},...,x_{n})=...", + "b976af1a7c5d4eb4.png": "A=\\int_{S}\\omega", + "b9773d6eb58f815a.png": "\\int f^{-}d\\mu", + "b97b36d647add467.png": "\\underline{P}X=\\{O_{1},O_{2}\\}\\cup\\{O_{4}\\}", + "b9809ea0d21cf3ec.png": "hr\\{\\begin{matrix}p\\\\ q\\end{matrix}\\}", + "b986e69e5a1bd459.png": "\\sigma_{ij}=\\sqrt{\\sigma_{ii}\\sigma_{jj}}", + "b987d0fe7b3bf20f.png": "(\\begin{matrix}0&0\\\\ 0&1\\end{matrix})", + "b989e55b1bca479c.png": "\\nu", + "b99398f4a677c33c.png": "\\hat{X_{a}}", + "b9970699db1048b2.png": "F_{r}=\\frac{v}{\\sqrt{g\\frac{A}{B}}}", + "b9a2e55dfa7ecc7c.png": "-\\frac{p\\dot{r}}{r^{2}}=-\\epsilon sin\\theta\\dot{\\theta}", + "b9a8232a68567905.png": "I(X;Y)\\le H(X)", + "b9ac5638b391058c.png": "E=1-\\frac{T_{Low}}{T_{High}}", + "b9b05e68f98a8ecf.png": "\\int vds", + "b9b95d1a3c61145f.png": "A=16\\pi G^{2}M^{2}/c^{4}", + "b9bff22ffea6e692.png": "\\hat{u}_{k}", + "b9c58a430739a813.png": "log_{2}(6^{5})", + "b9c721b79ffbd1c7.png": "x=\\sqrt[3]{u}+\\sqrt[3]{v}", + "b9cae7d1437c6e3f.png": "\\{1,2,3\\}\\notin\\{1,2,3\\}", + "b9cb0c1f58c492e3.png": "\\int e^{x}dx=e^{x}+C", + "b9daf32ade861ee9.png": "(\\begin{matrix}v&0\\cdot\\cdot\\cdot0\\end{matrix})", + "b9de3fb1edd031c2.png": "W=\\int PdV", + "b9df7a86ba91ebdd.png": "\\iint f(x,y)dxdy", + "b9e5216ea56e1114.png": "[\\begin{matrix}S/I&S/I\\\\ 0&S\\end{matrix}]", + "b9e61bbea57933d9.png": "Qf=\\int fdQ", + "b9e70a0d94b12008.png": "[\\begin{matrix}1&0\\\\ sC&1\\end{matrix}]", + "b9e958e4304bac76.png": "sin(\\theta^{1}(t)-\\theta^{2}(t))", + "b9f3d4441053b38e.png": "H=aP^{2}+bQ^{2}", + "b9fd722aa75288a1.png": "k\\ge exp(c\\sqrt{logd})", + "ba027fb686357819.png": "u(x_{1},...,x_{n})\\ge u^{*}", + "ba07259ae27bd391.png": "02b/2D", + "ba90fdd6d237ff2f.png": "Y_{i}-\\hat{Y}_{i}", + "ba92f93d0266bf21.png": "2347)", + "ba95ef9da2ca0514.png": "K\\\\ G/U=A_{+}", + "ba982b1889ef1d1f.png": "\\hat{\\alpha}=\\hat{\\beta}", + "ba9835f882e1d9b2.png": "\\mu y=\\int\\mu q(x)dx", + "ba9c82c75c3ef203.png": "\\Sigma_{\\varphi}^{\\varphi}", + "baa2fe4944e002c2.png": "[f]\\notin N", + "baaae1007825ff42.png": "\\sum_{k=1}^{\\infty}\\beta_{k}<\\infty", + "bab093a1cfaab2f1.png": "\\chi(S^{\\prime})=N\\cdot\\chi(S)", + "bab1b8ab3859fdef.png": "f(t,n)=\\sum_{i=0}^{n}(\\begin{matrix}t\\\\ i\\end{matrix})", + "bab7ae8a615a1356.png": "\\frac{dP}{dw}=\\frac{\\partial V}{\\partial E}\\frac{dE}{dw}-L", + "bab7d2184bb27ba6.png": "-\\hat{y}", + "babe8b7e2d5c55b7.png": "(\\begin{matrix}a&b/2\\\\ b/2&c\\end{matrix})", + "bac2feb29c050a81.png": "M=-EI\\frac{d^{2}w}{dx^{2}}", + "bad576cff7b1f57b.png": "ss\\{\\begin{matrix}2\\\\ 3\\end{matrix}\\}", + "bad7a60cac50de4b.png": "\\sum_{i=1}^{N_{\\lambda}}m_{i}=N_{v}", + "bad85cebf669e3d9.png": "R", + "badd00f97316b455.png": "\\frac{\\partial i_{l}}{\\partial x}=-i_{m}", + "bae14b617c17f07a.png": "E=E_{B}(1-\\frac{d}{D})", + "bae20018aca6f636.png": "N=(\\begin{matrix}n+d\\\\ d\\end{matrix})-1", + "bae8c7d71825a525.png": "a\\underline{x}^{-k}+b\\delta^{(k-1)}", + "bae8d6705be18d67.png": "C_{+},C_{-}", + "bae970ae86428ef6.png": "[x_{w}y_{w}z_{w}1]^{T}", + "baf0eaafca10933e.png": "2", + "baf6a34b9a663f87.png": "(\\begin{matrix}7\\\\ 5\\end{matrix})", + "baf87a8630e7dc82.png": "F^{\\bullet}\\Omega_{Y}^{p}(logD)", + "bafdf3f5da76c388.png": "(1\\pm i)/\\sqrt{2}", + "baff1a654627b871.png": "[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "bb030d6820ba2089.png": "\\sqrt{rs}", + "bb04ec0be50bba97.png": "(\\begin{matrix}0\\\\ 1\\end{matrix})", + "bb0d7a9367985ec4.png": "\\lambda_{j}=-\\frac{(2j-1)^{2}\\pi^{2}}{4L^{2}}", + "bb13f38c07874030.png": "(s-a)r_{a}=\\Delta", + "bb1744063f44cc79.png": "(\\frac{\\partial E}{\\partial v})_{k}", + "bb1b9f1ed8985133.png": "P_{ij...}=P_{ij...}(X,t)", + "bb1bb9a98a90092c.png": "\\int_{a}^{b}\\pi f(x)^{2}dx", + "bb1c7844ee41db0b.png": "\\int y^{2}dv", + "bb1f77e4845dd29a.png": "L^{2}\\ge4\\pi A-A^{2}/R^{2}", + "bb20e5d347cd0a3c.png": "M<|Q|", + "bb22762c43deb1d1.png": "\\alpha_{i}(\\alpha_{j}^{\\vee})=c_{ji}", + "bb23d449a0249bbf.png": "S_{a}=x+\\overline{X}a", + "bb2bad6d57fa4d3a.png": "\\int_{0}^{1}f(x)dx=\\infty", + "bb2d67438d2f7cc9.png": "-\\int E\\cdot dl", + "bb2e3cafaf5803da.png": "\\rho_{0}\\frac{\\partial u}{\\partial t}+\\nabla p=0", + "bb3fd35a8afe73ac.png": "\\frac{dA}{dt}=[A,H]+\\frac{\\partial A}{\\partial t}", + "bb3fef31a9ffd41b.png": "1+N\\times(-)", + "bb4142ef4640860c.png": "\\delta_{x}(s)=(s^{\\prime},0)", + "bb42f339e3bfc418.png": "\\{\\hat{f}_{n}\\}_{n=1}^{\\infty}", + "bb4dff154abfd0f5.png": "f(x)=A\\prod(x-c_{n})^{a_{n}}", + "bb50fadab0dcd047.png": "(\\alpha K+\\beta L)", + "bb51abec45d8300f.png": "\\int ds\\sqrt{v}", + "bb56b15f09688aac.png": "\\underline{f}(x)=f(x)", + "bb5806407d8c8f6d.png": "r=fr_{0}+gr_{0}^{\\prime}", + "bb5eea8aa6610708.png": "\\sum_{i=1}^{n}-p(x_{i})logp(x_{i})", + "bb61f1c3f1b5d06f.png": "W=\\int VdP", + "bb68249af44d5980.png": "||x-P_{F}(x)||^{2}", + "bb6db56b12e95113.png": "\\sum\\frac{1}{8n}", + "bb6e4b47e20d3065.png": "2r(X)+r^{\\prime}(\\sqrt{X})", + "bb71eabe02a21e24.png": "f(x)=\\prod_{i<4}(x-x_{i})", + "bb74a343a39fac0a.png": "(\\begin{matrix}6\\\\ 3\\end{matrix})", + "bb762f4ea197246f.png": "[m/2^{p},n/2^{p}]", + "bb7798263292a2e4.png": "(1+i)^{t}>1+it", + "bb79926aefaafba5.png": "[e_{i}^{\\prime}]=[L][e_{i}]", + "bb7bb957e92aeea3.png": "\\beta=\\omega\\sqrt{LC}", + "bb81e7721bdc5515.png": "\\int_{0}^{1}D(x)dx", + "bb88c030db1343c2.png": "C_{\\alpha\\dot{\\alpha}}", + "bb8a7b2e4554a852.png": "10^{-k}0)", + "bbf82152ed406b2e.png": "{\\rho^{\\lambda}}^{j}", + "bbfbae5683f05065.png": "I\\subset Z[\\eta]", + "bc0129d6a2315c41.png": "C\\propto1/\\sqrt{B}", + "bc07bc070c66cae8.png": "B^{\\prime}\\in(\\begin{matrix}C\\\\ B\\end{matrix})", + "bc132322ea4188ca.png": "\\overline{x}^{i}=Ax^{i}", + "bc172e4c5d8a2aac.png": "\\epsilon(t)=\\frac{\\sigma_{0}}{E}+t\\frac{\\sigma_{0}}{\\eta}", + "bc22450f67124ac1.png": "1/\\sqrt{n}", + "bc2d104379aec659.png": "L=\\mathbb{Q}(\\sqrt{d})", + "bc35bd51284b0aac.png": "(\\begin{matrix}5\\\\ 0\\end{matrix})", + "bc37359361339881.png": "[0]=\\emptyset", + "bc394ad2f5946a8d.png": "\\Theta_{(g_{u})}", + "bc3b1c0f0bad0d20.png": "\\Omega_{u}^{\\phi}", + "bc3d45eaea2f7c8d.png": "Z=(\\begin{matrix}x&y\\\\ y&x\\end{matrix})", + "bc3d69fffd70991e.png": "\\frac{\\partial F}{\\partial y}=J", + "bc40637f4b544835.png": "\\frac{dy}{dx}", + "bc427983714f192f.png": "\\prod_{x}\\frac{x+1}{x}=Cx", + "bc479496c32e49e1.png": "-\\mu_{e}E", + "bc59b9c029881b22.png": "\\prod_{i\\in I}R_{i}", + "bc5bcbe1f08db34e.png": "f(r)=\\frac{h^{2}}{p^{3}}\\frac{dp}{dr}", + "bc5f5bd05519b668.png": "a\\hat{x},a\\hat{y},a\\hat{z}", + "bc66dea79b63fdd2.png": "\\omega^{2^{p-1}}=-1", + "bc68a37d36cdf40e.png": "\\delta=\\hat{h}(n)-h(n)", + "bc6d023956d33e26.png": "\\lambda^{3}=(\\begin{matrix}1&0&0\\\\ 0&-1&0\\\\ 0&0&0\\end{matrix})", + "bc6d3433aee05702.png": "\\hat{V}", + "bc75d00e175ee3e5.png": "I=-\\frac{1}{2}log(1-\\rho^{2})", + "bc77ef9fc9c67460.png": "y=\\frac{\\int xe^{-x}}{e^{-x}}", + "bc7bb87054463fde.png": "F=S\\frac{(1+i_{f})}{(1+i_{d})}", + "bc7c6b709866a0c9.png": "p<\\frac{(1-\\epsilon)lnn}{n}", + "bc7f38e36af82c37.png": "\\int f(x)dx=1", + "bc898f36a9705b66.png": "L=\\sum_{n=1}^{N}\\rho_{n}\\langle f_{n},\\cdot\\rangle g_{n}", + "bc8f1b39bd6fe4af.png": "\\frac{d}{dx}", + "bc96950516557b55.png": "\\int p(x)dx=1", + "bc977ccb50392e5b.png": "Fe(x)=\\frac{\\varphi^{x}-\\varphi^{-x}}{\\sqrt{5}}", + "bc9aa779a6d31578.png": "\\frac{\\partial\\omega}{\\partial t}=\\nu\\frac{\\partial^{2}\\omega}{\\partial z^{2}}", + "bc9ae5db8701bc4b.png": "L(M=i)=[m\\le i]{(\\begin{matrix}i\\\\ N\\end{matrix})}^{-1}", + "bc9fc1e15a647ef2.png": "\\tilde{C}_{4}", + "bcaa2b3d8767a925.png": "I=\\int_{m}^{n}f(x)dx", + "bcb0289f7455f334.png": "{(x_{n})}_{n\\in N}", + "bcb07bd7c566068c.png": "O(nlogn)", + "bcb2c5625d7f572c.png": "y=\\int_{0}^{2}xdx", + "bcc117da816cdc98.png": "\\delta_{M,D}^{0}(h)=h", + "bcc3d6ae4f231d3d.png": "b=z_{j}^{-}", + "bcc704f13be183f0.png": "0\\le\\underline{d}(\\vec{X})\\le\\overline{d}(\\vec{X})\\le n", + "bcc71030c17e45a6.png": "[x_{k}]_{\\times}", + "bccd5287bd026767.png": "\\hat{P}", + "bcd17bdd322bacd5.png": "M^{(\\chi_{\\nu})}", + "bcdcb95033f81a35.png": "u(x)=\\frac{x^{1-\\gamma}}{1-\\gamma}", + "bcdd8495b74ee79d.png": "(n_{d/2+1},...,n_{d})", + "bce21656c04526c4.png": "p(z)=a\\prod_{n}(z-c_{n})", + "bce7260e0edebfc7.png": "-\\sqrt{\\frac{4}{15}}", + "bce826d2f517c144.png": "\\sqrt{p}", + "bce882eaffbb062e.png": "A=[\\begin{matrix}1&1\\\\ 1&1\\end{matrix}]", + "bcec8d1ac0ccbd32.png": "\\int_{K}f(gk\\cdot y)dk", + "bcf2e5a9a5054588.png": "S=\\int_{a}^{b}x^{x}dx", + "bcfcbea0e20bc197.png": "R=\\sqrt{x}u", + "bcff9ba526f8f49e.png": "q_{i}=2p_{i}(1-p_{i})", + "bd0e8d32deb4ca56.png": "-\\frac{d^{2}}{dx^{2}}", + "bd12461b1ea7b24f.png": "O_{Q(\\sqrt{-5})}", + "bd1724b3ce643a5a.png": "(\\begin{matrix}p+q+3\\\\ 2\\end{matrix})", + "bd186e4b0ef35027.png": "\\epsilon_{0}(\\rho,R,L)", + "bd1e2927d96ca3bf.png": "(\\begin{matrix}a\\\\ a+1\\end{matrix})=0", + "bd270de0eaebead5.png": "\\sqrt{n}\\in Z", + "bd2965383638d0ef.png": "\\frac{d\\theta}{dx}=\\frac{-4S}{S^{2}+4x^{2}}", + "bd3608529c683423.png": "2(\\begin{matrix}n\\\\ k\\end{matrix})", + "bd3900f118fa5c3f.png": "A_{p}e^{j\\theta_{p}}", + "bd390cb93a329839.png": "(\\begin{matrix}n\\\\ 5\\end{matrix})", + "bd3b80cf1951a9f7.png": "e_{v}=m_{v}g_{v}rln(\\frac{S}{r})", + "bd3bb5bc0aea08d0.png": "\\frac{dx}{dt}=\\dot{x}", + "bd3cea67864303b6.png": "Q=\\int_{R}q|\\psi(r)|^{2}d^{3}r", + "bd3e9bc1585b4762.png": "p_{s+1,l}(z)", + "bd40dffa84a972aa.png": "-\\frac{\\partial S}{\\partial t}=H", + "bd40fc8d79806fd8.png": "M,\\hat{d}", + "bd42cec068052359.png": "\\frac{T^{2}}{C_{V}}", + "bd4a8a7a71e49060.png": "\\prod_{p}f(p)", + "bd4b879190f64615.png": "\\lceil-x\\rceil=-\\lfloor x\\rfloor", + "bd51054088d5d2fa.png": "\\underline{O}^{n}", + "bd52b4ce408ed29b.png": "\\{\\begin{matrix}3\\\\ 6\\end{matrix}\\}", + "bd56e9edc4367686.png": "\\prod_{v}\\overline{M}_{g_{v},n_{v}}", + "bd5bd2ae3eb540a2.png": "\\int_{0}^{T}g(t)dt", + "bd5cf90b0fa78aca.png": "-S_{t}e^{r(T-t)}", + "bd5dc7709d3e2bd6.png": "\\tilde{c}(\\Pi)", + "bd61c334385b9002.png": "\\tilde{n}=\\frac{P_{r}}{P_{r}+P_{l}}", + "bd663d47700a1230.png": "\\mathbb{Q}", + "bd695b790bbe4264.png": "\\Lambda(e^{\\prime})=\\{1\\}", + "bd6d6bb55681d5f4.png": "-\\frac{1+\\xi^{2}}{2}\\partial_{\\xi}", + "bd722e37dbbf96eb.png": "\\sqrt{\\Psi}", + "bd7ed8bf25087539.png": "\\hat{u}_{k}", + "bd8474d5be4dfbd4.png": "\\frac{\\partial f_{k}}{\\partial x_{i}}", + "bd8516a6f83b2526.png": "(c:a:b)\\cdot\\tilde{ab}:2\\cdot m", + "bd8528690b230844.png": "(\\begin{matrix}t\\\\ 0\\end{matrix})=1", + "bd8c87bbac5b1315.png": "\\delta^{*}\\approx\\frac{1.72x}{\\sqrt{Re_{x}}}", + "bd9701518d05cc01.png": "w=\\sqrt{1-\\frac{U}{E}}", + "bd9eef740c29b453.png": "\\frac{1}{2NA_{o}}=\\frac{m-P}{mP}N", + "bd9f9290b68ce9e3.png": "M=(\\begin{matrix}1&-1\\\\ 0&0\\end{matrix})", + "bd9ffe579eb10d33.png": "2^{7/12}=\\sqrt[12]{128}", + "bda07c53c229bfa8.png": "1\\in H^{0}(X)", + "bda08c0667d38702.png": "\\hat{C}", + "bda420a7ab48a86e.png": "\\{0,1,-1\\}", + "bdaa6e29d7e6365d.png": "A=4A_{0}=\\sqrt{3}a^{2}", + "bdbfeb6830f413b0.png": "y=\\frac{1}{2}laea_{y}(\\frac{\\lambda}{2},\\varphi)", + "bdc2a6f1b00758b6.png": "\\lambda(y_{i})>", + "bf0f2370863968e1.png": "\\nabla v=(\\begin{matrix}0&0&0\\\\ \\dot{\\gamma}&0&0\\\\ 0&0&0\\end{matrix})", + "bf0f3ad44ef7d10c.png": "\\tilde{A}_{7}", + "bf119e4a38146b65.png": "\\int dx=x+C", + "bf146b7fc6f3ee79.png": "\\langle r,a|r^{3},a^{2},arar\\rangle", + "bf16a06b521e2663.png": "\\int(1/lnx)dx", + "bf203c5a8b460323.png": "\\frac{\\partial V}{\\partial Y}=\\lambda", + "bf215481dfb3b4bd.png": "\\beta_{n}+n=-a", + "bf2280bc3d0948ab.png": "1\\le\\frac{m}{d}\\le\\sqrt{2}", + "bf2316eeea831b27.png": "min_{i}Pr(R_{i}<\\underline{R})", + "bf23b76385cc3790.png": "K_{2}^{M}(Q_{p})", + "bf2425b57e8ea31b.png": "\\omega_{N}^{n}=e^{-\\frac{2\\pi i}{N}n}", + "bf29626a048822ce.png": "w_{i}=\\frac{\\partial u}{\\partial a_{i}}", + "bf2b30a5d5ed566a.png": "a^{2}+ba-ab-b^{2}", + "bf2b6311c52da256.png": "\\hat{\\zeta}", + "bf2d3925d6ca3d65.png": "\\int_{0}^{1}g_{n}=1", + "bf2d9d9a87788aa4.png": "sin^{2}(\\alpha_{0})=\\frac{B_{0}}{B_{m}}", + "bf32f0bfded7ae3b.png": "(\\overline{y}^{i})", + "bf35791f12724386.png": "\\hat{S}^{2}", + "bf37b1eb9fcc74de.png": "\\hat{y}\\in\\{-1,1\\}", + "bf3e77939d7a8ef5.png": "D(P_{max})=0", + "bf410c027265f921.png": "\\prod_{i\\ne\\beta}X_{i}", + "bf45febce2798116.png": "\\Pi_{\\omega}^{\\delta}", + "bf509db74779fff5.png": "(\\begin{matrix}8\\\\ 3\\end{matrix})", + "bf5264c8ebb855d2.png": "\\hat{y}(n_{1},n_{2},...,n_{m})", + "bf549c9b652bc778.png": "\\Omega=E[X^{2}]", + "bf5e90780df41b22.png": "I(X;Y)\\le H(X)", + "bf61d053233da174.png": "\\frac{1}{N}\\frac{dN}{dt}=\\frac{ln(\\frac{1}{2})}{T_{1/2}}", + "bf66825324cbac09.png": "\\int dV\\rho=q_{2}", + "bf69e10bb89390a9.png": "K_{G}(X)^{\\wedge}\\cong K(X_{G})", + "bf6f4a6fd45946d3.png": "S", + "bf700c166c7720e7.png": "(\\begin{matrix}N\\\\ n_{A}\\end{matrix})=\\frac{N!}{n_{A}!n_{B}!}", + "bf727dd5722f68ad.png": "\\Lambda\\otimes\\Lambda^{\\prime}=\\bigoplus_{i}L_{i}\\Lambda_{i}", + "bf73fcc97e81fbca.png": "E\\mapsto\\int_{E}fd\\mu", + "bf757b81a1aba163.png": "0()", + "bf77d0642ac75692.png": "(1-o(1))\\cdot lnn", + "bf780e8c0db13c99.png": "\\langle B\\rangle=tr(\\rho B)", + "bf7d75337998510b.png": "\\{H_{1},H_{1}\\}=0", + "bf87f8a29133e0f8.png": "\\hat{a}_{2}", + "bf8cc9968d11ca69.png": "[L_{z},X]=iY", + "bf93e85a73751ae9.png": "\\hat{t}_{i}", + "bf9728f78faee6b9.png": "\\int_{a}^{b}f(x)dx", + "bf976f55abd6b0c3.png": "(\\begin{matrix}1&1\\\\ -a&-c\\end{matrix})", + "bfa060da86f0d025.png": "\\tilde{c}_{n}", + "bfa08a12f586e185.png": "L=\\mu\\dot{r}d", + "bfa4897e60bda668.png": "\\{\\begin{matrix}q,p\\\\ r\\end{matrix}\\}", + "bfaf7431b36b69ce.png": "O_{i,j}=E_{i,j}\\forall i,j", + "bfb446357844a462.png": "\\frac{dy}{ds}=1", + "bfb4b4e44e953253.png": "\\tilde{d}", + "bfb4e11a93feaef2.png": "(S,V,\\{N_{j}\\})", + "bfb73ce10eb7dd89.png": "[\\begin{matrix}x&y\\\\ z&v\\end{matrix}]", + "bfb87e0ff8223a3c.png": "St=\\frac{f\\cdot\\frac{D}{2}}{V}", + "bfba62fb57f87a03.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "bfbab2727287b6ac.png": "\\overline{\\delta}=\\frac{\\sum c_{i}\\delta_{i}}{\\sum c_{i}}", + "bfbb2a1351bc3110.png": "\\sigma_{x^{\\prime}}=\\sigma_{y^{\\prime}}=\\sigma_{z^{\\prime}}", + "bfbe549f25406f19.png": "E=\\hbar\\omega-E_{k_{f}}-\\phi", + "bfbf5465ba42a697.png": "O(id^{2}+d^{3})", + "bfc03a9b336403d8.png": "(\\begin{matrix}n-1\\\\ n-x\\end{matrix})", + "bfc4fcdeae708084.png": "=1264.14", + "bfc55f235d96a8ef.png": "\\Omega_{u}^{\\phi}", + "bfcecad669bff7b9.png": "(\\phi_{n}),(\\psi_{n})\\in\\Delta", + "bfdb354aab332a1d.png": "\\overline{MG}", + "bfdf2bd9e0070647.png": "2^{5}3^{4}", + "bfe60c07d1904f2d.png": "(10x+7)dx", + "bfe76484324d2694.png": "\\dot{\\sigma}=C\\dot{\\epsilon},(1)", + "bfed4f2b75aabff1.png": "\\frac{M\\mu_{0}}{B+\\lambda M}=\\frac{C}{T}", + "bfed872cd8deac01.png": "\\int_{0}^{1}p(x)dx", + "bfee7fdcadcb39a1.png": "(\\begin{matrix}N\\\\ M\\end{matrix})", + "bff4d58946279bcd.png": "\\int_{a}^{b}\\cdot\\cdot\\cdot dx", + "bff7eaa7efc42f8f.png": "X(f)=L_{X}f", + "bffca6d7739bc19d.png": "\\Delta{\\Lambda^{\\mu}}_{\\nu}={\\Lambda^{\\mu}}_{\\rho}\\otimes{\\Lambda^{\\rho}}_{\\nu}", + "bffe18e08fc638f0.png": "E\\mapsto\\int_{E}fd\\mu", + "c00d4b344f00b2ed.png": "f_{p}^{D}(x)=(\\frac{1-x}{x})^{p}", + "c01c6999aca2af72.png": "\\hat{4}", + "c0237188e639d015.png": "[\\hbar]=M^{1}L^{2}T^{-1}", + "c028ba2cb2a181a2.png": "\\Theta_{(g_{u})}", + "c02a1a793c80e917.png": "\\int\\int_{X}\\int_{Y}^{Z}", + "c02b2ece477e59c8.png": "X:=\\prod_{i=1}^{n}X_{i}", + "c02e5fb928fb3951.png": "\\frac{\\partial f_{i}}{\\partial x_{i}}=0", + "c02f39266ca87d74.png": "\\overline{x}", + "c03afb6080feab96.png": "Loss=\\frac{\\rho\\lambda^{2}d^{4}}{(4\\pi)^{3}}", + "c044bb4da2b6469a.png": "\\frac{dE_{2}}{dE_{1}}=-1", + "c04661fd7f00eeb9.png": "(\\begin{matrix}0&0\\\\ 0&1\\end{matrix})", + "c047015173a85997.png": "[\\begin{matrix}1&0\\\\ 0&-1\\end{matrix}]", + "c04d6a3d32c45165.png": "\\theta_{k}^{b}", + "c052863fbd8c4969.png": "M_{s}+M_{l}=\\frac{M_{s}}{\\phi_{sl}}", + "c055d75424d1f53f.png": "f(x)=f^{**}(x)", + "c055e3214a89b952.png": "a:=(a_{0},a_{1},...,a_{n-1})", + "c05639749c5e1766.png": "gA=\\cap_{i}q_{i}", + "c056e931b73d975a.png": "\\prod_{k=1}^{x}f(k)", + "c05f0a0566f26500.png": "\\int fd\\mu", + "c071774cb2ce123c.png": "[\\begin{matrix}x\\\\ \\frac{1}{x}\\end{matrix}]", + "c071a925a3638072.png": "\\gamma_{\\mu}a/\\gamma^{\\mu}=-2a/", + "c07cc4b52be925e3.png": "g_{n}=(\\begin{matrix}N+n-1\\\\ n\\end{matrix})", + "c07d33b2ad77fce2.png": "\\sum_{k=0}^{n}k(\\begin{matrix}n\\\\ k\\end{matrix})=n2^{n-1}", + "c080a6ad6550dd5e.png": "V_{w}=\\sqrt{\\frac{2T}{\\rho A}}", + "c084954adfc4c820.png": "\\hat{w}_{j}", + "c088c5cc21b4255f.png": "\\prod_{n}(z-c_{n})", + "c08e2f64fc650d0a.png": "M<_{DM}N", + "c08f264bd94999fa.png": "\\int_{\\Omega}fw=0", + "c09d51f67ea61cfb.png": "=>T^{2}=4\\pi^{2}\\frac{l}{mB_{H}}", + "c09d9f39953e1e4d.png": "\\hat{H}", + "c0a465e750e9d025.png": "u\\notin C", + "c0a51453f8af023c.png": "\\prod(1-d_{i})", + "c0a96a3f1e56def0.png": "\\tilde{I}_{6}[f]=A_{1}\\sum_{i=1}^{6}f(a_{i}^{1})", + "c0b5d7217f52ff6e.png": "\\frac{20n}{4^{10}}", + "c0b91a061fe2b8b4.png": "\\frac{1}{\\frac{n}{2}+1}(\\begin{matrix}n\\\\ \\frac{n}{2}\\end{matrix})", + "c0ba0e79edf9dda1.png": "A=\\Gamma(F,X)", + "c0bbac9b529b2e92.png": "\\hat{D}", + "c0bd2fc36ce18312.png": "\\hat{\\alpha}", + "c0d077035720c702.png": "v=\\sqrt{\\frac{T}{\\mu}}", + "c0d13f2bec2a117f.png": "H=(\\begin{matrix}0&-i\\\\ i&0\\end{matrix})", + "c0d1b878197d09e9.png": "\\int\\sqrt{1+1/x}dx", + "c0d4325f0085bf4b.png": "\\int cos^{2}xdx", + "c0d598747bfa33e8.png": "B=(\\begin{matrix}1&1\\\\ 3&1\\\\ 0&2\\end{matrix})", + "c0d7f3dffb732eb6.png": "\\varphi", + "c0e44f9561740ca4.png": "x_{1}(t)=A+w(t)", + "c0e4b152038574a8.png": "=\\int cos^{2}(\\theta)d\\theta", + "c0e6868a2b76cea5.png": "r(t)=\\sqrt{k+(ct)^{2}}", + "c0e82a270643cb4f.png": "\\underline{P}(Cl_{t}^{\\le})", + "c0f5fcf9c9911180.png": "\\sqrt{2}+1", + "c0f901147fb51475.png": "\\frac{dP}{d\\tau}", + "c0fbce8fb4797fd9.png": "(\\begin{matrix}p^{r}\\\\ s\\end{matrix})", + "c0fd72dd80e4853f.png": "h(\\tilde{y})", + "c106e54f8de66808.png": "\\tilde{D}_{4}", + "c10dc7b7d1d2d97f.png": "Q,Q\\notin P", + "c112bc345fa490ad.png": "f(x)\\in S^{1}\\vee S^{1}", + "c1139f2f0cf06cbf.png": "\\Omega=N!/N_{1}!N_{2}!", + "c1151d6d564f319b.png": "\\sqrt{1-\\frac{v^{2}}{c^{2}}}", + "c1162742dbbe7943.png": "[H,Q]=0", + "c11ab26c62f15d86.png": "-\\vec{\\omega}\\times\\vec{R}", + "c124ffc7c1e42da4.png": "a,b\\in H_{1}(S)", + "c125824833a68223.png": "u_{2}=[\\begin{matrix}0\\\\ 1\\end{matrix}]", + "c12b13d09e608d4c.png": "v=Cl(])", + "c132695d14661af4.png": "\\sigma|_{[v_{0},...,v_{q}]}", + "c132df2fc8a99412.png": "\\frac{L(tx)}{L(x)}\\rightarrow1,x\\rightarrow\\infty", + "c1330fa52c0ea3ed.png": "44+4\\sqrt{3}+4\\sqrt{6}", + "c13e0c55bb30902b.png": "L=-mc^{2}\\frac{d\\tau}{dt}+L_{I}", + "c13e4cbfc252f2fc.png": "\\int_{0}^{1}x^{1/m}dx", + "c142d9e71aff2486.png": "-\\frac{d[A]}{dt}=k[A]^{2}", + "c1465b7142d23903.png": "||f||_{B}=sup_{x\\in X}|f(x)|", + "c14ac33dc3c2f61f.png": "R_{XY}(\\tau)=CR_{X}(\\tau)", + "c14c67e0e370203e.png": "F(x)=\\int_{a}^{x}f(t)dt", + "c14e132604db5dd8.png": "\\int_{1}^{3}(27-x^{3})dx", + "c15553bfbfea8e8f.png": "V=CR^{2/3}S^{1/2}", + "c156e15edc324c5a.png": "\\frac{1}{P}\\frac{dP}{dt}=k", + "c15b6f67a349701c.png": "\\lambda=e^{2\\pi}=1^{-i}", + "c15bbd641b01024d.png": "(\\begin{matrix}d\\\\ k\\end{matrix})", + "c15c04ab92ea7121.png": "\\overline{F}", + "c163bf4e53884d8e.png": "\\frac{dz}{z}", + "c168a6cd35462128.png": "\\int_{0}^{x}f(t)dt", + "c16c554b605db4e6.png": "-(2\\dot{r}\\Omega)\\hat{\\theta}", + "c16f19441e06eec9.png": "\\frac{1}{n_{i}}=\\frac{1}{v_{i}+1}", + "c17ba47bf5790360.png": "r(t)=\\sqrt{k+(ct)^{2}}", + "c17c504e70343ef4.png": "\\frac{P\\times C\\times(C-1)}{P\\times2!}", + "c186cf5da781fc5e.png": "e^{in\\mu-|n|\\gamma}", + "c1883158f90bca50.png": "f_{dp}=2f_{1}-f_{2}", + "c18a3281423115be.png": "\\theta_{0}=2\\pi r_{0}^{2}H_{0}", + "c19013826f99b771.png": "(\\nabla f)_{x_{0}}", + "c1935791610f19a0.png": "=x(p)=x", + "c196b94f5e87788d.png": "\\frac{\\partial P(z)}{\\partial z}=\\rho g", + "c19a3c7e14ac9441.png": "L=\\mathbb{Q}(\\sqrt{d})", + "c19ad24c57f6df1f.png": "\\sqrt{2E}", + "c19ddf18c027e8aa.png": "\\overline{y}^{n}\\notin q", + "c1a65b4da0a56b10.png": "(\\tau_{h}S)[\\varphi]=S[\\tau_{-h}\\varphi]", + "c1a9724a51c29899.png": "lim\\frac{x}{y}=\\frac{limx}{limy}", + "c1b4727715cb5821.png": "P=\\frac{24}{35}\\times\\frac{1}{4}=\\frac{6}{35}", + "c1b828f24df854b6.png": "(-\\vec{\\infty},\\vec{\\infty})", + "c1bde461cdedc1a4.png": "V_{T+1}(k)=0", + "c1be1510e32e3b1d.png": "(\\prod_{i=1}^{N}x_{i})^{1/N}", + "c1c0e03ea6d57fbc.png": "Y", + "c1c0e042c0dc96c9.png": "Kn=\\frac{Ma}{Re}\\sqrt{\\frac{\\gamma\\pi}{2}}", + "c1c48873189aa16f.png": "\\frac{\\partial f_{k}}{\\partial x_{j}}", + "c1c98d972eee81ae.png": "\\sqrt{\\gamma}", + "c1d238df2e3d2f9e.png": "\\frac{1}{2\\sqrt{3}}", + "c1d49326e10d4548.png": "(\\begin{matrix}2&-2\\\\ -2&2\\end{matrix})", + "c1d57bfded101c98.png": "F_{<:}^{\\omega}", + "c1da001e6fe827ec.png": "\\tilde{C}_{7}", + "c1db0c56db933cdd.png": "2x+3|8x-4", + "c1df3c96f173a5d3.png": "E(S_{z})=DS_{z}^{2}", + "c1dfbd362ad53b73.png": "\\lambda_{k}^{1/2}", + "c1e543c288b8e868.png": "0<\\tau<2/(||A||^{2})", + "c1e7e478dfed9254.png": "\\sum_{k=1}^{n}\\frac{z(1-z^{k})}{1-z}", + "c1ea0c5b123c2716.png": "E[\\hat{\\sigma}^{2}]=\\frac{n-1}{n}\\sigma^{2}", + "c1f0d3819f1caff4.png": "L=10\\cdot0.5=5", + "c1f754c4721204fa.png": "(ax+b)^{5}=c", + "c1fa704b536b1866.png": "[\\begin{matrix}0\\\\ 1\\end{matrix}]", + "c2011a9d85c5c9b4.png": "(5.c)\\gamma_{,z}=2\\rho\\psi_{,\\rho}\\psi_{,z}", + "c202385fa7ffaaef.png": "lim_{n\\rightarrow\\infty}\\int_{0}^{\\infty}e^{-e^{x^{n}}}", + "c206612993281e6e.png": "R\\cup\\{-\\infty,\\infty\\}", + "c20e950dff739008.png": "\\omega_{r}=\\frac{kv_{E}}{1+\\psi_{0}}", + "c2174762ff8ea5ef.png": "\\int\\sqrt{x^{3}+1}dx", + "c21a6cfe964ebd2d.png": "\\tilde{g}_{ij}", + "c21cca1c98d5b0b7.png": "\\bigcup_{x\\in S^{c}}B_{ct}(x)", + "c222fee08876925e.png": "\\kappa_{d}=R_{d}/c_{pd}", + "c22695132bb809be.png": "\\vec{x}(i)\\approx\\vec{x}(j)", + "c229fea47ac734fa.png": "A_{12}>0", + "c22b150a4fcff741.png": "v=\\frac{dr}{dt}", + "c22fb5e67f9bfed4.png": "x_{2}=b+\\sqrt{b^{2}-c}", + "c2320093e191fce6.png": "g(X)=\\frac{dF_{1}(X)}{dX}", + "c2352b7bf795f3aa.png": "a\\mapsto a_{u}^{\\#}:g\\rightarrow T_{u}P", + "c237ae4dd90f4c8d.png": "\\Rightarrow r=-\\frac{3}{4}\\pm\\frac{\\sqrt{17}}{4}", + "c238b6dc259629b8.png": "\\hat{D}(\\alpha)", + "c245fa61046cbd86.png": "(\\begin{matrix}3\\\\ 4\\end{matrix})", + "c246735eb6da6899.png": "\\overline{X_{t}}", + "c24b7834cbaad5db.png": "1/\\sqrt{1+\\epsilon^{2}}", + "c24b97d5d4878b0c.png": "\\frac{\\partial I}{\\partial y}", + "c24d7daf660025e4.png": "P=1.854kd^{n-2}", + "c251852a80973860.png": "[\\begin{matrix}a&b\\\\ b&a\\end{matrix}]", + "c252d63783935a42.png": "\\delta W=Q\\cdot\\delta q=0", + "c253af4465403739.png": "m^{*}(B)=inf_{S\\supset B}m(S)", + "c2587cf557d3a124.png": "\\frac{\\partial u}{\\partial x}", + "c259241c08fed6ed.png": "\\sqrt{\\lambda}", + "c259dcefb7c990ad.png": "H_{n}(\\underline{q},\\underline{x})", + "c262fb7a485ca3c9.png": "\\hat{x}\\in X", + "c26845dce9386faf.png": "(\\begin{matrix}n\\\\ i\\end{matrix})", + "c268d175b54adbae.png": "\\langle(\\Delta N)^{2}\\rangle=\\langle N\\rangle", + "c27719a664937302.png": "q^{\\prime\\prime}=h(T-T_{\\infty})", + "c277457618b66f5e.png": "\\gamma=\\gamma^{o}(1-\\frac{T}{T_{C}})^{n}", + "c2781a947acf3390.png": "0/0=0", + "c27a9b6ee08c280b.png": "(\\begin{matrix}n\\\\ c\\end{matrix})", + "c27cfc8438e79b63.png": "E=0,t_{B}=", + "c280ce2f1f0c9c41.png": "\\hat{f}=e^{-\\pi\\xi^{2}}", + "c28f5bd9b725a6fe.png": "\\tilde{\\delta}", + "c2944e76e63d2236.png": "\\vec{r}=[\\begin{matrix}0\\\\ 0\\end{matrix}]", + "c2986660b7f1ed1e.png": "9", + "c29ab1fc3803cd76.png": "\\{1,2,3\\}\\notin\\{1,2,3\\}", + "c29c5f88ead479b8.png": "\\int_{0}^{T}wx(t)dt", + "c29f1422c3ecf480.png": "A_{i}=T^{-1}(A_{i}^{\\prime})", + "c2a0d31ac0782789.png": "\\rho^{\\otimes n_{1}},\\rho^{\\otimes n_{2}},...", + "c2ab019e2a83f16a.png": "x", + "c2af0b306d94a084.png": "\\sqrt{(}t)", + "c2b17b63a78faac9.png": "\\tilde{E}(t)", + "c2b950db09aeaa71.png": "P(H_{1}|E)", + "c2ba1a5917a40383.png": "\\int_{a}^{b}f(x)dx", + "c2bdfa651989d8a6.png": "\\int_{a}^{a}g(x)dx=0", + "c2c132b270623085.png": "x\\notin B", + "c2c41c2751cb035b.png": "n^{\\mu}=\\frac{1}{\\sqrt{2}}(\\hat{t}-\\hat{r})", + "c2c4a651daa16296.png": "a=(1-2t)^{1/2}", + "c2cd819f02a2dbe4.png": "\\pi_{w}^{\\eta}", + "c2d18d07312a8036.png": "\\frac{\\partial R}{\\partial z}", + "c2d6fc3dde4e12b6.png": "\\lambda_{n+1}/\\lambda_{n}\\rightarrow1", + "c2db2b504750fc6b.png": "\\Delta=\\frac{\\partial V}{\\partial S}", + "c2dbe6ab306e1882.png": "\\sum_{n=0}^{\\infty}x_{1}^{n}x_{2}^{n}", + "c2e852299aee95d9.png": "S\\subset[\\omega_{1}]^{\\omega}", + "c2f00f9af9427093.png": "\\nabla_{(\\alpha}K_{\\beta\\gamma)}=0", + "c2f14c953b350748.png": "|x_{1}-x_{2}|=2hv/c", + "c2f41cb156a2c1e6.png": "\\gamma=i\\underline{k}^{*}", + "c2f848396f929eac.png": "\\overline{r_{0}}=r\\cdot\\hat{r}", + "c2f97f126166b087.png": "\\{\\sqrt{\\pi},2\\pi+1\\}", + "c3027573304cbc53.png": "S^{s}(S^{n})", + "c3032c79613048df.png": "r=\\frac{1}{2}\\sqrt{ab}", + "c3055e398a1876c3.png": "d\\overline{\\mu}=\\frac{d\\mu}{\\sqrt{g_{00}}}", + "c3083b0ac6022658.png": "A=\\frac{1}{2}(b+d)a", + "c30aace39fa08ce5.png": "U_{0}=[\\begin{matrix}0&1\\\\ 1&0\\end{matrix}]", + "c30cbe46e0e1d6c8.png": "\\int f(v)dv=3N", + "c30f34986586d243.png": "(a+b)^{\\prime}=a^{\\prime}+b^{\\prime}", + "c30f7b634f1e63ad.png": "\\sqrt{x}", + "c317b61aa1428b1b.png": "Df=(Dg)^{-1}", + "c317f1062802e119.png": "[\\frac{\\alpha}{\\pi}]=[\\frac{\\alpha}{\\theta}]", + "c319398abc445fc4.png": "e\\in[0..1]", + "c31b1c17319491a9.png": "(\\begin{matrix}a&b\\\\ b&1-a\\end{matrix})", + "c31e07c009afd352.png": "\\overline{K_{q}}", + "c32db67d7fb6ef51.png": "y=\\prod_{\\sigma}\\sigma(x)", + "c32f31f60bc4a908.png": "W_{1-2}=\\int PdV", + "c3462147676c75a6.png": "\\{\\begin{matrix}5\\\\ 5\\end{matrix}\\}", + "c34a973b1997b8e7.png": "\\{0,1,-1\\}", + "c34ae7d802a10af8.png": "|T_{r}f|\\le f^{*}.", + "c34c0e1bf7e812e3.png": "11-\\frac{\\sqrt{274}}{2}", + "c3506fe7941b26ff.png": "a_{2}(p_{R})=\\frac{3}{p_{R}}", + "c3542ef6a3a79275.png": "p_{i}=mg_{ij}\\frac{dq^{j}}{dt}", + "c35c0caa546c7ce8.png": "(\\begin{matrix}4\\\\ 2,2\\end{matrix})/2=3", + "c360dbda65635fe1.png": "(-e^{\\frac{i\\pi}{N}})^{k}\\cdot W_{0}(k)", + "c36438d725af9835.png": "\\hat{j}", + "c3649cf2d98dbfa2.png": "125-25=100", + "c36d8a9686ae39d7.png": "\\alpha=(2k+1)\\pi-\\beta", + "c3786d7fbd4b56f2.png": "\\frac{\\partial u}{\\partial y}", + "c37c9a498db62e3d.png": "|p^{n}\\frac{a}{b}|_{p}=p^{-n}", + "c37d00ea5a333e23.png": "\\hat{f}(k)", + "c37e38968368e777.png": "\\overline{y}=\\frac{1}{n}\\sum_{i=1}^{n}y_{i}", + "c38036b6dc18dbdc.png": "\\frac{dp}{p}=\\frac{-g}{R\\cdot T}dz", + "c380ec3497e89f1c.png": "(\\tau_{h}S)[\\varphi]=S[\\tau_{-h}\\varphi]", + "c38dc89494bf2de5.png": "\\tilde{C}(u)=W(u)", + "c390b463264f98ae.png": "Q(x)=\\prod_{i=1}^{k}f_{i}(x)", + "c396f675946a8ba7.png": "c^{a}=c^{ub^{-1}}=c^{b^{-1}}", + "c3980119bb710e2a.png": "\\overline{F}:A/B\\rightarrow C", + "c398b8a3fea8af4a.png": "\\overline{op_{1}}^{\\prime}", + "c3a041e8a8f95ae6.png": "\\hat{u}_{k}", + "c3a2ff6386a8635f.png": "R_{G}=\\prod_{i=1}^{m}(Y-P_{i})", + "c3a43ac98cb68ce3.png": "K-W", + "c3a88c3405676051.png": "[-P^{T}|I_{n-k}]", + "c3af238e646aeeb5.png": "\\int dx=0", + "c3af5f4a3d6a9855.png": "\\hat{f}(n)", + "c3b7aa6be6a6d340.png": "R/Z\\cong S^{1}", + "c3bdd24b2b352e32.png": "\\mathbb{P}", + "c3be66d47b21d014.png": "[\\overline{x}-\\frac{cs}{\\sqrt{n}},\\overline{x}+\\frac{cs}{\\sqrt{n}}]", + "c3c9b3fa628a0646.png": "df:T_{y}Y\\rightarrow T_{f(y)}X", + "c3caa1a9e04abb8a.png": "\\sigma^{z}=(\\begin{matrix}1&0\\\\ 0&-1\\end{matrix})", + "c3d05511b166f14e.png": "|E|<-NJ\\sqrt{log2}", + "c3d768cf76cdf6ad.png": "(b-a)e^{n(f(x_{0})-\\eta)}", + "c3d9bef2c2095a1b.png": "\\frac{dN}{dt}=\\frac{Nln(\\frac{1}{2})}{T_{1/2}}", + "c3dc70acf8b75ab4.png": "E=Q(\\lambda)", + "c3dd8b9eb16c641f.png": "v\\notin C", + "c3e4fc1b2e532251.png": "\\hat{A}(t)", + "c3e685727eff126b.png": "G=K_{I}^{2}(\\frac{1}{E})", + "c3e98f77edc186cd.png": "v(\\sum_{k=1}^{n}1)\\le1", + "c3eb87fb3f70f75f.png": "c_{j,k}^{*}=\\frac{c_{j,k}}{\\lambda_{j}^{k}}\\Gamma(k)", + "c3ee5544fbab30eb.png": "(k_{n}),f\\in C(T)", + "c3f4be915cbf381c.png": "\\prod U_{p}", + "c3ff86e9ddd23de4.png": "44+4\\sqrt{3}+4\\sqrt{6}", + "c40066d0e95893b6.png": "h=\\frac{\\sqrt{3}}{2}a", + "c40115e7dee9aee6.png": "\\frac{10\\sqrt{a}}{a}", + "c409572f2c15100d.png": "\\sum_{b\\in B}l_{b}b\\mapsto\\sum_{b\\in B}l_{b}^{\\sigma}b", + "c409e9036e2d6770.png": "\\frac{d\\varphi}{dt}+c^{2}\\nabla\\cdot A=0", + "c411e41eae1ed408.png": "(19/20)^{4}", + "c417abbfe67fbc8a.png": "\\prod_{n=1}^{\\infty}(1+a_{n})", + "c41a888fc133655b.png": "s\\in\\alpha,t\\notin\\gamma", + "c422c9934333e7fc.png": "\\frac{\\partial u}{\\partial t}=0", + "c4264243d99b486b.png": "ta_{jj}+(1-t)a_{kk}", + "c42ec3de2abf1974.png": "Le=\\frac{\\alpha}{D}=\\frac{Sc}{Pr}", + "c42faea41824115a.png": "-\\hat{k}", + "c4318cbe8afd9ce5.png": "\\gamma_{\\mu}^{*}\\ge h>0", + "c433365f1734ce02.png": "PB-C=\\sqrt{\\gamma}Q", + "c434b9803ccda36b.png": "\\frac{\\partial f_{i}}{\\partial x_{i}}=0", + "c43dbfa82cfec8cf.png": "[\\begin{matrix}v_{1}&\\cdot\\cdot\\cdot&v_{k}\\end{matrix}]", + "c442a9c9ad36a379.png": "\\tilde{\\delta}_{i}", + "c443738b304b91e9.png": "\\hat{x}_{i}", + "c4498ba8b9f6b603.png": "[\\begin{matrix}v_{1}&\\cdot\\cdot\\cdot&v_{k}\\end{matrix}]", + "c449a8e4743a705c.png": "Z=\\frac{X-E(X)}{Var(X)^{1/2}}", + "c44a64c6a9c262a6.png": "n", + "c44cd0ba5ed576be.png": "H_{n}=\\sum_{1\\le k\\le n}k^{-1}", + "c4511a48c7ef9ae1.png": "P_{c}=\\frac{\\lambda^{2}}{8\\pi n_{0}\\overline{n}_{2}}", + "c452a7df5cb7f349.png": "\\psi_{1}({\\Omega_{2}}^{\\Omega_{2}})", + "c452bcc6d7f03635.png": "\\alpha s_{x}+\\beta s_{y}+\\gamma=0", + "c454b165976b926a.png": "\\int_{X}dxf(x)", + "c45660d42b8cf43a.png": "Map([0,\\infty),X)", + "c4566c6508972749.png": "\\tilde{a}_{k}=a_{k}^{*}", + "c45758082e4db2b3.png": "I=\\overline{I}", + "c458f863b6e22461.png": "O(\\sqrt{p})\\le O(n^{1/4})", + "c468be50c4f6a810.png": "{(\\beta^{\\chi})}^{\\eta}", + "c46b08b0259b1c19.png": "\\delta\\int ds=0", + "c46f848147fa6bb7.png": "U_{n}=a\\varphi^{n}+b\\psi^{n}", + "c4777ca69697e4b1.png": "U_{E}(r_{ref}=\\infty)=0", + "c4785f5003dfdd7c.png": "s=\\int ds", + "c4789cb214e02513.png": "(\\begin{matrix}p\\\\ n\\end{matrix})", + "c48229222ba03787.png": "M\\int vds", + "c48247efa4fa7b62.png": "C_{J}-", + "c4873e6a5ba87342.png": "(\\begin{matrix}X\\\\ k\\end{matrix})", + "c49227b8548075c1.png": "x^{2}+0.9x-3", + "c493682e4aefe647.png": "2+\\sqrt{5}", + "c495035b45dfd7e2.png": "\\delta t_{b}=\\frac{x^{*}}{(c+v)}\\cdot", + "c497b3b54b0a500d.png": "V=V_{\\infty}+\\frac{\\lambda}{P_{0}+P}", + "c49a94b72659c488.png": "(S\\cup T)^{*}=S^{*}\\cup T^{*}", + "c49c9352ee02bc5f.png": "[\\begin{matrix}4\\\\ 1\\\\ 8\\end{matrix}]", + "c4a650d2644f811f.png": "A_{f}=\\langle f|P\\rangle", + "c4ae968216e5f3f9.png": "\\frac{1}{2}-\\epsilon", + "c4b113550f494271.png": "\\hat{f}(n)", + "c4b93edbc29d36f3.png": "O(|E|log(|V|))", + "c4bd16dcc4e0ad73.png": "S=F(\\mu)+L(\\mu)", + "c4c0db88b1c5c94d.png": "\\frac{K_{i}}{K_{d}}=\\omega_{0}^{2}", + "c4d20f4ac5a946a6.png": "0,c_{i},-c_{i},c_{i}^{*}", + "c4d35eba64ede0c6.png": "\\Omega^{\\prime},\\Omega_{0},\\Omega_{1}", + "c4d8b9b1866d043d.png": "\\Omega^{(d+2)}=d\\Omega^{(d+1)}", + "c4dc37cdbac88f86.png": "\\sqrt{y}", + "c4de00372003c9d6.png": "Tr(Q\\rho^{\\otimes n})\\ge\\epsilon", + "c4dfb51fdedf9ae6.png": "\\prod_{x}f(x)", + "c4e0dbe31e3b6d92.png": "||e_{i}||=||e_{i}^{*}||=1", + "c4e3aabff0abf58a.png": "p(m_{i}|z_{1:t},x_{1:t})", + "c4ea482ca66a537c.png": "\\overline{V^{\\prime}R}", + "c4ec70d72314533c.png": "s\\{\\begin{matrix}2\\\\ 3\\end{matrix}\\}", + "c4ed3fb52d071b31.png": "\\int_{\\gamma}dz=0", + "c4f06dca9b646bee.png": "U=[\\begin{matrix}U_{1}&U_{2}\\end{matrix}]", + "c4f0d2f37d843cdf.png": "\\tilde{G}^{K}", + "c4fb018f57ae3d42.png": "=\\frac{T(x,t)-T_{\\infty}}{T(0,t)-T_{\\infty}}", + "c4fb93476042d0fd.png": "w(3)=\\frac{3}{\\sqrt{\\pi}}", + "c4fe8dcd45707689.png": "(\\begin{matrix}n\\\\ c\\end{matrix})", + "c4ffc0fbac6e80a2.png": "K_{h_{\\lambda}}(X_{0},X)", + 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"c5b0519c2be865f1.png": "H=(\\begin{matrix}0&-i\\\\ i&0\\end{matrix})", + "c5b7399555d240c5.png": "x_{1}=\\sqrt{\\frac{L^{2}-a^{2}}{3}}", + "c5b8596f6d2dd406.png": "\\nu_{p}(n!)", + "c5b9b3b045c08da5.png": "-\\langle u_{r}\\nu_{r}\\rangle", + "c5bb60239a788322.png": "X_{k}=A_{k}\\otimes B_{k}", + "c5bdc7fd45853d84.png": "\\sqrt{K}", + "c5c6b85aaef2c7f9.png": "hu", + "c5c8b2d0d1113b53.png": "\\frac{dB}{dz}", + "c5c9437b618b4666.png": "\\beta=\\sqrt{n/logn}", + "c5c9b095785b94d1.png": "0.5<\\frac{a}{L}<2", + "c5d313ba96d1112b.png": "\\frac{F=d(ma)}{dt}", + "c5d3578d7586916c.png": "(\\begin{matrix}14\\\\ 5\\end{matrix})=2002", + "c5d5de6685fd02ba.png": "GH^{\\top}=P-P=0", + "c5ec8bd60f131c07.png": "(\\begin{matrix}8\\\\ 1\\end{matrix})", + "c5ef50bc64d4606e.png": "\\{\\underline{y}_{1},\\underline{y}_{2},\\underline{y}_{3}\\}", + "c5f0fdc4697bea8f.png": "(p(e_{0}),...,p(e_{n+1}))", + "c5facc89c14b7863.png": "\\hat{x}^{o}", + "c5fb29d0aa5f9e81.png": "\\int e^{\\theta x}dF", + "c5ff18495b36f154.png": "D^{(t_{\\gamma})}", + "c60404bc85acabf3.png": "\\langle\\pm2i,Z_{4}\\rangle", + "c6075269c146c2b4.png": "\\rho_{ij}\\rightarrow-1", + "c60b5240db2e3dfe.png": "\\tilde{Q}", + "c60b6f875a7dfdd8.png": "\\tilde{u}", + "c611049eb8a57801.png": "n_{1,t+1}=\\lambda n_{1,t}", + "c6182e43c325e1d2.png": "A^{2}S^{2}|F(q)|^{2}", + "c61a0c344da743ab.png": "(\\begin{matrix}13\\\\ 4\\end{matrix})", + "c61a7e0c024cdb89.png": "(\\begin{matrix}1\\\\ 0\\end{matrix})", + "c62545e45fed442d.png": "\\frac{dC}{dt}", + "c6273cc023313d43.png": "H=(\\begin{matrix}E_{+}&0\\\\ 0&E_{-}\\end{matrix})", + "c62bd8a7b9931e68.png": "F_{r}=\\frac{v}{\\sqrt{g\\frac{A}{B}}}", + "c630132a481cb2b9.png": "(\\begin{matrix}0&1\\\\ -1&0\\\\ \\end{matrix})", + "c63020900263edc8.png": "\\hat{Y}^{A}", + "c63364118fec02c7.png": "\\prod_{j9", + "ca3a2cbd3748550b.png": "\\int_{1}^{x}(1+1/t)dt", + "ca48d76616092a59.png": "\\sqrt{ax^{2}+b}(a\\ne1)", + "ca4ae781c610536a.png": "1/|G|", + "ca4c57f272120b43.png": "\\alpha_{k}^{2}+\\beta_{k}^{2}>9", + "ca4c8e5018864c22.png": "B=\\{\\underline{b}_{1},...,\\underline{b}_{r}\\}", + "ca4c9770c0d563d9.png": "\\omega=\\sqrt{\\frac{k}{m}}=\\frac{2\\pi}{T}", + "ca5268ecadb7e7af.png": "Q_{i}[x_{\\alpha}^{j}(t)]=t\\delta_{i}^{j}", + "ca588c94b95b67fd.png": "I_{2}=\\frac{4|A_{1}|^{4}\\chi_{0}^{2}L^{2}}{\\pi^{2}}", + "ca5f30541139dc30.png": "(Pf)^{\\wedge}=Q\\hat{f}", + "ca60c55f91c3963b.png": "[K^{j},P^{k}]=i\\delta^{jk}H", + "ca6dbb47bc8a383d.png": "E_{e}^{-}=X", + "ca6ef41945acb187.png": "\\sum_{-\\infty}^{\\infty}b_{i}f_{i}", + "ca71ddfc5779091a.png": "2drtan(0.5^{\\circ})", + "ca77639676b5fe94.png": "Z=(\\begin{matrix}z&0\\\\ w&-z\\end{matrix})", + "ca78da7209f4a4d5.png": "\\sqrt{a}", + "ca7c0fda2fb2fcee.png": "\\hat{N}", + "ca7fc69c646148e1.png": "x\\notin C", + "ca89568e06e4d736.png": "\\sigma=\\sqrt{\\sigma_{i}^{2}+\\sigma_{j}^{2}}", + "ca8cdc0ca18d3be9.png": "r=g^{e}y(modp)", + "ca9591274b786f6e.png": "\\Delta E=\\frac{(y_{2}-y_{1})^{3}}{4y_{1}y_{2}}", + "ca96e9d90e2771af.png": "\\int_{X}||f||_{B}d\\mu<\\infty", + "ca99668ee99adf78.png": "\\sum_{n=0}^{\\infty}2^{-2^{n}}", + "ca9e43a5d4fbd83a.png": "P_{C}^{\\prime}/a_{LC}^{\\prime}", + "caa3faee081a166e.png": "\\frac{t-3}{2t+1}", + "caa47b90a84192c4.png": "\\hat{v}_{i}", + "caa7b27eba312b37.png": "(c:a:b)\\cdot\\tilde{ab}:2\\cdot\\tilde{c}", + "caa7c8f695d4242d.png": "s\\notin T", + "caa8d746395717f8.png": "\\overline{V^{\\prime}R}", + "caac93acce4f99ed.png": "C=p_{t}+C^{\\prime}(x,p)", + "cab9edd706a53352.png": "V=||v_{1}\\wedge\\cdot\\cdot\\cdot\\wedge v_{n}||", + "cabeb1acc47c4f8d.png": "\\frac{\\partial}{\\partial\\theta}", + "cac79e8beb77ed34.png": "=4n(n-1)+1", + "cacda20f9576debe.png": "g\\sqrt{J(J+1)}", + "cad146bc6dc93cad.png": "\\partial\\psi(\\theta)/\\partial\\theta", + "cad3af1059073302.png": "S^{n}/\\sim=S^{n}\\vee S^{n}", + "cadbacac237716c3.png": "\\frac{dy}{dx}=\\frac{x}{y}", + "cadefdd3d1357f70.png": "2(\\sqrt{xy}-\\frac{x+y}{2})", + "cae1dd7f3a24abc0.png": "\\pi_{n}(X,p)\\cong\\langle S^{n},X\\rangle", + "caea048d9d622ace.png": "\\int_{0}^{3}|x^{2}-4|dx", + "caf0ff352c19ce8a.png": "\\pi0", + "cc040cc15fdb6c89.png": "I_{C}=C\\frac{dV_{in}}{dt}", + "cc0422cc54feee00.png": "\\frac{d}{dx}(x!)", + "cc0459dce87b199e.png": "log^{-1}(\\delta^{-1})", + "cc0abd5bc8ccd8a8.png": "(4)\\frac{du}{dt}=\\frac{-u}{1+u}", + "cc0c58cf81491d49.png": "\\frac{du}{dx}", + "cc0f0db997a991ba.png": "Z=\\frac{y\\cdot c^{6}}{\\sqrt{3-\\frac{|v|^{6}}{c^{6}}}}", + "cc15c0986a6c9b4b.png": "E=U\\frac{(c_{y2}+c_{y3})}{\\frac{1}{2}c_{2}}", + "cc16c34fd0bd4f7f.png": "\\delta t_{b}=\\frac{x^{*}}{(c+v)}\\cdot", + "cc17d450718f2c9f.png": "I", + "cc1cf4e676786b73.png": "\\langle\\overline{\\psi}\\gamma_{0}\\psi\\rangle", + "cc2d6cf834871209.png": "D_{(j_{u})}", + "cc2fd59aa7da3b67.png": "\\int_{X}1d\\mu", + "cc2fd5f853e33697.png": "\\{\\begin{matrix}3,3,3\\\\ 3,3,3\\end{matrix}\\}", + "cc32885ca97709f6.png": "F_{X}=0.5", + "cc41924ecc12910f.png": "\\frac{s}{s_{0}}=[1+\\frac{K\\theta}{1-\\theta}]^{-1}", + "cc42c666e367239a.png": "3N^{3}log_{2}N", + "cc463a833bedb20c.png": "\\frac{\\partial^{2}}{\\partial x^{2}}", + "cc475c122d2ace13.png": "\\int dy", + "cc484b1b6d767226.png": "M=[\\begin{matrix}m_{1}&0\\\\ 0&m_{2}\\end{matrix}]", + "cc4a1b46a0e48f47.png": "A=\\pi-A^{\\prime}", + "cc512ac64b1ee0ec.png": "\\partial_{t}L=\\frac{1}{2}\\nabla^{2}L", + "cc5454eaec94c382.png": "\\int_{\\Omega}u_{j}u_{j}=1", + "cc54c732b565eb9c.png": "0<\\tau<2/(||A||^{2})", + "cc5554cad628c903.png": "[\\frac{t^{2}+1}{2};t;\\frac{t^{2}-1}{2}]", + "cc55734f9f843e1d.png": "-\\sqrt{3}", + "cc56fa7d62db562b.png": "Y_{i}-\\hat{Y}_{i}", + "cc66ebfa3768e356.png": "\\frac{1}{2}r^{2}(\\theta)d\\theta", + "cc68c95b24f5dba0.png": "\\sigma_{1}\\mapsto(-t)", + "cc68e52a587dd64c.png": "V_{j^{n}(\\kappa)}", + "cc6cc2697b6dc4f8.png": "[\\begin{matrix}p&t\\\\ q&u\\end{matrix}]", + "cc6d4736244dbf8b.png": "C\\int F", + "cc70c0587f0caeca.png": "\\langle x,0\\rangle=\\langle0,x\\rangle=0", + "cc772e9d920b9fef.png": "\\rho(v)=\\sum v_{i}\\otimes e_{i}", + "cc7efd68131765aa.png": "(\\begin{matrix}v&0\\cdot\\cdot\\cdot0\\end{matrix})", + "cc85cd23614b0b4b.png": "r=\\{x|\\{x\\}\\notin u\\}", + "cc8a98568bee71fe.png": "\\prod_{i=2}^{2002}1", + "cc8c808e69f9dd26.png": "\\int_{0}^{t}Y(r)dr", + "cc8eff00b321dbb7.png": "M/X=(M^{*}\\backslash x)^{*}", + "cc91ea4058fb9122.png": "(\\frac{1}{2}+\\epsilon)s", + "cc98544817c8e860.png": "\\sum_{n=1}^{\\infty}a_{n}e^{-\\lambda_{n}s}", + "cc99649e334e9d42.png": "A_{eff}=\\frac{P_{o}}{PFD}", + "cc9f7d49ba451bb8.png": "\\sum_{j}|c_{ij}|^{2}=1", + "cca904d5599ec20a.png": "\\frac{dy}{dx}", + "ccb3b157174ee293.png": "\\tau_{g}^{\\delta}", + "ccbbf98786227705.png": "\\int_{c}^{d}f(x)dx", + "ccbc897d1f85adb1.png": "f(0,\\overline{u})=g(\\overline{u})", + "ccbd959739b40bdb.png": "L_{f,P}\\le L_{f,P^{\\prime}}", + "ccc2adc5339a429d.png": "16", + "ccc2e4ad49b19372.png": "P=", + "ccd11f05bcefa5c7.png": "(\\begin{matrix}m\\\\ 3\\end{matrix})", + "ccd22003fdf0cbd9.png": "E=E_{0}-\\int PdV", + "ccd3ee40a82c5988.png": "Q(x,y)=y-4x^{2}", + "cce16b743342a038.png": "3\\frac{(k+1)(k+2)}{2}", + "cce4ff76d30f490f.png": "f_{dp}=2f_{1}-f_{2}", + "ccead452b3ba19ee.png": "\\sum_{n=a}^{a+q-1}c_{q}(n)=0", + "ccf06eb171de1cfc.png": "(L-K+1)^{2}", + "ccfb30ff2c9656f0.png": "\\frac{i}{n}x[n]", + "ccfb828cc4b1d00a.png": "|\\psi_{y-}\\rangle", + "cd0ad49cf4adc1ca.png": "x^{3}-2x^{2}-5x+6", + "cd0e16ab8034abb7.png": "\\hat{h}_{k}", + "cd17a99e3829ba0b.png": "\\lambda=\\sqrt[3]{2+11i}", + "cd1950c246cff156.png": "\\frac{dx}{dt}=-\\frac{F}{\\omega}cos\\omega t", + "cd1e9fd2a8bb39a1.png": "f^{-}=\\frac{|f|-f}{2}", + "cd201ac5311d63c5.png": "\\sigma^{z}=(\\begin{matrix}1&0\\\\ 0&-1\\end{matrix})", + "cd209442dd08c04f.png": "O(n^{2}(log(q)+n))", + "cd22ffefa4ad1d6d.png": "\\sqrt{a\\pm b\\sqrt{c}}=\\sqrt{d}\\pm\\sqrt{e}", + "cd25a1c364b820ef.png": "|\\epsilon_{n+1}|\\le M{\\epsilon_{n}}^{2}", + "cd25d5797a897de0.png": "6-3=?", + "cd285d8e91b90121.png": "A^{\\prime}(z)", + "cd2d21637c7a6c2e.png": "gA=\\cap_{i}q_{i}", + "cd2e091a3add29c2.png": "\\omega^{2}=\\omega_{p}^{2}+k^{2}c^{2}", + "cd3a10dc6e0058f8.png": "r=\\{x|x\\notin x\\}", + "cd3c7207b9789b0e.png": "k^{i}sin\\theta^{i}=k\\frac{sin\\theta}{M}", + "cd43b394546e3582.png": "X(\\omega)=tri(\\frac{\\omega}{2\\pi W})", + "cd43f0fa8fcfabe0.png": "a=0.3+i0.3", + "cd46634fe0dac686.png": "\\frac{dx}{dt}", + "cd4b3fd8e3726fb4.png": "\\hat{\\Gamma}", + "cd4f518c9f3529e1.png": "R=\\frac{\\omega_{A}}{\\omega_{B}}=\\frac{N_{B}}{N_{A}}", + "cd58356b63b2d05c.png": "f^{\\prime}=f-By^{\\prime}", + "cd590e270235854c.png": "f=g\\prod_{1}^{k}u^{a_{j}}", + "cd5bf58ca23a04eb.png": "[\\begin{matrix}4&3\\\\ 2&1\\\\ 1\\end{matrix}]", + "cd5dbedcd826e0c9.png": "\\overline{x}", + "cd5e46dc74a07766.png": "O(1,n)/O(1)", + "cd5f868d23fe28bf.png": "(t^{a}A_{a}^{i})", + "cd64f6b81a3678ad.png": "PG_{a}=\\frac{4}{3}PG_{v}", + "cd66c56777159ab4.png": "\\int_{0}^{L}F(x)dx", + "cd697953904a394e.png": "\\hat{f}(3)", + "cd6af70a5a134da5.png": "\\tilde{C}_{2}", + "cd6cfd15609d9553.png": "A=3\\sqrt{7+4\\sqrt{2}}", + "cd6e2f06ed3720a5.png": "MSD=6D_{a}t^{\\alpha}", + "cd758a314ed05c54.png": "\\overline{A^{2}}", + "cd787f0fa25cc92f.png": "S_{1}=S_{1}^{\\prime\\prime}", + "cd7915a829d4c23e.png": "\\int dqE(q)=I", + "cd7a8a4a30b19217.png": "\\overline{K}", + "cd7ce5f801d2baaf.png": "W\\underline{A}", + "cd8141cff24e1997.png": "\\int Fdx", + "cd8fd947ac8f2362.png": "log_{4}(8)=\\frac{3}{2}", + "cd90276a87d07214.png": "\\partial_{\\mu}\\hat{A}^{\\mu}", + "cda77547c0f721f4.png": "Y=\\{Y_{1},Y_{2},..,,Y_{l}\\}", + "cda840634f80f6f6.png": ">z>", + "cda9c0faee652bf1.png": "B_{A^{\\prime}}^{\\prime}", + "cdb54c473ae8f0a4.png": "v=\\sqrt{\\frac{T}{\\rho}}", + "cdb67aca0a14243f.png": "L_{2}", + "cdb852195d146def.png": "\\tilde{B}_{4}", + "cdb887fb78c30e2d.png": "L^{\\prime}C^{\\prime}=\\epsilon\\mu", + "cdc3572bb08b3bf2.png": "-\\int\\frac{du}{u}", + "cdc55248c963b93d.png": "ss\\{\\begin{matrix}2\\\\ 3\\end{matrix}\\}", + "cdc8d635516d5533.png": "E(\\overline{K})", + "cdcacdf913c3a221.png": "1,2,3,5,8,13,...", + "cdce45d6d6a93d0d.png": "\\dot{m},P_{D}", + "cdd0a4dc1fdf3ad1.png": "\\underline{d}(X)=\\overline{d}(X)", + "cdd27abbd45f41ce.png": "S_{0}\\subseteq S_{1}\\subseteq...\\subseteq X", + "cdddc60e0dcc3fae.png": "f_{0}\\frac{\\partial v_{g}}{\\partial p}=-\\frac{R}{p}\\frac{\\partial T}{\\partial x}", + "cde36d59f2a29844.png": "[\\begin{matrix}0&1\\\\ 0&0\\end{matrix}]", + "cde3b63236c3a27d.png": "S_{+}|+\\rangle=0", + "cde5e0534a3ed62c.png": "\\int_{S}dS", + "cdec2e36ca507f21.png": "\\iint_{S}FdS", + "cdf776d0cba911a1.png": "h=\\frac{\\sqrt{3}}{2}a", + "cdfb33fedc24e75b.png": "Q=-k\\frac{dT}{dz}", + "cdfe779da8c6581b.png": "\\frac{df}{dX}", + "ce00d2e505931ab3.png": "lim_{x\\rightarrow a}f^{\\prime}(x)=DNE", + "ce010b7854bf717d.png": "J=[0,1)^{s}", + "ce0645a33d785a9e.png": "(\\begin{matrix}n\\\\ c\\end{matrix})", + "ce0c9ef4e99f433f.png": "S=[\\begin{matrix}1&1&1\\end{matrix}]", + "ce197744bc3aaf4a.png": "s\\{\\begin{matrix}2\\\\ 5\\end{matrix}\\}", + "ce2e17428c186159.png": "(S\\cup T)^{*}=S^{*}\\cup T^{*}", + "ce35253102c1208d.png": "\\Delta\\tau=Gb\\sqrt{C_{s}}\\epsilon^{3/2}", + "ce3662deba569e31.png": "\\Lambda_{n}=(X^{T}X+\\Lambda_{0})", + "ce3afdd721ea8fcb.png": "\\nu=1/(2p+1)", + "ce3d9a6bde1a9945.png": "r=1+\\frac{a_{c}}{100}", + "ce3e786fd6a91579.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=(\\begin{matrix}n-1\\\\ k\\end{matrix})+(\\begin{matrix}n-1\\\\ k-1\\end{matrix})", + "ce3e92d5417ec739.png": "u_{1}=[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "ce57e26c8c0a22d0.png": "\\frac{\\partial q(t)}{\\partial t}", + "ce5f2ca47c364e24.png": "R=\\sqrt{3}/2", + "ce617b02f5e174d9.png": "P(r)=\\frac{1}{Z}e^{-\\frac{F(r)}{kT}}", + "ce639d338899c211.png": "-\\sqrt{s}", + "ce6899cff29c9879.png": "0.75\\overline{0}", + "ce699c7626bc16f1.png": "x^{\\prime}\\in X^{*}\\mapsto\\langle x^{\\prime},x\\rangle", + "ce6a02064350e367.png": "A=\\int_{S}\\omega", + "ce6d1693725a2789.png": "n=[\\begin{matrix}0&1\\\\ 1&0\\end{matrix}]", + "ce6ecb9ca93a7cf1.png": "\\int pdq", + "ce6fe7d1ccd23c05.png": "(\\begin{matrix}n\\\\ 2\\end{matrix})p", + "ce78da52130f1767.png": "(\\begin{matrix}n\\\\ q\\end{matrix})", + "ce7cb3334d1f7088.png": "D(f)\\mapsto M[f^{-1}]", + "ce8832743b2ac1da.png": "L(\\chi_{-3},s)", + "ce8eec97cc0aa610.png": "s\\{\\begin{matrix}4\\\\ 4\\end{matrix}\\}", + "ce9586fc02c2366f.png": "S_{m}^{2}=m(a+b)+1", + "ce98eee1b8359c5c.png": "S_{Z_{1}}S_{Z_{2}}=\\pm S_{Z_{3}}.", + "ce99dbafafb70e79.png": "\\frac{d^{3}}{dx^{3}}[x^{4}]=24x", + "ce9fc765a37168cd.png": "r^{-l_{1}}+r^{-l_{2}}", + "cea08c63fed277c3.png": "\\underline{X}=X^{+}\\cup X^{-}", + "cea74634353447bd.png": "\\frac{du}{ds}=0", + "cea9884f89384062.png": "\\overline{p}-p=\\gamma\\nabla\\cdot\\hat{n}", + "ceae00b84db3a7f2.png": "\\lambda_{i}=\\frac{(r-1)^{i}}{2i}", + "ceaf154205f6647d.png": "B=[\\begin{matrix}1&0\\\\ 0&0.6\\\\ 0&0.8\\end{matrix}]", + "ceb68622000784c1.png": "=\\int_{0}^{h}A(y)dy", + "ceb95cf4d9f249c1.png": "u:=\\int_{a}^{b}v(t)dt", + "cebc6964323771a5.png": "\\int_{\\mu^{\\circ}}^{\\mu}d\\mu=\\int_{P^{\\circ}}^{P}\\overline{V}dP", + "cec11a0e1fc94a38.png": "|\\frac{\\partial S}{\\partial y}|\\ll1", + "cec2fbaa4e74c58c.png": "[\\Lambda]=[\\begin{matrix}I_{1}&0&0\\\\ 0&I_{2}&0\\\\ 0&0&I_{3}\\end{matrix}]", + "cec447bc388e73e1.png": "\\int(1/lnx)dx", + "ced23d86fae09547.png": "\\overline{W}", + "ced3e0d13c371bf8.png": "\\frac{\\partial u}{\\partial\\nu}(x_{0})>0", + "ced4a086c7e5d0c9.png": "\\forall v\\in W(w,v)\\notin R", + "ced4a90acd8b36b5.png": "1/x=o(1)", + "ced8e7dbf11de8be.png": "u(x)=\\tilde{u}(x)^{\\frac{1}{\\lambda}}", + "cedf09138706d4ec.png": "\\tilde{k}\\in B^{20m+64}", + "cee13a5b29517a54.png": "(\\begin{matrix}n+1\\\\ k\\end{matrix})", + "cee19112733104f1.png": "0=E\\{(\\hat{x}-x)y\\}", + "cee4f5bdb56f4153.png": "X_{n}<\\tilde{\\theta}<\\theta", + "cee7d1b9b7d460b5.png": "P_{r}=A\\frac{G}{4\\pi r^{2}}P_{t}", + "cee87266ac14147a.png": "(\\begin{matrix}a&b\\\\ c&-a\\end{matrix})", + "ceee16a9c7b986a7.png": "\\underline{\\varphi\\vdash\\psi}", + "ceee85a9e9df131a.png": "u_{e}=\\sqrt{\\frac{2\\mu}{r_{p}}}", + "cef12ae5483745e2.png": "\\int Fdx", + "cef240a95e795c79.png": "\\tilde{u}\\in L^{2}(\\mathbb{R}^{n})", + "cef30c1d08ada57a.png": "V=(\\begin{matrix}0&1\\\\ 1&0\\end{matrix})", + "cef465627585804a.png": "\\hat{y}\\in\\{-1,1\\}", + "ceff9072e22ab92b.png": "h(G,U_{L})=[L:K]", + "cf032bbce6fc9b77.png": "d:\\{0,1\\}^{*}\\rightarrow[0,\\infty)", + "cf05dff1707c321d.png": "\\frac{\\partial z}{\\partial x}=2x+y", + "cf09742ce37c8ce5.png": "\\sigma=2\\mu\\epsilon+\\lambda tr(\\epsilon)I", + "cf0d2492c09fa204.png": "-i(b\\overline{g}-g\\overline{b})/\\sqrt{2}", + "cf14f0fb179523ab.png": "P", + "cf180918c85e999c.png": "\\tilde{p}(x)", + "cf1a3b087fdfe35a.png": "\\sqrt{31}\\times\\sqrt{31}", + "cf1a64ca8ad39d30.png": "N(1+\\sqrt{5})=6", + "cf1c25719a82c61c.png": "\\overline{G}_{k}(X)", + "cf2118be88ac7259.png": "S=\\int_{M}BF", + "cf22b81e5f029c74.png": "(\\begin{matrix}0&a\\\\ -a&0\\end{matrix})", + "cf22c4583593e591.png": "\\int e^{-x^{2}}dx", + "cf260ca12dd3b801.png": "\\hat{Y}_{j}", + "cf29714fcf731fd8.png": "4\\times(\\begin{matrix}6\\\\ 2\\end{matrix})", + "cf2b379a46e7f48f.png": "s_{j}=[s_{j-1},x]", + "cf30931fe2375690.png": "|pp^{\\prime}|\\le(2/s)|pq|", + "cf323fc68da8f94e.png": "\\int_{0}^{1}D(x)dx", + "cf32e39b35719e71.png": "\\mathbb{F}", + "cf36b2b848bb4188.png": "\\lambda^{\\xi_{q}}", + "cf3b40d12513ce1f.png": "|\\omega_{i}|=q^{1/2}", + "cf3da20a32be0db2.png": "X_{k+N}=-X_{k}", + "cf3e90fe2dc5167d.png": "\\frac{\\partial f_{i}}{\\partial x_{i}}=0", + "cf42812e8d3ba8cf.png": "V=R(\\frac{Tn}{P})", + "cf4343088515d8e8.png": "\\tilde{g}=e^{2\\varphi}g", + "cf4461e2076fe65f.png": "F=S/S_{P}", + "cf449f1ce5c2316d.png": "\\hat{S}_{a}", + "cf5b35758654ab20.png": "\\frac{dV}{dt}", + "cf5bb9915814384f.png": "Z\\overline{Z}", + "cf5c04f821ab2b9c.png": "F_{n}^{(0)}=F_{n}", + "cf5d3498fd68e6d1.png": "\\tau:E_{p,0}^{2}\\rightarrow E_{0,p-1}^{2}", + "cf6010bf4672205a.png": "\\tilde{E}(t)", + "cf608f42cb5d5d03.png": "\\phi:M\\rightarrow\\prod_{i\\in F}R", + "cf68b251a19b612e.png": "[a_{j},a_{k}^{*}]=\\delta_{j,k}", + "cf708e681d528dd6.png": "[\\begin{matrix}1&0\\\\ 1&0\\end{matrix}]", + "cf736ce6e79cec51.png": "nH(p)-o(n)", + "cf7ea5d65d8902c3.png": "a\\frac{x^{n}-1}{x-1}=p", + "cf819895cefbadd0.png": "(\\begin{matrix}12\\\\ 5\\end{matrix})", + "cf8ab270bb56af4f.png": "\\mathbb{I}", + "cf8e398b2a61a01d.png": "U=\\frac{-GM}{r}", + "cf928b1af7b03f54.png": "(2^{r}+1)|(2^{rs}+1)", + "cf96fee8409ea8b0.png": "(\\begin{matrix}a&0\\\\ b&a^{-1}\\end{matrix})", + "cf999b9b104359f1.png": "E\\mapsto\\langle F(E)\\xi|\\xi\\rangle", + "cfaba2db642f57d1.png": "(r,z_{k_{-}}(r),\\theta)", + "cfb612c6063fa3b4.png": "(\\begin{matrix}x&y\\\\ -y&x\\end{matrix})", + "cfb72c43fca39ccc.png": "C[S_{n-1}]", + "cfb9ac3015f92c35.png": "f(a)=\\prod q_{i}^{n_{i}}", + "cfc4a0dca9edd05f.png": "\\sum\\frac{\\kappa}{sin(\\theta)^{3}}=0", + "cfca7aebccfd2d8c.png": "rel_{i}\\in\\{0,1\\}", + "cfcd96c3d365c217.png": "\\psi_{-}^{(0)}", + "cfd3741b3bd4b29c.png": "\\int_{Q}r^{2}dm", + "cfd8c3877081527b.png": "\\vec{u}(\\vec{r})", + "cfe2a715308d73d4.png": "\\{(x_{n},f(x_{n})\\}", + "cfe9ad3ae895819a.png": "AI_{T}=100\\times\\frac{d}{n}", + "cfe9f6489d374699.png": "C\\rightarrow\\frac{\\omega_{c}^{\\prime}}{\\omega_{c}}\\frac{R^{\\prime}}{R}C", + "cfeb02b5d757aa13.png": "d_{\\hat{K}}", + "cfedb0a807332ced.png": "(x_{1},x_{2},x_{3},...,x_{n})", + "cfedc204e7465b07.png": "i=-\\frac{dq}{dt}", + "cff0b777088953b1.png": "sys^{2}\\le\\frac{\\pi}{2}\\cdot area", + "cff52f59c88d1347.png": "i=C\\frac{du}{dt}", + "cffb3a50b87d48ef.png": "Z_{h}^{\\alpha}", + "cffcad827c136ad6.png": "\\frac{dh}{dr}=\\frac{m\\omega^{2}r}{mg}", + "cffe073fa753bddd.png": "4log_{2}n-4", + "d003acd16c84b386.png": "\\int_{0}^{T}y_{2}dt", + "d0062883ce9fbb81.png": "t\\notin E", + "d007eca304cddecc.png": "\\overline{K_{q}}", + "d00812400cc7e34b.png": "\\sqrt{B}", + "d0097d35e9d039c6.png": "2^{n}(an+1)", + "d00bb7b51ad2e371.png": "A=\\frac{1}{2}(b+d)a", + "d014737f7f3ce11e.png": "\\int dy-2y=\\int-dx", + "d01d7dff2173548b.png": "A=(Q,\\Sigma,\\delta,q_{0},F)", + "d01e5b955cb6e054.png": "C^{\\infty}(J^{k}(\\pi))", + "d022bd1d6dbce399.png": "\\sqrt{\\rho}", + "d02f1bcf71768006.png": "\\tilde{M}", + "d0329e77938af51f.png": "(\\frac{N}{2}\\times\\frac{N}{2})", + "d03d17979228ec5b.png": "AH", + "d0403ce0f230c245.png": "\\hat{\\zeta}", + "d042f729eefaaf3c.png": "X_{0}=-ct,X_{j}=x_{j}", + "d047914037e8645d.png": "\\sqrt{-7}", + "d047f5f1a3457a0c.png": "\\frac{dx}{x}", + "d04d354382af3caf.png": "B=\\prod B/I_{i}", + "d04d478cd831dbc3.png": "{C_{n}}^{k})", + "d0504312c5c33013.png": "x[n]\\cdot e^{-i2\\pi fTn}", + "d050af1b7c42165b.png": "\\tilde{I}", + "d055571c0499b464.png": "\\hat{X}_{q}", + "d05c6378cc0e86ae.png": "J_{k}(n)=\\mu(n)*n^{k}", + "d05e8bc9734ebd52.png": "f(x):=\\int_{0}^{x}\\omega", + "d062e4458136ed44.png": "Z=\\int_{x}f(x)dx", + "d064d8ca2cc00643.png": "\\int e^{x}cosxdx", + "d06885fa0ff59afe.png": "x^{\\mu}\\rightarrow x^{\\mu}+\\epsilon h^{\\mu}(x)", + "d0692616051d9118.png": "f(z)=\\sum_{k=0}^{\\infty}(\\begin{matrix}1/2\\\\ k\\end{matrix})z^{k}", + "d07079a3d9e77f5b.png": "\\int_{\\gamma}f(z)dz=0", + "d0726b38a9b18d8b.png": "A=(\\begin{matrix}1&0&2\\\\ 0&2&0\\\\ 1&1&0\\end{matrix})", + "d07385cfa979ac77.png": "a,b\\in A;p,q\\in P", + "d07452b0277eca52.png": "L_{2}\\phi=L_{3}(|u|^{2})", + "d074ccc34464b15f.png": "\\sqrt{x}", + "d078e04377c03468.png": "\\frac{4^{4}}{4}=64<70=(\\begin{matrix}8\\\\ 4\\end{matrix})", + "d07a24db0323ce15.png": "\\prod_{i}p_{i}^{e_{i}}", + "d07a2aad55275116.png": "\\int d^{3}xJ^{0}", + "d0814d5513e112a3.png": "\\tilde{\\Omega}", + "d082c9452bef8a0e.png": "h=(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "d08483a0b909f31a.png": "a_{1}=-\\sum_{n=2}^{\\infty}a_{n}", + "d08fda3ec8c9f7fc.png": "0^{\\prime\\prime}", + "d08ff553a142d25e.png": "1/2^{O(T)}", + "d0a6bc5cb925a777.png": "G_{k}(s)=\\frac{k-1+s}{k}", + "d0ad1f3d155b3840.png": "\\hat{f}(k)", + "d0b4a668a8547ce4.png": "[\\begin{matrix}4&2&1\\\\ 3&1\\end{matrix}]", + "d0c7dcdd6c74890a.png": "NSE_{i}=h_{i}^{t}\\times G", + "d0ce2c025b3d7060.png": "(r,z_{k_{+}}(r),\\theta)", + "d0ce305e1e06b193.png": "\\hat{\\nu}", + "d0ebc1697991cc2e.png": "K_{i}^{*}=\\frac{K_{i}k_{4}}{k_{3}+k_{4}}", + "d0ee8873c7ed1af7.png": "cos\\theta_{o}=-\\frac{v}{c}", + "d0f0770cfb2ddcbe.png": "G_{p}=\\frac{1.5B_{n}\\Delta f^{2}}{W^{3}}", + "d0f1cd5bee9e42ec.png": "(\\begin{matrix}0&F\\\\ -F&0\\end{matrix})", + "d0f49e2e87c36a7b.png": "w(2)=\\frac{2}{\\sqrt{\\pi}}", + "d0f742b3de5a2696.png": "\\prod_{p^{k}}f(p^{k})", + "d0fe47e019e6e6bd.png": "\\nu_{x}^{r}", + "d0ffb0925f58b4b4.png": "(\\begin{matrix}N\\\\ n_{A}\\end{matrix})=\\frac{N!}{n_{A}!n_{B}!}", + "d10306a73bcc3b49.png": "[a_{j},a_{k}^{*}]=\\delta_{j,k}", + "d108540ecd41d303.png": "1-2^{1-s}", + "d10c697569d9f90c.png": "\\dot{r}_{1}=\\lambda_{1}r_{1}", + "d1111fd032fe438f.png": "\\sqrt{2t}", + "d1155003c6165be9.png": "\\frac{V_{t}}{V_{d}}=\\frac{1}{1.2}", + "d12b79ada14a2c2b.png": "\\lambda(s)=f_{s}^{\\prime}(0)", + "d12ea1e6e92ca7e6.png": "5\\sqrt{7}", + "d132c463f00289d7.png": "\\frac{\\partial f}{\\partial y}=\\beta", + "d134663cae138c8b.png": "\\tilde{M}=M//G", + "d1383231903b9590.png": "w^{\\prime\\prime}\\notin W^{p}", + "d13c5f40561a3339.png": "F\\underline{A}", + "d142e5419fe8c2e9.png": "\\int_{0}^{t}Z_{s}ds", + "d145394ea1637a6a.png": "(\\lambda F.M)N", + "d14609ef4ed6677b.png": "\\int_{a}^{b}f(k)dk", + "d14f03a4cf4f3dbe.png": "f(x)=\\prod_{i}(x+\\alpha_{i})", + "d15410ba48de503c.png": "(\\gamma_{0},Bn)", + "d15860a951d0b309.png": "\\int\\frac{\\delta F}{\\delta\\rho}(x)\\phi(x)dx", + "d1608f6b0c980bea.png": "(x_{1},x_{2},x_{3},...,x_{n})", + "d162dd30e57b62d4.png": "\\frac{\\partial U}{\\partial p}", + "d166af3c5a020179.png": "\\sigma^{-1}(m-m^{\\prime})", + "d166c85dc3f68952.png": "u=+\\frac{\\partial\\psi}{\\partial y}", + "d17a0d54d34215c5.png": "-s", + "d17ce59ac4f8a9f2.png": "F(n)=x-q_{n}", + "d1801c5655051188.png": "\\Delta V_{w}=V_{w1}+V_{w2}", + "d1807ec53275f743.png": "\\tilde{D}_{6}", + "d1886f1a9dca3387.png": "\\frac{\\partial V}{\\partial h}=\\frac{\\pi r^{2}}{3}", + "d18c3625931e1e68.png": "z=\\frac{f_{e}}{f_{o}}-1", + "d191977d5bcf5433.png": "p\\notin F(t)(\\partial\\Omega)", + "d19cf30b6c53b86d.png": "\\int_{-\\infty}^{\\infty}", + "d1a3cf9b91d096e3.png": "5x^{4}y-10x^{2}y^{3}+y^{5}", + "d1b2fe1e9620647b.png": "\\phi(r,\\theta)=-\\frac{Q}{2\\pi}lnr", + "d1b5b78e7ef8dae5.png": "\\frac{1}{\\tau_{B}}=\\frac{V}{D}(1-p)", + "d1c27a6cba3d75cc.png": "s=\\sqrt{(4a)^{2}+p^{2}}", + "d1c5be6df9c8c4c5.png": "P_{n}=n(\\begin{matrix}n+1\\\\ 2\\end{matrix})-(\\begin{matrix}n+1\\\\ 3\\end{matrix})", + "d1c617eff786d45b.png": "L_{f,P}\\le L_{f,P^{\\prime}}", + "d1d4f444290e4eb0.png": "x\\in\\hat{R},A\\subseteq\\hat{R}", + "d1d5b3881a1ff7b3.png": "(\\hat{\\theta}-\\theta_{0})/SE(\\hat{\\theta})", + "d1dbdbd58e97b75b.png": "\\sqrt{Z}e^{T}|\\phi\\rangle", + "d1e02bd32faf41a8.png": "z/\\overline{z}", + "d1e07a84fe91375a.png": "HT_{r}\\tilde{x}=H\\tilde{x}_{r}", + "d1e8add50656b8a9.png": "m_{H}=\\sigma_{0}\\sqrt{2\\lambda}", + "d1eac017f7b41ba8.png": "h=2\\frac{dA}{dt}", + "d1f4bf60634127b3.png": "S=\\int Ldx_{3}", + "d1f51250016b3301.png": "Eq.1\\frac{dV}{dx}=w", + "d1f6798e4666f869.png": "t_{max}=\\frac{1}{b}ln(a)", + "d1f9c0828c666290.png": "((a,b),[\\infty])\\notin I", + "d1fa68108c2ca130.png": "x_{1}=b-\\sqrt{b^{2}-c}", + "d1fb20adb3d2c513.png": "\\hat{A}_{n,\\alpha}^{\\dagger}", + "d1ff4556120a0fe7.png": "\\tilde{\\phi}(xU)=\\phi(x)", + "d1ffbb450bc0412f.png": "\\sqrt{\\pi}=\\pm\\sqrt{\\pi}", + "d2067451f35bd8d9.png": "B(0,1+\\sqrt{2})", + "d208535e7c9bcf28.png": "1-\\frac{C^{2}}{6}\\approx\\frac{2\\sqrt{2}}{\\pi}", + "d209f2da05a68f48.png": "|Q_{0}|=|Q_{L}|=\\frac{P}{2}", + "d20b8d3efec7c00a.png": "\\hat{u}[n]", + "d21c9b0dcffa5784.png": "\\frac{l_{x+1}}{l_{x}}=p_{x}", + "d2219bb0ad4b4c08.png": "H(\\underline{w})", + "d226803ff0c8a04c.png": "\\int e^{x}cos(x)dx", + "d23a593a01ebc50e.png": "p_{i}|\\phi_{i}\\rangle", + "d23c3cca40dcb87b.png": "\\dot{y}=\\frac{1}{\\mu}x", + "d23d0bf9e85336c7.png": "var(T)=\\frac{2n(\\sigma^{2})^{2}}{(n+2)^{2}}", + "d240dfdc635cd191.png": "\\hat{y}_{d}", + "d242aeaec019f455.png": "\\hat{F}", + "d24391aee6e56442.png": "A=(\\begin{matrix}1&1\\\\ 0&1\\end{matrix})", + "d24b1469f9496fd6.png": "g_{j}=1\\pm\\frac{g_{S}-1}{2l+1}", + "d25d326abd6bbb41.png": "\\tilde{g}_{ij}=e^{2\\varphi}g_{ij}", + "d260ddfe2dd7487d.png": "\\frac{\\partial M}{\\partial\\alpha}", + "d265ad3941c8fa5e.png": "\\int xsinx^{2}dx", + "d266695b335ede5b.png": "\\hat{Z_{b}}", + "d26cac8f0d918180.png": "\\overline{CD}", + "d26ebfbe250d2b0e.png": "{\\tilde{H}^{\\perp}}_{S}", + "d27f89d13b2d94ff.png": "\\frac{\\partial u}{\\partial y}", + "d28984c7c6c696f8.png": "\\frac{dT}{dt}=0", + "d28c31fbdea7d695.png": "R_{01}=\\frac{W}{{I_{1}}^{2}}", + "d28cb7399f7e7b91.png": "|x_{1}-x_{2}|=2hv/c", + "d293001849bd3166.png": "F(x+b)=\\int f(x+b)dx", + "d296a3ec5fbff9fb.png": "P(\\theta|D,M1)", + "d296cec82a9e2ea4.png": "C^{g}\\cong R^{2g}", + "d29f09e1dcdaa06f.png": "A\\rightarrow A_{p}\\rightarrow k(p)", + "d2a04c0f13d75582.png": "-\\infty<\\omega_{a}<+\\infty", + "d2a119a66bf4b693.png": "M\\int vds", + "d2aa3ea486389906.png": "\\tilde{n}=\\frac{P_{r}}{P_{r}+P_{l}}", + "d2aa67004ac477a2.png": "(s,\\pi_{v},r_{i,v},\\psi_{v})", + "d2aec97a79cd1c17.png": "(A-\\lambda I)^{k_{1}-1}", + "d2b64fb08c22ca7d.png": "H=G^{2}-\\frac{p^{\\prime\\prime}(x_{k})}{p(x_{k})}", + "d2b71978e55efba5.png": "u_{i}\\in[\\underline{u}_{i},\\overline{u}_{i}]", + "d2b7e0935eb142da.png": "X=e^{\\mu+\\sigma Z}", + "d2b830c38d896434.png": "\\Phi=-\\frac{1}{\\sqrt{r^{2}+\\epsilon^{2}}}", + "d2b9f4a28ae1e007.png": "\\sqrt{-g}", + "d2c1b5939578507e.png": "\\hat{C}_{I}", + "d2c2a11cc54ef225.png": "\\int udu", + "d2c4ae7973efda78.png": "\\frac{\\partial^{2}z}{\\partial y^{2}}", + "d2c9ad5c247417f7.png": "{(\\Omega^{c})}^{\\mu}", + "d2c9d52cbc9cd0a2.png": "\\dot{\\partial}_{\\mu}=\\partial_{\\mu}", + "d2da7e34e61e5994.png": "\\hat{n}_{b}", + "d2e5da0809a4ca07.png": "\\int_{now}^{\\infty}\\frac{cdt}{a(t)}", + "d2ecacbb46c3c0f6.png": "\\frac{\\partial F}{\\partial n_{1}}=0", + "d2f2b252e15f85d3.png": "\\rho^{\\prime}=\\rho-\\rho_{w}", + "d2f7445c9c40ee79.png": "\\{[n,n+1]:n\\in Z\\}", + "d2f82d1723d9d806.png": "\\hat{f}(a)", + "d2f9501a7aafc283.png": "\\int_{E}f(x)\\mu(dx)", + "d2fd05e4efdbb8e2.png": "I\\frac{d^{2}\\theta}{dt^{2}}=N", + "d3027f58ad475f6e.png": "Z_{in}=\\frac{V_{i}}{I_{i}}=\\frac{Z}{1+A_{v}}", + "d30645a3b6074839.png": "\\forall A,\\exists X,X=A", + "d30e57d4267c9a45.png": "\\prod_{p\\le x}p", + "d31185422ea82b3f.png": "\\Xi_{q}^{z}", + "d3167cc86f273c2c.png": "\\sqrt{\\alpha}", + "d320eebf80b1bc31.png": "0()", + "d326e0337e4d5d4f.png": "max|x_{i}-m|", + "d3277fb9f5c88fcc.png": "\\langle J(0)\\rangle_{F_{e}}=0", + "d32f75895ba214f8.png": "\\Rightarrow P(z)=\\rho gz+C", + "d331436470a215c7.png": "\\tilde{L}", + "d3351eed3a931e7a.png": "1_{x,y}", + "d33ced4063cbb116.png": "\\frac{d}{dt}N_{2}=-c_{1}N_{1}", + "d34038b50a0eaf45.png": "B=(\\begin{matrix}1&1\\\\ 3&1\\\\ 0&2\\end{matrix})", + "d34490c547687c5b.png": "\\hat{K}_{G}", + "d347f831e4baa89a.png": "\\Pi_{i}=\\frac{k_{i}}{\\sum_{j}k_{j}}", + "d34c23b4b1163a2c.png": "(W;M_{0},M_{1})", + "d3523197ae896b67.png": "A_{1},B_{1}", + "d356723e352157d2.png": "\\tilde{x}\\sim F(\\tilde{x}|\\theta)", + "d3571e583f01c383.png": "\\frac{\\partial f}{\\partial a}", + "d357a0d4954e729f.png": "K_{k}(\\tilde{M})", + "d35a8fa741e6cb32.png": "E=\\frac{h\\nu}{e^{h\\nu/kT}-1}", + "d36509afaaf0d644.png": "\\hat{H}=\\hat{H}(\\hat{P})", + "d368f798db04c9c9.png": "\\hat{u}_{k}", + "d36a8b79c5ad95af.png": "D=N-K+1", + "d36f3bf95db5d049.png": "7-5\\sqrt{2}=-0.07106...", + "d36f974b5961cbaf.png": "\\tilde{E}_{7}", + "d37079f1a8ec5c11.png": "\\int_{E}\\varphi=\\infty", + "d371035daec9faaf.png": "x^{n}={x_{M}}^{n_{M}}", + "d3716f9d2e1b22cc.png": "M,\\hat{d}", + "d375e2da42d83401.png": "{z_{1}}^{z_{2}}=e^{z_{2}log(z_{1})}", + "d37ccdd2306552bd.png": "f_{xx}=\\frac{d^{2}f}{dx^{2}}", + "d37f48128e8b8a2c.png": "C(\\vec{N})", + "d381eec72dcccd7d.png": "Set_{\\ne\\emptyset}\\times Set_{\\ne\\emptyset}", + "d38552593d77d8b9.png": "\\kappa=A_{p}^{-1}(\\overline{R})", + "d38a2f220979be53.png": "S=\\frac{2e^{3}}{\\pi h}|V|\\sum_{n}T_{n}", + "d3960c847bdabe80.png": "(\\tau_{1}^{-1},...,\\tau_{g}^{-1})", + "d3a10e0f330de471.png": "0,1,3,9,45,285,...", + "d3a29760569e261d.png": "\\frac{\\nu\\tau^{2}}{\\nu+2}", + "d3a380f37dbf14f1.png": "(-b+\\sqrt{b^{2}-4c})/2", + "d3a59bd005109a77.png": "\\frac{dE_{r}}{dx}", + "d3a6afa376720db3.png": "\\frac{dy_{p}}{dt}=2At+B", + "d3ac7891467e3bfa.png": "|A|\\cdot|B|", + "d3b68cc1cc7aa978.png": "L=-\\tilde{F}\\dot{v}^{2}+2\\dot{v}\\dot{r}", + "d3b88975349a542e.png": "U_{e}(\\vec{R})", + "d3c22bc911ea3f81.png": "x\\frac{d}{dx}", + "d3c9a66c85352cf6.png": "L(\\phi,\\partial_{\\mu}\\phi)", + "d3cb7d63d5b6accc.png": "\\underline{d}(X)=\\overline{d}(X)", + "d3d21303f1633a4c.png": "n!:=n\\times(n-1)!", + "d3d464b7fd426df7.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "d3d567301b470265.png": "\\nabla^{2}\\Phi=4\\pi Gm|\\Psi|^{2}", + "d3db58be98be396a.png": "\\frac{dM}{dx}=V", + "d3e046447fe5628e.png": "0=MU_{x}+MU_{y}\\frac{dy}{dx}", + "d3e1c3836fe02ee3.png": "A=\\int2\\pi R(s)ds", + "d3e40ef2d8b09ffc.png": "I(t)=I_{0}\\cdot e^{-\\frac{R_{2}}{L}t}", + "d3e7640c1ccc4243.png": "\\overline{w}=0", + "d3f5300e55a625ac.png": "f_{b}(r)=0,r>w", + "d3f5d82fe8724d56.png": "P=-\\frac{dE}{dt}=\\frac{K_{ev}}{M^{2}}", + "d3f8a5de21e6f7ab.png": "110=5^{2}+6^{2}+7^{2}", + "d3fdb8f315773bf9.png": "\\frac{\\partial u}{\\partial x}", + "d40110d28a418811.png": "\\int_{L}f(z)dz", + "d4023f6891ac9cae.png": "f(t,n)=\\sum_{i=0}^{n}(\\begin{matrix}t\\\\ i\\end{matrix})", + "d40e475118464bc4.png": "p=\\frac{RT}{\\underline{V}}", + "d412808a9a38d413.png": "A(x_{1},y_{1})", + "d414cfa11268edd1.png": "u_{g}=\\frac{1}{f}\\hat{z}\\times\\nabla\\phi", + "d419ce33a83bbbed.png": "\\frac{V_{t}}{V_{d}}=\\frac{1}{1.2}", + "d41c07288afa919e.png": "cf(\\prod A/D)<\\lambda", + "d41e9026dd532de2.png": "E=\\sqrt{m^{2}c^{4}+p^{2}c^{2}}", + "d41f3a0db6b55702.png": "\\int_{E}f\\mu", + "d41feacb540d2cbe.png": "K=\\sqrt{abcd-(eg-fh)^{2}}", + "d42061fb8b8a4d29.png": "\\sum_{p\\le x}\\frac{a_{p}a_{p}^{\\prime}}{p}=O(1)", + "d424838d28a0ebc7.png": "x\\mapsto\\frac{1}{x},y\\mapsto\\frac{1}{y}", + "d4257f88faa276f5.png": "f(x)=|x|^{k+1}", + "d42de7106723be05.png": "(I=\\Sigma mr^{2})", + "d42e53ef7023b501.png": "\\overline{g}", + "d431a011629c49db.png": "g(\\theta)=exp(\\xi\\theta)g(0)", + "d43d817d52a0df2b.png": "d=\\sqrt{a^{2}+b^{2}+c^{2}}", + "d43e4a9e1fb770a8.png": "126", + "d440b797df6877bb.png": "u^{h}(x^{h},z^{h})", + "d4422e195b1b15dc.png": "k_{c},\\overline{k}", + "d447cf385acdf2bb.png": "(\\begin{matrix}-1&1\\\\ 0&1\\end{matrix})", + "d44e40a33a633cc5.png": "(2^{r}+1)|(2^{k}+1)", + "d45335963aac4135.png": "\\sqrt{T}", + "d4568c3ae7b55808.png": "\\int f^{-}", + "d45d7420fbb1d44c.png": "S", + "d4661910f744ee78.png": "2(\\begin{matrix}n\\\\ k\\end{matrix})", + "d46777884c442a8c.png": "B\\rightarrow K^{*}l^{+}l^{-}", + "d4684c8c0f6d6956.png": "(\\begin{matrix}6\\\\ 3\\end{matrix})", + "d46e0277ed68ee90.png": "G=U(1)", + "d46f51d6d36d308b.png": "\\prod B_{\\lambda}", + "d46fc69f19d7337b.png": "\\tilde{J}_{il}", + "d4725c4e42d247d5.png": "\\Delta E^{tot}=Q+W", + "d47da9ecb97826f1.png": "\\frac{dy}{ds}=1", + "d47fe63a8664e3bd.png": "\\sqrt{K}", + "d48081bf8798bf3e.png": "-\\sqrt{3}", + "d4841df9ec270d10.png": "0", + "d48686f0ad449415.png": "\\hat{D}(\\alpha)|0\\rangle=|\\alpha\\rangle", + "d489ce0aef262842.png": "\\frac{\\partial(\\varphi f)}{\\partial x}+\\frac{\\partial(\\varphi g)}{\\partial y}", + "d48c5bfdcdeed0dd.png": "\\overline{K}^{*0}", + "d49257426cb30419.png": "x^{\\prime}\\in X^{*}\\mapsto\\langle x^{\\prime},x\\rangle", + "d493b18259786ea7.png": "\\tilde{s}", + "d494c976af51cb9f.png": "1\\le k3", + "d58a330e0cbafc2d.png": "||x||>\\gamma_{2}", + "d58bd74c1fc63128.png": "(\\begin{matrix}1&0\\\\ 0&-1\\end{matrix})", + "d58fff5233260c88.png": "\\sqrt{yz}", + "d59bbaa111f976d1.png": "sin(2\\pi ft+\\pi/2)sin(\\phi)", + "d5a33c19d0243e8a.png": "\\hat{I}_{S},\\hat{I}_{B}", + "d5a463ff102d0a98.png": "\\nu=\\frac{\\partial V}{\\partial\\sigma}", + "d5a53203366e5dae.png": "\\tilde{u}(x)", + "d5a63a3ea6624ab7.png": "X:=\\prod_{i=1}^{n}X_{i}", + "d5a84ee139f5434c.png": "(\\begin{matrix}n\\\\ 3\\end{matrix})", + "d5abdd08f1f8054b.png": "\\pi_{i}\\ge0,\\sum\\pi_{i}=1", + "d5ac972f8ebfbf07.png": "(\\begin{matrix}m\\\\ n\\end{matrix})", + "d5ad7302a298e1dd.png": "{\\varphi^{\\phi}}^{\\psi}", + "d5b1a05dcccc65b9.png": "\\prod_{i=2}^{2002}1", + "d5b9315763b87f1e.png": "(\\begin{matrix}a\\\\ a+1\\end{matrix})=0", + "d5c810a2b6f92ebd.png": "g_{j}=1\\pm\\frac{g_{S}-1}{2l+1}", + "d5c875cc78c5017f.png": "g_{n}<2\\sqrt{p_{n}}+1", + "d5cfb88c4af9c30d.png": "\\int uvdx", + "d5d5209792bc447b.png": "{(w^{j})}^{1}", + "d5d75e9d5b50d914.png": "x", + "d5d7ff2bb9ecb2a5.png": "\\int_{0}^{\\infty}|g(r)|dr<\\infty", + "d5d981d4d98b01e3.png": "(\\begin{matrix}0&1\\\\ -1&0\\end{matrix})", + "d5e72673053b0979.png": "\\langle B\\rangle=tr(\\rho B)", + "d5e85905ac1706b6.png": "Z_{x}^{\\gamma}", + "d5e960ea97f3d1df.png": "\\frac{1}{2}n_{1}(n_{1}-1)\\le N", + "d5eebe21be6ed5d5.png": "m-2r<-1", + "d5ef0c9323c2bc7d.png": "x^{10}+x^{7}+1", + "d5fac175145ebe15.png": "x\\notin P", + "d5fbeaff6dbf5fc7.png": "\\rho^{\\prime}=\\rho-\\rho_{w}", + "d5fc7ab635dcd164.png": "\\tilde{v}", + "d602b8873478ef16.png": "\\theta/(\\theta+J-1)", + "d6042a416e607c86.png": "\\int sin^{2}xcos^{2}xdx", + "d6065f6f44a9b615.png": "(\\begin{matrix}12\\\\ 5\\end{matrix})", + "d6070e6ed49ea8a6.png": "\\hat{y}-y", + "d60862e5fd39e365.png": "\\Delta=\\frac{\\partial\\rho}{\\rho}", + "d6093fabe51e9d64.png": "[\\begin{matrix}2&2\\\\ 3\\end{matrix}]", + "d60d6bf97dd95012.png": "\\hat{f}=e^{-\\pi\\xi^{2}}", + "d60d945bb62b40e8.png": "g=(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "d610624cee2c2667.png": "N", + "d6155f017c74b030.png": "\\pi<\\hat{1}", + "d61fa6976a2fbcd4.png": "-\\sqrt{x}", + "d626202f9a6718de.png": "Rg(x):=g(-x)", + "d628bdb3d9ddcba1.png": "g:=g^{+}-g^{-}", + "d62a2b93da0a1d22.png": "\\int_{0}^{T}e^{-st}dg(t)", + "d62c3bc126e0b3a6.png": "\\int_{0}^{t}p^{\\prime}(s)p(t-s)ds", + "d62eb5aebb97434a.png": "\\hat{P}^{\\mu})", + "d62fe56be2189c86.png": "\\chi_{\\omega}^{\\phi}", + "d6353f14bbc27fd4.png": "V=\\sqrt{P\\bullet R}", + "d638d5bb6e885534.png": "(\\begin{matrix}3\\\\ 4\\end{matrix})", + "d640629569f08736.png": "E_{p,m}=\\frac{1}{2}LI^{2}", + "d6453f7e16feb11f.png": "\\frac{\\rho v^{2}}{2}+\\rho gz+p=C", + "d6473d5374513cc2.png": "\\sum_{k=1}^{i}\\frac{A}{i}k=\\frac{A}{2}(i+1)", + "d6480525764a3f92.png": "y\\in\\sum_{n}", + "d6486b3a1399fb51.png": "\\frac{f_{2}}{f_{1}}=10^{s/1000}", + "d6514f6b2077e50c.png": "\\frac{\\partial(x,y)}{\\partial(s,t)}", + "d65346aefacb9d15.png": "(A-\\lambda I)^{k_{1}-1}", + "d65dc59daaf1265c.png": "4.\\overline{f*g}=\\overline{g}*\\overline{f}", + "d65f6bd73c120d5e.png": "N=[\\begin{matrix}1&2\\\\ 2&1\\end{matrix}]", + "d66050f0931e09f8.png": "P_{c}^{(2)}(0)=P_{c}^{(3)}(0)", + "d6618c7fa882fbc2.png": "P_{n}(K)=(P,G,\\in)", + "d664f5dfcab8e47a.png": "\\langle\\phi|\\psi\\rangle=0=\\langle\\phi|\\psi\\rangle^{2}", + "d66694cde5190878.png": "|E\\cup E^{\\prime}|>1", + "d669b0e9cd2cf975.png": "Q:2^{X}\\longrightarrow2^{R^{n}}", + "d66c1f51824c0f2b.png": "\\sum_{d\\in D,dBc}...", + "d671c4188f89a156.png": "H_{0}:m(\\theta_{0})=0", + "d673f68c69f502b7.png": "(\\nabla^{2}+k_{0}^{2}n^{2})\\psi=0", + "d679b6e659e655b0.png": "de-let[\\lambda q.f(qq)]", + "d67f8a7ed637ade5.png": "(A-B)\\sqrt{g}=1.", + "d6822ff786aead17.png": "x\\mapsto\\{\\langle e_{k},x\\rangle\\}_{k\\in N}", + "d683470efdbb46f5.png": "F", + "d68c9fe060e042a8.png": "f=\\sqrt{h^{2}+(a+b)^{2}}", + "d68de39c1715f138.png": "(\\begin{matrix}x&-y\\\\ y&x\\end{matrix})", + "d69f787c51d4fbf0.png": "(11)T_{ab}k^{a}k^{b}\\ge0", + "d69fd82acdd7b413.png": "j=\\beta O_{K}", + "d6a1f1553f777b22.png": "\\frac{\\partial p}{\\partial z}=0", + "d6a36861fe9d23b5.png": "(\\begin{matrix}4\\\\ 3\\end{matrix})=4", + "d6a44cd122deda35.png": "\\prod_{k=1}^{n}f(k)", + "d6a8bbf94f8e79c8.png": "a_{i}-a_{j}=a_{k}-a_{l}", + "d6aaab555bfaef3d.png": "\\hat{\\alpha}>0", + "d6b25f33bd4278a3.png": "E(\\underline{x}|y)", + "d6b793bdcb34cfbf.png": "\\int_{a}^{b}f(x)dx", + "d6b7b0040d0f874e.png": "t_{1}s_{2}\\overline{t_{1}s_{2}}^{-1}=(123)", + "d6bcfd001a8de712.png": "T=\\frac{m\\overline{v^{2}}}{3k_{B}}", + "d6bf0375c863243a.png": "Nu=\\frac{1}{2}u\\frac{d^{2}}{dx^{2}}", + "d6c66c00e4d5b90e.png": "\\int_{1}^{x}(1+1/t)dt", + "d6c91aaa351c799a.png": "\\tilde{\\pi}", + "d6cee3e961dc35af.png": "P_{max}=\\frac{1}{4}p_{max}Q_{max}", + "d6d3e89eb9d13d12.png": "C_{0...m_{j}...0}", + "d6d421d8997124e9.png": "Z_{\\gamma}^{f}", + "d6d4852a9175574c.png": "\\mu_{1}=E(x)", + "d6d507b419d10fb3.png": "\\sqrt{-3}", + "d6de66b5ce3aa9f5.png": "e(t)dt=dw", + "d6de9f715c5dcf5b.png": "\\int_{-2}^{6}\\frac{dx}{x}", + "d6e49a3894e21dd9.png": "(m-M)_{0}=", + "d6e8c1ee27b51038.png": "b=\\sqrt{c^{2}-a^{2}}", + "d6e9faf789042763.png": "\\hat{x}=i\\hbar\\frac{d}{dp}", + "d6eac6464504c3d0.png": "\\hat{6}", + "d6f4faabfd3ce0f1.png": "f(z)\\in f^{-(n-1)}(t)", + "d70607baa8d35241.png": "y(x)=\\int g(x)dx", + "d706600ab9fd41f8.png": "\\frac{q}{A}=-k\\frac{dT}{dx}", + "d71035db87f25072.png": "\\Delta V_{w}=V_{w1}+V_{w2}", + "d7155d3c1c32ec3a.png": "a\\hat{x},a\\hat{y},a\\hat{z}", + "d715e8702adacb0d.png": "=\\int cos^{2}(\\theta)d\\theta", + "d71695c95ed0452f.png": "\\hat{\\alpha}>0", + "d717eb5258db8715.png": "\\hat{f}(3)", + "d7191f8e0e15fe67.png": "\\tilde{x}_{1},...,\\tilde{x}_{n}", + "d71ae38ee2eb9a72.png": "H(\\tilde{x}|\\alpha)", + "d721f63bd57af657.png": "(X_{i})_{i\\notin I}", + "d72615cdd03b1df7.png": "9801\\sqrt{2}/4412", + "d7289eeedf7cffb4.png": "\\frac{\\partial^{2}}{(\\partial x^{i})^{2}}", + "d73408793fb502da.png": "Z=(\\begin{matrix}z&0\\\\ w&-z\\end{matrix})", + "d73523db08793a35.png": "\\frac{d\\psi}{dt}", + "d739827c10b65a57.png": "\\frac{\\partial X_{i}}{\\partial P_{Y}}>0", + "d73a7206aa75ae66.png": "p_{A}>\\sqrt{\\frac{1}{2r}}", + "d73fbb12b1a36cbf.png": "\\rho_{mv}<\\frac{-\\sigma_{m}}{2\\sigma_{v}}", + "d73fd357be649184.png": "G=\\int_{0}^{T}k(t)x(t)dt", + "d74a514f90c294ed.png": "\\int f(x)dx=1", + "d74ac3084f15358c.png": "\\frac{\\partial q(t)}{\\partial t}", + "d74c2c7bd3cc99cb.png": "\\sum_{n=a}^{a+q-1}c_{q}(n)=0", + "d74db36d0b314ccd.png": "\\prod_{i=1}^{n}f(x_{i})", + "d74df9e095139d44.png": "MCG(S^{2})\\simeq Z/2Z", + "d751ea8f236cf76a.png": "{(\\nu^{\\phi})}^{\\alpha}", + "d757ae1ca837e4e5.png": "W(A_{n})=S_{n+1}", + "d7693c9762ff0c3c.png": "\\hat{c}", + "d77313825821f515.png": "\\Delta_{K}(t^{-1})=\\Delta_{K}(t)", + "d773c20af5afc072.png": "H^{2}(X,S^{1})", + "d77510d24830a9d7.png": "\\frac{1}{r}e^{-m_{W,Z}r}", + "d777813f086134e1.png": "\\{\\frac{1}{\\pi_{ji}},\\pi_{ij}\\}", + "d778718cd0e5e356.png": "\\hat{p}_{i}", + "d779449534b6e6ce.png": "u|_{t=0}=f(x)", + "d785c1602ba0ce07.png": "(\\begin{matrix}7\\\\ 3\\end{matrix})=35", + "d78a02e66740b73a.png": "\\frac{2}{n}\\times x_{i}^{2}", + "d78f1b3880840d25.png": "A=[\\begin{matrix}a&b\\\\ c&d\\end{matrix}]", + "d7902013dc7cf6cb.png": "(f(x)+c)^{\\prime}=f^{\\prime}(x)", + "d79bdba3edf0a429.png": "\\hat{X}|_{F_{SO}(M)}", + "d79cdfa27f7ee733.png": "15", + "d7a1957a0a0b7af9.png": "\\tilde{\\phi}\\circ\\omega_{U}=\\omega_{V}\\circ\\phi", + "d7a35b7d48b17f0b.png": "v=\\sqrt{2}\\cdot v_{o}", + "d7a9b41981ce6b61.png": "(x-\\sqrt{2})(x+\\sqrt{2})", + "d7ad34795ea2b7f3.png": "E_{p,q}^{2}=H_{q}(F)", + "d7b048f38879860b.png": "O(id^{2}+d^{3})", + "d7c4d0f23ef39564.png": "\\frac{|\\tilde{X}-mode|}{\\sigma}\\le3^{1/2}", + "d7ca29ba4fe9432d.png": "e^{aX+bX}=e^{aX}e^{bX}", + "d7cba234ef788ef5.png": "z=\\frac{t}{\\sqrt{n-1}}", + "d7cec6fbfb6eb276.png": "|\\overline{VU}|", + "d7cfa19fccb43a29.png": "[\\begin{matrix}0&0\\\\ 1&-1\\end{matrix}]", + "d7d7b242f5d57b51.png": "E=\\rho e+\\frac{1}{2}\\rho u^{2}", + "d7e4374a7df35846.png": "\\tilde{A}_{1}", + "d7ed038a7da5bd1d.png": "x^{-}=\\frac{t-x}{\\sqrt{2}}", + "d7f29f598ff81311.png": "Z=\\prod_{j=1}^{N}\\zeta_{j}", + "d7f2ac88aaa25f36.png": "1\\notin A\\Rightarrow\\sigma A=0", + "d7f75c341334e2a0.png": "\\overline{w}_{g}\\in R^{d}", + "d7f96a06405c4478.png": "\\tilde{X}", + "d7fa9380e00c152e.png": "\\tilde{X}\\rightarrow X", + "d7fc9222651d38df.png": "T_{1}^{2}-T_{2}^{2}", + "d7fed7ba7e8ba3fb.png": "\\frac{0.5}{L}", + "d8002e05c60eb067.png": "H", + "d805579029254834.png": "\\tau=\\sqrt{t^{2}-x^{2}}", + "d809963531a6e1fa.png": "\\pi-arccos(\\frac{1}{3})", + "d80a8ade4693802a.png": "\\frac{dq}{dt}=\\frac{M}{B}", + "d8124cb4aa9d2cb5.png": "\\tau=\\sqrt{1-v^{2}/c^{2}}", + "d81ba3122f908a71.png": "A=(\\begin{matrix}2&1\\\\ -1&0\\end{matrix})", + "d81d20764d15955b.png": "\\overline{A^{2}}", + "d827159f479b8c65.png": "[\\Lambda]=[\\begin{matrix}I_{1}&0&0\\\\ 0&I_{2}&0\\\\ 0&0&I_{3}\\end{matrix}]", + "d82a41fbecec359f.png": "F=G\\frac{Mm}{r^{2}}", + "d82b1ff5048f8d16.png": "-W(-Q)/Q", + "d82c8d7237e35816.png": "G_{1}\\cdot G_{2}\\cdot G_{3}\\cdot\\cdot\\cdot", + "d832818b2a745743.png": "\\tilde{H}^{*}(X)", + "d8330f02c7909023.png": "\\frac{\\partial f(M,T)}{\\partial T}<0", + "d8345471abd10350.png": "[\\begin{matrix}1&0\\\\ G&1\\end{matrix}]", + "d8382e943ef26531.png": "\\int_{0}^{T}wx(t)dt", + "d842eb68f4703559.png": "w\\in\\hat{C}\\backslash\\overline{D}", + "d84442c737573758.png": "\\prod_{i=a}^{b}", + "d845fb4fe588993f.png": "f_{5}(x)=log_{c}x", + "d8483b1f6ec3e22e.png": "A_{(k)}=U_{k}\\Sigma_{k}V_{k}^{T}", + "d84872515098a9c4.png": "\\dot{x}=\\Gamma V(x)", + "d84bb7f6b5409395.png": "[x_{k}]_{\\times}", + "d850751a4f655d37.png": "(G:H_{i})=p", + "d85636284de29d2a.png": "\\frac{\\partial F}{\\partial n_{1}}=0", + "d8597d3865270248.png": "\\prod_{i}S_{i}", + "d85dbf74fef87775.png": "2x=O(x)", + "d86b7379dc7487c3.png": "[\\begin{matrix}a&r\\\\ d&s\\end{matrix}]", + "d871fd9f57c93bdc.png": "p_{i}=\\frac{\\partial u}{\\partial x_{i}}", + "d8730ae903277ff0.png": "M=(\\tilde{B}\\times F)/\\pi_{1}B", + "d877b10ba942fab4.png": "\\Psi(r)=\\sqrt{\\frac{N}{V}}e^{ik\\cdot r}", + "d87b775cd6a2fcb5.png": "(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "d87cd41fef6cc20a.png": "h_{f}=f_{D}\\frac{L}{D}\\frac{V^{2}}{2g}", + "d88118ef74c191da.png": "(\\begin{matrix}n^{2}+r-1\\\\ r\\end{matrix})", + "d88251953d48229b.png": "\\frac{26}{100}=\\frac{x}{65}", + "d8853b4437af67d2.png": "P_{i,i-1}=P_{i,i+1}=q_{i}", + "d88e97862ba4049f.png": "\\epsilon\\sim exp(1)\\cdot q_{sig}\\cdot\\epsilon^{\\prime}", + "d88f58ca69c4116f.png": "\\nabla_{t}f(x^{*}(t),t)", + "d890acc33d9f02c4.png": "\\hat{\\beta}=(\\overline{y/x})", + "d89889d77fdecd8a.png": "hv", + "d898f87a2e2bd1ed.png": "w_{2}l^{*}>D_{1}", + "d89a15fcdc0d9754.png": "[\\gamma^{\\mu},\\gamma^{\\nu}]_{+}=2g^{\\mu\\nu}", + "d89eb35efe0fb28f.png": "N=[\\begin{matrix}A&B\\\\ 0&C\\end{matrix}]", + "d8a0e2bc2bc75ba3.png": "\\int a(x)d\\mu", + "d8b2b22f30665944.png": "(\\begin{matrix}n\\\\ 3\\end{matrix})", + "d8b8883f9d312594.png": "\\tilde{g}=e^{2\\varphi}g", + "d8b97290b7261c40.png": "\\overline{n}_{m}", + "d8bd592e1a6fa4a4.png": "\\frac{dP}{dw}=\\frac{\\partial V}{\\partial E}\\frac{dE}{dw}-L", + "d8bd688721263f31.png": "(\\hat{\\theta}-\\theta_{0})/SE(\\hat{\\theta})", + "d8be7b3aecc10a9a.png": "R", + "d8c2bbdf21d4745c.png": "\\frac{\\partial}{\\partial t}=0", + "d8c5196bf0f2a167.png": "8\\sqrt{3}", + "d8ccae2475118f5e.png": "n>0\\Rightarrow q=[\\frac{a}{n}]", + "d8ccc31015a766b3.png": "[\\begin{matrix}U_{1}\\\\ U_{2}\\end{matrix}]", + "d8d33be162cb451e.png": "0\\le a_{1}T^{2}=4\\pi^{2}\\frac{l}{mB_{H}}", + "d95245ac854a9000.png": "t=\\int\\frac{dy}{iy+F}", + "d959aa57c93b6870.png": "I(\\hat{x},u)", + "d969b21aa0c9b5f4.png": "I=\\int e^{x}cos(x)dx", + "d96a9353dc9648f2.png": "\\Delta T=\\dot{Q}R", + "d96ddde2efc0da7a.png": "\\hat{S}^{2}", + "d96e053e7ea40c48.png": "F_{<:}^{\\omega}", + "d97069dac4679195.png": "V=|a\\cdot(b\\times c)|", + "d97ba3e4ff35653a.png": "\\tilde{f}_{i}", + "d980d4da2db6aacf.png": "n=\\prod_{i}p_{i}^{a_{i}}", + "d981e99ea4d18e83.png": "\\frac{\\partial i_{l}}{\\partial x}=-i_{m}", + "d983b569ec2cb9af.png": "W=\\int P(V)dV", + "d98619756b07864b.png": "(\\begin{matrix}-1\\\\ 0\\end{matrix})", + "d989fe22c1c7f428.png": "(0,N-y-1)", + "d98da030583049d3.png": "\\sqrt{\\pi}", + "d98e9bb3932f38d0.png": "\\tilde{f}", + "d9916d0892908b75.png": "h\\le(\\begin{matrix}k+l\\\\ k\\end{matrix})", + "d999eb6682b087c7.png": "V(P,e(P,u))=u", + "d99ebf45252988d2.png": "S\\notin W", + "d9a5426bf64d9554.png": "\\tilde{H}_{i}/\\tilde{H}_{i}^{\\prime}", + "d9a8c2b563f0e2bf.png": "y_{i,j}=\\sqrt{x_{i,j}}", + "d9aed3affbbd86b9.png": "(\\begin{matrix}m\\\\ n\\end{matrix})", + "d9af73e23c09d788.png": "C_{2}=\\{U^{3}=-I\\}", + "d9b02d85b16548ee.png": "f(x)-a^{2}(x)", + "d9b0b2e43a0832f1.png": "x_{n}4\\pi", + "db9f077b2ad0b31f.png": "\\overline{h_{i}}=h_{i}^{*}", + "dba834b62c0a5395.png": "D_{1}(D_{1}\\ne C)", + "dba85dac59342c7c.png": "\\frac{1}{\\rho(s)}=\\kappa(s)=\\frac{d\\theta}{ds}", + "dbaae1eebd0c4ec4.png": "[1;\\frac{2t}{t^{2}+1};\\frac{t^{2}-1}{t^{2}+1}]", + "dbab8b74238fabad.png": "M(x)=\\int V(x)dx", + "dbb07d618ef36d1a.png": "\\varphi=(1+\\sqrt{5})/2", + "dbb76fb78bb27de3.png": "e^{\\int f(x)dx}", + "dbb942778ed52b49.png": "\\mu", + "dbba7aab267317cd.png": "\\int_{0}^{x}cos(1/t)dt", + "dbbbed984587a2c2.png": "\\sqrt{x}/lnx", + "dbc093ce16a5368d.png": "\\int f^{2}dP<\\infty", + "dbc57bcb8e17a699.png": "(\\begin{matrix}0&a\\\\ a&0\\end{matrix})", + "dbc896ffd21b052b.png": "\\frac{dA}{dr}=C", + "dbd063aedaa73153.png": "(G=1)", + "dbd115e1e638836d.png": "L_{D}[\\rho_{S}(t)]=0", + "dbdc73275407b5ae.png": "-\\sqrt{\\frac{1}{70}}", + "dbe48239fab8264b.png": "(1-a)S=4\\epsilon\\sigma T^{4}", + "dbe5c50959805af6.png": "-a_{+}^{*}", + "dbedaf2b0082541b.png": "\\underline{T}(t)=\\frac{d\\gamma}{dt}", + "dbeeb061e5ca55a3.png": "\\vec{I}=(I,Q,U,V)", + "dbf7374c0770dd06.png": "\\rho_{ij}\\rightarrow-1", + "dbf80f131cc6a747.png": "Pc=E_{c}", + "dbfb8f9fc9c95c23.png": "\\hat{y}_{t}", + "dc01a2971d5e7c52.png": "\\bigcup_{f\\in F}f(U)", + "dc068f375596a19a.png": "\\{1,2,3\\}\\notin\\{1,2,3\\}", + "dc070e7bc2c8c936.png": "(A-B)\\sqrt{g}=1.", + "dc0c94e86dd26689.png": "{(\\Lambda^{\\psi})}^{\\nu}", + "dc104bee66c48789.png": "p=-\\frac{1}{\\sqrt{3}}z", + "dc131f9ea29a6501.png": "arg(L(j\\omega))=\\frac{\\alpha\\pi}{2}", + "dc18912067d941c8.png": "\\sqrt{K}", + "dc208b6dfd55a3a6.png": "0.5<\\frac{a}{L}<2", + "dc2be897a457d336.png": "[\\begin{matrix}-2&-1\\\\ -1&2\\end{matrix}]", + "dc2c0853c997d035.png": "\\sqrt{3/2}\\approx1.225", + "dc2f842f7f2f5aae.png": "(E\\otimes C)_{R}=E\\oplus E", + "dc3535957cfbb755.png": "(\\begin{matrix}r+1\\\\ 2\\end{matrix})", + "dc3c4d33ccb09c7f.png": "P_{TOT}=\\frac{3V_{P}^{2}}{2R}", + "dc4748757e2e67a5.png": "F(x)=\\int_{x}^{0}f(y)dy", + "dc4afb777e1d861d.png": "\\int f^{-1}(y)dy", + "dc4ea7fcec6ec3e4.png": "-\\hat{y}", + "dc51f10bdf72692f.png": "1+\\frac{1}{n-2}", + "dc60a00ac0f7bd6e.png": "cot(\\frac{\\alpha}{2})=\\frac{s-a}{r}", + "dc60b0e38407355b.png": "\\int sin^{2}xcos^{2}xdx", + "dc64943f08add386.png": "P(y|do(x))", + "dc6727519eb43327.png": "\\hat{O}", + "dc6975a40d39a5e0.png": "\\{\\begin{matrix}3\\\\ 6\\end{matrix}\\}", + "dc6c8332afe6246b.png": "\\frac{d^{2}y}{dx^{2}}", + "dc6ef1293ffca1b6.png": "\\tilde{Y_{k}}", + "dc71defe0fc53917.png": "\\{A,B,C,...,\\}", + "dc7a70a45833a504.png": "\\frac{MX}{MY}=\\frac{XX^{\\prime\\prime}}{YY^{\\prime\\prime}}", + "dc855385da54514a.png": "\\tilde{k}", + "dc86855a076906cd.png": "\\int_{0}^{r}4\\pi u^{2}du", + "dc8b6723faf5ca3f.png": "\\sqrt{\\Psi}", + "dc9521adbbb0d79f.png": "AI_{T}=100\\times\\frac{d}{n}", + "dc98933707a3dbd6.png": "\\hat{X}^{n}", + "dc9a4ebdb5140a90.png": "1^{1}\\cdot2^{2}\\cdot3^{3}", + "dc9cdacd0a2baa47.png": "\\hat{s}^{\\prime}", + "dc9d4f72b4c5878a.png": "\\frac{1}{L-\\epsilon}C", + "dd608035c95e5d82.png": "\\sqrt{1}=+1", + "dd6669135a5b0807.png": "\\tilde{C}_{2}", + "dd69e9ba19b73f5a.png": "\\sigma(\\tilde{\\nu})", + "dd6cc78ac4a9d19a.png": "\\hat{I}_{3}", + "dd6ee9b82a55f87f.png": "\\Lambda^{\\cdot}g^{*}", + "dd71a2ff93cfb065.png": "E(\\theta)=\\frac{N}{N-1}", + "dd737ff9a22f15bb.png": "C\\int F", + "dd7628771df93563.png": "[\\overline{x}-\\frac{cs}{\\sqrt{n}},\\overline{x}+\\frac{cs}{\\sqrt{n}}]", + "dd8014e2ef73ddbb.png": "|det(Dg(x))|", + "dd891ac67936c6f0.png": "(\\begin{matrix}1&1\\\\ 1&0\\end{matrix})^{m}", + "dd897cee2f9c95f8.png": "[K]\\{d\\}=\\{-f\\}", + "dd897e06f147aa7a.png": "A(0,u_{k},v_{k})", + "dd8a6ea9adb47fd2.png": "C=(\\begin{matrix}1&i\\\\ i&1\\end{matrix})", + "dd8bcc645fb9e6d7.png": "f_{23}=-B_{z}", + "dd90a0ce3f029792.png": "\\overline{B}(x_{1},r_{1})\\subset W\\cap U_{1}", + "dd91ba64db57c497.png": "\\prod_{n=1}^{\\infty}a_{n}=a_{1}a_{2}a_{3}\\cdot\\cdot\\cdot", + "dd9b10985892aa13.png": "2N^{2}/h+\\sqrt{\\pi N^{3}h}", + "dd9d316128f7fefc.png": "\\int_{0}^{360}", + "ddaac671566e62ce.png": "s\\{\\begin{matrix}2\\\\ 7\\end{matrix}\\}", + "ddb033e2f564796e.png": "2-\\frac{2}{l+1}", + "ddb391f40fab462d.png": "\\sqrt{-h}", + "ddb8605f18945b6c.png": "E(Y|X)=\\frac{3}{10}X", + "ddbf5bea1f2b36bd.png": "\\mathbb{H}", + "ddc0e15f24178c7d.png": "\\tilde{f}_{ij}", + "ddc7221dcaaf3833.png": "\\sqrt{x^{2}+y^{2}}-L=0", + "ddc7f82b2f8b3da3.png": "\\hat{\\mu}_{0}=34/3=11.33", + "ddcc39dcd1e3cc1c.png": "\\int g(u)du", + "ddcd4463180538a3.png": "(=\\hat{\\beta}\\hat{\\alpha})", + "ddce75cb53b1a4fa.png": "\\hat{\\alpha}<\\hat{\\beta}", + "ddd223b4fcd269a9.png": "\\frac{1}{y}\\frac{dy}{dx}=ln2", + "ddd40528d674dae0.png": "\\int_{0}^{1}D(x)dx", + "ddd4a4d75438032a.png": "\\hat{q}_{o}", + "dddb163cdd82d141.png": "\\tau=(1+\\sqrt{-163})/2", + "dde73f56bec5e4a6.png": "m\\frac{dU}{dt}", + "dde741db76f92223.png": "\\int y^{2}dv", + "dde7d8eaef9c881f.png": "\\Psi:H(n)\\rightarrow u(n)^{*}", + "ddf126c69ccac7e1.png": "{L_{th}}^{2}=\\frac{D}{\\Sigma_{a,th}}", + "ddf5494d7a34aea6.png": "\\tilde{C}_{5}", + "ddf9e3b6637f3ccb.png": "\\frac{\\partial w}{\\partial\\overline{z}}=\\mu\\frac{\\partial w}{\\partial z}", + "ddfa0cb1d4760d3e.png": "\\int_{\\Omega}u_{j}u_{j}=1", + "ddfb1466863057c0.png": "\\int x^{3}e^{x^{2}}dx", + "ddfd6eadd2883c4e.png": "(t^{a}A_{a}^{i})", + "de01553ec8fea26e.png": "E[(X-\\mu_{X})^{2}]", + "de0485c1d6a31a0c.png": "E_{c}=\\frac{V_{m}}{E_{m}}+\\frac{V_{f}}{E_{f}}", + "de04bedd404515cc.png": "v=\\int\\frac{dv}{dx}dx", + "de058f685bf2cb1c.png": "\\sum_{j}\\mu(E_{j})=\\infty", + "de065d9fdfc9cb15.png": "S\\in(\\begin{matrix}[n]\\\\ m\\end{matrix})", + "de1242f877b7a26d.png": "\\Theta^{c_{v}}", + "de1305d88b0e25c7.png": "\\frac{\\partial f}{\\partial y}(X,Y)=0", + "de13f3785689b10e.png": "M_{R}=e^{M_{B}}", + "de1942bed7413547.png": "\\hat{\\rho}", + "de1fdcae19d5bcb5.png": "V:=L(\\underline{b}_{1},...,\\underline{b}_{r})", + "de228c3fc04f2fd9.png": "dim\\hat{R}=dimR", + "de2a8036685ca32f.png": "\\tilde{D}_{\\eta}", + "de2b81538c56c69c.png": "\\tilde{x}_{0}=(0,0,0)", + "de3af671647936e7.png": "\\frac{E}{m}=K(\\frac{\\sigma}{\\rho})", + "de428a360edd97b9.png": "t", + "de4377a5e074f251.png": "|P|=2N^{3}", + "de441eedfc176004.png": "125-25=100", + "de4967aee76cf306.png": "H(t):=\\int_{0}^{t}h(s)ds", + "de4fc92a5cd0c143.png": "=(\\frac{95-5}{2})", + "de5216b9a2485975.png": "\\xi\\notin\\Omega", + "de5731d470a0ab93.png": "a_{i}-a_{j}=a_{k}-a_{l}", + "de58c7eb5c99d2cd.png": "\\hat{A}_{n,\\alpha}^{\\dagger}", + "de5f191e6b9c6747.png": "[\\begin{matrix}17&23\\\\ 11&7\\end{matrix}]", + "de6129f768f07811.png": "C_{AB}=r(v_{AB})", + "de6434fa60ff6e68.png": "V=\\frac{|a\\cdot(b\\times c)|}{6}", + "de6768c0e198773c.png": "|x|\\le1,|y|\\le1", + "de69e07244c31082.png": "(s,\\pi_{v},r_{i,v},\\psi_{v})", + "de705294ada43455.png": "M=\\frac{3}{2}PV\\frac{\\rho}{\\sigma}", + "de70a2dfa4fc6286.png": "\\eta(x)\\frac{\\partial w}{\\partial t}", + "de7284bfbb38a25c.png": "\\frac{dv}{dz}", + "de75f3403894e42a.png": "y=x^{2}\\iff x=\\sqrt{y}", + "de7d51c55254767c.png": "(\\begin{matrix}2n-2\\\\ n-2\\end{matrix})", + "de7d621e0b3d066e.png": "lim_{n\\rightarrow\\infty}\\frac{T_{n}}{L_{n}}=\\frac{1}{3}", + "de7e5a137b361c6e.png": "(\\begin{matrix}a\\\\ a+1\\end{matrix})=0", + "de7fc4630f6b0e5f.png": "S_{i}=\\sum_{j}d(v_{i},v_{j})^{2}", + "de80c1cea1f4e30c.png": "(\\begin{matrix}1&1\\\\ 1&-\\end{matrix})", + "de831fb17317b935.png": "a(n)=\\sum_{i=1}^{n}(\\begin{matrix}n\\\\ i\\end{matrix})a(n-i)", + "de8335f322c0ae75.png": "hr\\{\\begin{matrix}p\\\\ q\\end{matrix}\\}", + "de83fc61fd564a20.png": "\\hat{B}_{i}", + "de85cca161083751.png": "\\int f^{-}d\\mu", + "de94cf50587a4354.png": "P_{e}^{(n)}\\rightarrow0", + "de9dbb41872bd3eb.png": "T>T_{c}=1/(2\\sqrt{log2})", + "de9f1a3d000fac79.png": "v=D\\int idt", + "dea5f8a7563a1f96.png": "\\tilde{R}_{n}", + "dea60384a254e2fa.png": "lim_{\\epsilon\\rightarrow0}\\frac{1}{\\epsilon}L=6t(t-x)", + "dea7c5ab897d9a17.png": "(Q_{*}(\\mu_{\\cdot}))_{S}=\\mu_{S\\circ\\theta}", + "deaee1a1cbf58ed8.png": "arctg(\\pm\\infty)=\\pm\\frac{\\pi}{2}", + "deaf3db716e4821b.png": "2^{\\aleph_{0}}\\ne\\aleph_{\\omega}", + "deb1c79bd2cb1d90.png": "(\\begin{matrix}q+n-1\\\\ q\\end{matrix})", + "deb2ace930ab358a.png": "I(Y_{1};Y_{2};Y_{3};Y_{4})", + "dec1b3185c435d5a.png": "E\\{e^{2}(n_{1},n_{2})\\}", + "dec4fac977906ce5.png": "-\\sqrt{x}", + "deceabdd2d5a246d.png": "arg(x+iy)", + "ded22533f3a378ae.png": "c\\prod(x-a_{i})", + "ded6dd9c29be00bf.png": "\\hat{f}(5)", + "ded7d857ebf2776f.png": "\\frac{R(1)}{R(-1)}=R(-1)", + "dedb102055260798.png": "1+X(1-YX)^{-1}Y", + "dedbd4f7e07fb293.png": "[a,b]", + "dee337dd1f3eabc8.png": "|\\Psi(0)\\rangle=|1\\rangle", + "dee33f39f5b09ac6.png": "V\\approx\\sum\\pi y^{2}\\cdot\\delta x", + "dee65e530a817035.png": "\\tilde{V}_{N}", + "deeaa35c9c1759c5.png": "Li_{2}(z)=\\sum_{k=1}^{\\infty}\\frac{z^{k}}{k^{2}}", + "deeddc07f419bc00.png": "\\frac{(h-y)^{2}}{h^{2}}", + "deef9d02ed787eb2.png": "(\\begin{matrix}n\\\\ 2\\end{matrix})p", + "def9ccc604d5e291.png": "\\overline{DR}", + "df00e65b84c24b6b.png": "\\int_{\\gamma}D\\gamma", + "df06d777f0bdcd3e.png": "A", + "df1040e1a3e466ca.png": "\\int_{-1}^{1}x^{-1}dx", + "df14745608f9ff29.png": "\\tilde{E}=\\Gamma(-,E)", + "df162eed9c760f92.png": "(j^{r}\\sigma)(p)=j_{p}^{r}\\sigma", + "df18ea13d96d8db0.png": "U_{n}=\\beta z_{n}+\\epsilon,\\epsilon\\sim", + "df19ec333e64b274.png": "\\hat{R}", + "df24c4cff0b88574.png": "r=fr_{0}+gr_{0}^{\\prime}", + "df25e64a2b6b5ec0.png": "(\\hat{b})", + "df291b76d25bc8c5.png": "K^{\\times}/(K^{\\times})^{n}", + "df2aa626e7482e1f.png": "\\overline{K}_{n}", + "df3008ea9bd1ce3d.png": "G\\underline{A}", + "df30dc0a42020b80.png": "A", + "df38df473dce703c.png": "\\underline{u}\\in U", + "df3e33c490c32e68.png": "\\tilde{A}_{9}", + "df3f79108dab754f.png": "\\hat{\\zeta}_{0}(\\omega)", + "df449e241a918233.png": "d\\overline{\\mu}=\\frac{d\\mu}{\\sqrt{g_{00}}}", + "df4cc5422cc107a0.png": "b=\\sqrt{c^{2}-a^{2}}", + "df4e2a19d62cc0ee.png": "y_{y^{2}}", + "df536014581e985d.png": "\\sigma=\\sigma_{H_{2}O}\\times\\frac{m}{m_{H_{2}O}}", + "df5f14dc3506c41c.png": "[\\begin{matrix}a&r\\\\ d&s\\end{matrix}]", + "df6438180b8db27c.png": "\\lfloor1/x\\rfloor^{-1}", + "df660eb8ac02c748.png": "\\tilde{x}_{i}", + "df66e85210a2da7f.png": "\\tilde{f}(s)=\\frac{a_{N}}{s-N}+\\cdot\\cdot\\cdot", + "df6a5605c4f6b553.png": "\\hat{f}=e^{-\\pi\\xi^{2}}", + "df6c2b07f1b35f39.png": "L(q_{j},\\dot{q}_{j},t)", + "df72904380479e0a.png": "2+\\frac{12}{\\sqrt{13}}", + "df7713c67ebd1c23.png": "O(h^{p+1})", + "df775c763c7fbd3c.png": "\\frac{2-a}{\\sqrt{2-2a}}", + "df78868320aad110.png": "E_{i\\ne j}[lnp(Z,X)]", + "df7e1f6c9dda0b75.png": "\\int dm=M", + "df828ce232e2871d.png": "\\int_{X}fd\\mu", + "df872e92dba38238.png": "{(x_{n})}_{n\\in N}", + "df875fe781369341.png": "-1F_{0}", + "e025c3768f227d29.png": "\\frac{dx}{dt}=\\dot{x}", + "e025eb50868a3530.png": "\\hat{p}_{y}", + "e026ba9f05e58be5.png": "\\frac{dq}{dt}=\\frac{M}{B}", + "e029a1c632bfbea7.png": "-\\int dx^{\\mu}dx^{\\nu}B_{\\mu\\nu}", + "e02b150ba4a715cb.png": "\\tilde{\\gamma}:[0,1]\\rightarrow P", + "e02eca9d6956f12c.png": "K_{+}\\subset K_{+0}", + "e02fadbe72300991.png": "\\tilde{X}=\\tilde{Y}", + "e030be5593495a93.png": "(+\\alpha,-\\alpha)", + "e038861bc7073106.png": "\\underline{x}=(x_{1},x_{2},x_{3},...,x_{N})^{T}", + "e038d01f332500e9.png": "F_{e}>0,F_{w}>0", + "e0441698ffc340c8.png": "m\\frac{du}{dt}=X-mg\\gamma", + "e0470f9a26bb218f.png": "\\sqrt[12]{2}:1", + "e04a658e0b73a795.png": "\\tilde{L}", + "e04f1c10aaad0173.png": "\\overline{R_{F}}", + "e05527204060c920.png": "\\tilde{f}_{0}()", + "e0581b33d73981c1.png": "a\\sqrt{D}", + "e062603ebde6fc62.png": "\\sqrt{m}", + "e06a351d9eefed55.png": "\\neg\\psi\\vee\\neg\\varphi", + "e0716d7eeeaed307.png": "\\langle E\\rangle=u=-\\frac{1}{Z}\\partial_{\\beta}Z", + "e07d0da27e607b97.png": "E[P^{(k)}]=-k\\alpha", + "e08d6eaf6899b512.png": "\\overline{126}_{H}", + "e09067d545624ce8.png": "p_{i}((x_{j})_{j\\in N})=x_{i}", + "e09a11270f4cad6c.png": "\\sqrt{\\Omega}", + "e09be2b0702e49ee.png": "\\frac{d}{dt}N_{2}=-c_{1}N_{1}", + "e09cf90e353ec17b.png": "\\tilde{t}_{i}", + "e0a71cb366f1b57e.png": "t_{r}=\\sqrt[]{\\rho R_{0}^{3}/\\gamma}", + "e0a77dd986da62d8.png": "\\int_{-2}^{6}\\frac{dx}{x}", + "e0b031afc7f964d9.png": "(G,U)\\in Obj(G_{0})", + "e0bbb5e7afd5c8ec.png": "\\hat{t}_{g}(t,\\omega)", + "e0c6285143b1d850.png": "-\\sqrt{\\frac{1}{60}}", + "e0c8535eeee2c4dd.png": "\\prod_{pb=a}g_{b}=g_{a}", + "e0ca608a29954c3c.png": "\\int\\frac{1}{u}du", + "e0cce393fafcd820.png": "\\prod R_{i}", + "e0d2ee0ad5bcbb38.png": "\\hat{u}_{R}", + "e0d2fa3902642874.png": "lim_{t\\rightarrow\\infty}\\overline{x}(t)", + "e0d589b64805fca8.png": "(A,m_{A})", + "e0d8afc07158f9cc.png": "\\tilde{\\nu}:M\\rightarrow X_{k}", + "e0d93e5b964c6492.png": "lim_{z\\rightarrow a}\\frac{1}{f(z)}", + "e0dab0cdb4c88abf.png": "k=\\frac{5+5\\nu}{6+5\\nu}", + "e0df363e0061e866.png": "\\overline{MG}", + "e0e2db6e59bdb205.png": "\\frac{\\partial f}{\\partial x^{i}}", + "e0e474396e022a7f.png": "(0<\\frac{dB}{dt}<\\infty)", + "e0e70ce889665687.png": "g(x)=\\int_{0}^{x}f(t)dt", + "e0f40cde6329488f.png": "\\frac{1}{min_{i}h_{c}(O)-t_{i}}", + "e0fc9ca50f644329.png": "B\\rightarrow K^{*}l^{+}l^{-}", + "e1027494b64f3ff2.png": "\\alpha_{1},\\alpha_{2},\\alpha_{3}.....\\alpha_{k}", + "e103d501d3485de8.png": "-logp(s|m)", + "e10e5be4d7947629.png": "u_{i}\\in(0,1]", + "e110a56b5a259a86.png": "ae^{-kt}+3", + "e114dc4792bbb1f0.png": "g=\\epsilon_{0}\\chi^{(m)}H", + "e1154495e65a520b.png": "-\\frac{3}{2}\\pi1", + "e6a957a950dd5619.png": "z\\notin S", + "e6ad5dbb4c1a9fa5.png": "\\frac{1}{T}=\\frac{dS}{dE}", + "e6b3a6be3b42f013.png": "\\sqrt{n}", + "e6b4f3838e1d21b4.png": "-x", + "e6bb1813503ae597.png": "D(-\\infty,\\infty)", + "e6c0b55697fa3578.png": "\\frac{R_{x}}{R_{g}+R_{y}}=\\frac{R_{B1}}{R_{B2}}", + "e6c5d297dd061e4f.png": "C", + "e6c81785b6551eba.png": "\\frac{PV}{T}=\\frac{k_{1}(T)}{T}", + "e6cb3292b10c9d45.png": "(\\begin{matrix}14\\\\ 5\\end{matrix})=2002", + "e6cdaa950a0eb08c.png": "i\\notin(2+i)", + "e6cdb26f471c47e2.png": "P_{t}=P_{t-1}\\cdot e^{RC_{t}}", + "e6ce291fcdbd3566.png": "\\prod p_{i}^{t_{i}-1}", + "e6d3e93e0f5a9764.png": "g=\\frac{dv}{dx}", + "e6d922042d8e530e.png": "\\int vds", + "e6d94efcd5e8dc68.png": "B_{e}=\\overline{B}(R_{e})", + "e6dcf9269488ba44.png": "G=H-TS_{int}", + "e6e6cc9e0632cd8e.png": "\\int f(t)dt=0", + "e6ec53f129bf437a.png": "\\overline{A}D", + "e6f1b4b6618fb319.png": "r^{\\beta_{\\epsilon}}", + "e6f1b6f02835f68b.png": "A\\times-", + "e6f25659e859eaa4.png": "T=\\frac{2L}{\\sqrt{gh}}", + "e6fdd6deec83bc7f.png": "\\Xi_{g}^{d}", + "e70727981d616a86.png": "\\hat{y}_{d}", + "e70f7a7dab5beac2.png": "\\alpha,\\beta\\in\\Phi^{+}", + "e717b565d646578e.png": "x=\\sqrt[4]{5}=5^{1/4}", + "e718a3b10eac7824.png": "\\frac{1}{6}+\\frac{1}{6}+\\frac{1}{6}=\\frac{1}{2}", + "e71974d3378dd6eb.png": "\\hat{f}:E^{\\prime}\\rightarrow E", + "e72661e229146e3a.png": "2K_{||}+K_{\\perp}", + "e729361013849ef9.png": "|1\\rangle=(\\begin{matrix}1\\\\ 0\\end{matrix})", + "e729c69f81fe5c27.png": "\\int\\int_{X}\\int_{Y}^{Z}", + "e730d9fe69367007.png": "(+\\alpha,-\\alpha)", + "e7324450d82dd02b.png": "e^{in\\mu-|n|\\gamma}", + "e73ab1de15db2980.png": "\\int_{E}f(x)\\mu(dx)", + "e73e1fb68316608f.png": "\\int_{a}^{b}f(x)dg(x)", + "e73ea4541800d694.png": "\\tilde{B}_{6}", + "e74040dd05598fef.png": "E=-\\frac{\\partial A}{\\partial t}", + "e744010fdd3acd3c.png": "\\mu_{XN}=E[x^{N}]", + "e744673faaefff5f.png": "(1)Z(V,0)=1", + "e74aaaf31c61562a.png": "\\hat{U}|\\psi_{i}\\rangle", + "e75085542d11c8e6.png": "M=(D^{(\\alpha)})^{-1}L^{(\\alpha)}", + "e75549764add5dd6.png": "cot(\\frac{\\alpha}{2})=\\frac{s-a}{r}", + "e755a7947f1f7dad.png": "(k^{\\prime}+p^{\\prime})^{2}\\approx", + "e756965645b9e5b8.png": "lim_{x\\rightarrow0}f^{-1}(x)=-\\infty", + "e75f4647be6f148a.png": "b(t)=b1\\times e^{\\frac{-t}{\\tau}}", + "e763832ec5f53e6b.png": "A=4\\pi{R_{p}}^{2}", + "e76bc13b2aca5c0e.png": "\\frac{\\partial V}{\\partial S}", + "e76ebb33aad20857.png": "X^{q}-X=\\prod_{a\\in F}(X-a)", + "e77770ac857cd92d.png": "\\sqrt{n}/ln\\sqrt{n}", + "e77ebf4bb6580999.png": "v=\\int\\frac{dv}{dx}dx", + "e78726c04296d920.png": "x(a+b)+c", + "e78d7fc1a3383911.png": "(\\begin{matrix}6\\\\ 3\\end{matrix})", + "e78fbda600b0ffef.png": "\\omega_{1}\\propto\\vec{d}\\cdot\\vec{E}\\hbar", + "e7912fb45e15e59e.png": "3\\sqrt{x}", + "e793819c01b2b157.png": "\\int Mvds", + "e794d1611ec76a33.png": "\\mu-s\\le x\\le\\mu+s", + "e7972200a100e50c.png": "D_{L}=10^{\\frac{(m-M)}{5}+1}", + "e7a02bed7723d6f6.png": "\\mu=\\frac{1-e^{-r}}{r}", + "e7a8627f6e2f1618.png": "2^{2^{2}}+2^{1}+2^{0}", + "e7aa0f4c196fbef8.png": "\\int dy", + "e7b5ec80de2fd24a.png": "w\\notin B(v)", + "e7c00790dc45eb72.png": "A", + "e7c229bfaa46482e.png": "\\hat{T}T\\rho=\\rho", + "e7c3c2db4a931d25.png": "\\hat{z}_{a}", + "e7c553b6b96f403a.png": "V(\\tilde{\\beta})", + "e7c7a44ee9bf3cc3.png": "P-AP>0", + "e7c8d804d62e509b.png": "[\\begin{matrix}4&4\\\\ 6\\end{matrix}]", + "e7c9488274b72bf9.png": "\\int_{0}^{t}", + "e7ce2faa70e2733a.png": "\\tilde{b}_{i}", + "e7cf6bb213645a9f.png": "\\frac{m}{s^{2}}", + "e7cfa2357d9a849b.png": "(AA^{*})^{-1}", + "e7d31c73869c4610.png": "X:=\\prod_{i=1}^{n}X_{i}", + "e7d76757daa61208.png": "\\sqrt{G}", + "e7d9c30b7982a4bc.png": "S_{1}=S_{1}^{\\prime\\prime}", + "e7e032d3dd527ba1.png": "2ax=-b\\pm\\sqrt{D}", + "e7e1bdae96b76bf7.png": "f(3,0.5)=0", + "e7e7ce1ff878e7fc.png": "\\sqrt{n}", + "e7ec07b896683bd0.png": "4^{-N}(\\begin{matrix}2N\\\\ N\\end{matrix})\\approx\\frac{1}{\\sqrt{\\pi N}}", + "e7ec37aee7f377f3.png": "\\frac{dQ_{T}}{dQ_{*}}", + "e7ecf93bc5364a5e.png": "(0,\\sqrt{3})", + "e7ef1fcfcb45a274.png": "\\omega=\\frac{d\\theta}{dt}", + "e7f8095c64ab0426.png": "MPM=\\frac{dI}{dY}", + "e7f995dd63b51f46.png": "\\beta=\\frac{\\partial f}{\\partial y}", + "e802f8cee0e2b99f.png": "x\\le\\frac{-4}{5}", + "e8096f5d8a5dbbd5.png": "q(1)^{2}+q(1)-1", + "e80ca6f20ba4d51d.png": "\\tilde{O}(m^{2}n)", + "e80ce3077690d16b.png": "i:\\underline{A}", + "e80d80a171f3dd2d.png": "[\\begin{matrix}1&1\\\\ 0&1\\end{matrix}]", + "e8140fa19705cb6d.png": "\\int Mvds", + "e8156e29df871f86.png": "\\sqrt{x^{2}+\\epsilon^{2}}", + "e81770fdbc1b7b7f.png": "[\\begin{matrix}.7&0\\\\ .3&1\\end{matrix}]", + "e81852f5ce0c1f6d.png": "V_{t}=\\sqrt{\\frac{\\mu}{r}}", + "e81a77dbf31f194f.png": "|\\psi(t)\\rangle", + "e81a84aa2cbdca3c.png": "\\partial^{2}f/\\partial x^{2}", + "e820f3caf5129a72.png": "\\Omega^{\\prime},\\Omega_{0},\\Omega_{1}", + "e82ac2a34d2fd5d1.png": "(\\begin{matrix}c_{i}\\\\ i\\end{matrix})", + "e82deedd63f0d2b1.png": "=\\lambda_{n}x^{T}x", + "e82e598a6f281053.png": "\\int_{a}^{b}g(x)dx", + "e8328d531812bd37.png": "\\Delta Q=-\\frac{\\Sigma rQ_{0}^{n}}{\\Sigma nrQ_{0}^{n-1}}", + "e83ee59db801fd6f.png": "g=\\int Gdz", + "e843f6acdc75dc53.png": "\\overline{op_{1}}", + "e84621b95a166dae.png": "\\theta_{0}=2\\pi r_{0}^{2}H_{0}", + "e8482a0b20326c1d.png": "V_{-}=Be^{\\frac{-1}{RC}t}", + "e84a137bd92c30a4.png": "(\\overline{\\xi},\\overline{\\zeta})=(0,0)", + "e84b1e35b5578a5f.png": "\\int_{a}^{b}dx", + "e84d76d2419f8e6b.png": "\\overline{s}\\in\\alpha,t\\notin\\gamma", + "e85c091bd4ca9e8a.png": "(y^{\\prime},x^{\\prime})\\sim(y,x)", + "e86120f7ed62efbc.png": "b^{2}(w^{2},m_{1}^{2},m_{2}^{2})", + "e868d5b6b2ea71fe.png": "\\frac{\\partial V}{\\partial t}", + "e8732b876d9331c5.png": "E=-\\vec{\\mu}\\cdot\\vec{B}", + "e8740b1c52bdeaa9.png": "[\\begin{matrix}Z&Q\\\\ 0&Q\\end{matrix}]", + "e879fc06ced009db.png": "a,b\\in\\hat{R}", + "e87b9266f2ae60b9.png": "\\tilde{h}_{u},\\tilde{h}_{d}", + "e87bed73f799b112.png": "\\hat{H}_{0}^{\\prime}=\\beta p_{0}", + "e87dd95e30ede926.png": "\\langle x,y|x^{2}=y^{3}\\rangle", + "e883a7408975d7ef.png": "(\\begin{matrix}5\\\\ 5\\end{matrix})", + "e88af3fb3194b959.png": "v=\\frac{\\partial g}{\\partial y}", + "e88c7b6d0c2d9fc2.png": ",_{\\alpha\\beta}=\\frac{\\partial^{2}}{\\partial x^{\\alpha}\\partial x^{\\beta}}", + "e89124d8e66627c2.png": "\\hat{f}=e^{-\\pi\\xi^{2}}", + "e8929416374ec8c2.png": "S=\\frac{P_{t}G^{2}\\lambda^{2}}{(4\\pi)^{3}R^{4}}\\sigma", + "e89c11c4ee0b9f94.png": "(V_{a,b}:b\\in B)", + "e89c374c9ab6713d.png": "\\langle2x,2y\\rangle=\\langle x,y\\rangle", + "e89d02c3d976a0d4.png": "f=\\frac{x}{1-x-x^{2}}", + "e89d5d49db66e709.png": "g:=k\\oplus m", + "e8a6a4b4bcafcf7e.png": "[\\begin{matrix}0&-1\\\\ 1&1\\end{matrix}]", + "e8a896e0e60c730d.png": "q=-K\\frac{\\partial h}{\\partial z}", + "e8acb4ee37701cf1.png": "\\bigoplus_{i+j=n}C_{i,j}", + "e8ada36b54b63152.png": "(\\alpha,\\beta,id)", + "e8b429e8544ccb98.png": "\\sqrt{N}\\le M4\\sqrt{q}", + "e8f5912da089fac2.png": "H_{a}^{a}\\hat{a}^{\\dagger}\\hat{a}", + "e8f7a6e5f0e1dd74.png": "H_{trt}=\\frac{2GM}{3r^{2}}", + "e8faddbc75539736.png": "(s_{x_{0}},...,s_{x_{n}})\\in V_{F}", + "e8fe0c9c623adfa5.png": "\\tilde{E}_{7}", + "e9001b8aed801a59.png": "\\frac{dr}{dt}=-r", + "e901e09bb930ec3c.png": "(\\begin{matrix}0\\\\ 1\\end{matrix})", + "e90edc9c04fabfef.png": "\\int e^{x}cos(x)dx", + "e911331afe67bb10.png": "A=\\frac{\\pi D^{2}}{4}", + "e9169b0bfc97f2c7.png": "\\sum(\\overline{X}-X_{i})=0", + "e924f2d4dd67b8b8.png": "r^{-l_{1}}+r^{-l_{2}}", + "e92a95f0a7652df6.png": "(\\begin{matrix}n\\\\ n/2\\end{matrix})", + "e93a5640fb2fa8fd.png": "\\varphi=(1+\\sqrt{5})/2", + "e94a60feae94f4f7.png": "T", + "e95450992e04a3d4.png": "r^{\\beta_{\\epsilon}}", + "e954a351c1c61d1a.png": "4:sum+=tmp", + "e954cc35cfd7f9f8.png": "(\\begin{matrix}n\\\\ 5\\end{matrix})", + "e954e7c9145d30ce.png": "\\int xsinx^{2}dx", + "e95b1d0d40f2d89b.png": "\\Gamma(t)=\\{Me^{-x}\\}(t)", + "e9649f520ea5b01a.png": "\\tilde{g}(a)", + "e97bde8b5b24bf37.png": "\\vec{t_{2}}\\langle s^{\\prime\\prime}\\rangle=\\vec{t_{2}}\\langle s^{\\prime}\\rangle", + "e97f103913e72ae4.png": "k=(1/\\lambda)\\hat{e}_{\\angle}", + "e9804c0d92c7a42a.png": "U_{bias}^{LE}(Q;t)", + "e991840e64153d18.png": "\\frac{dF}{dL}", + "e99701a22e5f2fc7.png": "\\tilde{M}", + "e99969c212efd4fb.png": "(f(-t)=-f(t))", + "e99c60ce19314963.png": "\\lambda^{3}=(\\begin{matrix}1&0&0\\\\ 0&-1&0\\\\ 0&0&0\\end{matrix})", + "e9aea24a585d39b9.png": "\\Sigma r(Q_{0}+\\Delta Q)^{n}=0", + "e9af18e3bd8dc991.png": "\\underline{X}=X^{+}\\cup X^{-}", + "e9b386f86ee87ca4.png": "k_{x^{b}}", + "e9b5ae3dab30b1f2.png": "(1-\\frac{N}{K})", + "e9be1873b2f00bbc.png": "s\\{\\begin{matrix}2\\\\ 8\\end{matrix}\\}", + "e9c25c762d0f4f64.png": "\\hat{Y}_{j}", + "e9c55109de5db5c1.png": "\\underline{P}(Cl_{t}^{\\le})", + "e9c852a6feee4b7c.png": "\\frac{d}{dx}(x!)", + "e9ca1e5e03a8fa0f.png": "f(a)=(f,E_{a})", + "e9cadf7f65628788.png": "T_{m}=\\frac{m\\nu^{2}c^{2}a^{2}}{k_{B}}", + "e9d5202fb0fee79a.png": "\\eta_{IJ}=e_{\\beta I}e_{J}^{\\beta}", + "e9d69f813db68091.png": "[g]\\notin N", + "e9d9baac2afc0ac9.png": "\\delta t_{b}=\\frac{x^{*}}{(c+v)}\\cdot", + "e9d9bbee25c9829c.png": "E_{i}\\frac{x^{i}}{i!}", + "e9df6d7daccdc6c8.png": "e^{\\int f(x)dx}", + "e9e61b3d94cb7e5a.png": "G^{*}(f)=G^{\\prime}+jG^{\\prime\\prime}", + "e9e770b100263c07.png": "\\int_{0}^{1}D(x)dx", + "e9e8966d9f73ebe4.png": "\\hat{C}_{I}", + "e9eac58d3de5c432.png": "Q>\\sqrt{\\frac{1-k^{2}}{2}}", + "e9eba703fcf0cbea.png": "H^{1/2}(\\partial\\Omega)", + "e9f3ffdcdc04f6bc.png": "\\frac{\\partial}{\\partial x^{\\sigma}}j^{\\sigma}=0", + "e9fc10a387a807b0.png": "\\sqrt{s}\\cdot\\sqrt{s}=s", + "e9fdbbe3f6d1ad35.png": "G(y)=\\int_{0}^{y}g(z)dz", + "ea001a25e780afea.png": "\\tilde{E}_{i}^{3}", + "ea021631d9bb276e.png": "A_{c}=A_{c}^{i}T_{i}", + "ea03082cc89a259f.png": "s\\{\\begin{matrix}8\\\\ 3\\end{matrix}\\}", + "ea0cc511ed50fd4e.png": "11-\\frac{\\sqrt{274}}{2}", + "ea0d90699e0d337e.png": "Re(\\underline{n})=\\frac{ck}{\\omega}", + "ea1511c1c4b2881d.png": "arctg(\\pm\\infty)=\\pm\\frac{\\pi}{2}", + "ea163ab4689989de.png": "(\\begin{matrix}n\\\\ r\\end{matrix})", + "ea1f99f48f33ba02.png": "|z|^{n}<\\epsilon", + "ea1fa912db0e05b1.png": "O(N!z^{-N})", + "ea2470ec5ed22c26.png": "\\tilde{p}", + "ea267632cad8a198.png": "W:[x_{1},x_{2}]\\rightarrow R", + "ea2be42a4f43e923.png": "(d,(\\begin{matrix}d+1\\\\ 2\\end{matrix}))", + "ea2c54cdb113ca80.png": "(\\begin{matrix}14\\\\ 5\\end{matrix})=2002", + "ea33bdccc189e26e.png": "\\oint dS=\\oint\\frac{dQ}{T}=0", + "ea3781c25b138179.png": "\\int f^{-}d\\mu", + "ea3fb29e8d41b7ec.png": "\\hat{\\alpha}", + "ea400b1e5a405bfe.png": "[\\begin{matrix}0\\\\ \\frac{\\pi}{2}\\end{matrix}]", + "ea573371f33594bd.png": "P_{t+1}-P_{t}", + "ea605d59be670e65.png": "\\hat{\\theta}\\in\\Theta", + "ea65e4a8368d0ab1.png": "\\tilde{f}(k)", + "ea6b587a7acc492c.png": "q_{i}=2p_{i}(1-p_{i})", + "ea6d050dae792344.png": "\\int_{E}f(t)d\\mu(t)", + "ea6e48028183f132.png": "\\hat{D}=D", + "ea74e49402fe5a98.png": "-\\sqrt{\\frac{6}{35}}", + "ea75c59034fa0130.png": "\\frac{1}{T}\\frac{d^{2}T}{dt^{2}}=-k^{2}", + "ea76e88ba55e2eea.png": "1-e^{-e^{2.6-0.00024K}}", + "ea79c750bce0c983.png": "p_{k}=\\frac{\\partial S}{\\partial q_{k}}", + "ea834c803db7353f.png": "\\forall x\\notin L", + "ea856f29def9699d.png": "H(t)=\\frac{2}{3}kcoth(kt)", + "ea8afd823ab350db.png": "L", + "ea90a08b1ae1f160.png": "z=\\prod_{p_{i}\\in P}p_{i}^{a_{i}}", + "ea90b799f3713be7.png": "\\frac{\\alpha+n}{\\beta+n\\overline{x}}", + "ea916a0ff36677a2.png": "\\sqrt{B}", + "ea950feb6d4f0f1f.png": "\\overline{\\overline{x}}^{i}=B\\overline{x}^{i}", + "ea981eae0330a6b4.png": "\\frac{a}{b}=\\frac{dy}{dx}", + "ea9849645f632fa7.png": "\\aleph_{0}<|S|<2^{\\aleph_{0}}", + "eaac94e344f73901.png": "\\sum_{y\\in A}|\\langle x,y\\rangle|^{2}\\le||x||^{2}", + "eab0f0eddb4d135f.png": "\\sqrt{x^{2}+y^{2}}\\le r", + "eab103e6114c7901.png": "x=c_{0}+\\sum_{i=1}^{m}k_{i}x_{i}", + "eab98cd7ab00a4b7.png": "p_{2}>0,...,p_{n}>0", + "eaba3d97ab255e0a.png": "\\exists x[...]", + "eac0e70f56d6b36a.png": "\\hat{5}", + "eac86d6c75af163a.png": "\\pi_{i+j}A", + "eac8cedd24e46e78.png": "\\int e^{-x^{2}}dx", + "ead0ef3b0ff6c628.png": "4^{-N}(\\begin{matrix}2N\\\\ N\\end{matrix})\\approx\\frac{1}{\\sqrt{\\pi N}}", + "ead37717aca42b77.png": "[\\overline{x}-\\frac{cs}{\\sqrt{n}},\\overline{x}+\\frac{cs}{\\sqrt{n}}]", + "eada03f54bf482d5.png": "{d^{\\chi}}^{m}", + "eae2546d74877d89.png": "G=\\int_{0}^{T}k(t)x(t)dt", + "eae26691f9f9632f.png": "h(x)=\\int_{0}^{x}f(t)dt", + "eae2e11d759ca8f2.png": "C_{0}=D/V_{blood}", + "eae31a15f7e471c8.png": "\\int dx=0", + "eae3331055c64dcf.png": "\\frac{dv}{dr}", + "eae5d63107c78188.png": "\\sum_{k=1}^{n}\\frac{1}{p_{k}}\\sim loglogp_{n}", + "eae92df0100e31ef.png": "\\frac{2-p}{\\sqrt{1-p}}", + "eaecc8a5ebd15300.png": "\\hat{\\mu}_{3}=56/3=18.67", + "eaee38c9f1988c47.png": "[\\begin{matrix}a&c\\\\ 0&b\\end{matrix}]", + "eaeea9a4de410a5a.png": "B=\\prod B/I_{i}", + "eaf86e69cc050cae.png": "S=\\frac{\\rho-\\rho^{n+1}}{1-\\rho}", + "eafa3e4960370e3e.png": "d^{2}N(>\\lambda)/dzd\\Omega", + "eafec7701b9140ca.png": "\\int u^{1/2}du", + "eb05c50d9755c263.png": "x^{\\prime}=\\gamma(x-vt)", + "eb07edc37276184e.png": "M(l)_{n}=M_{n+l}", + "eb0cd381c09cff2d.png": "[\\begin{matrix}0&1\\\\ 0&0\\end{matrix}]", + "eb0dcd8fb327fb2b.png": "P=-(\\frac{\\partial F}{\\partial V})_{T}", + "eb114037d3929a5d.png": "n![z^{n}]g_{m}(z)=[\\begin{matrix}n\\\\ m\\end{matrix}]", + "eb129c9baa32e1e8.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=\\frac{n^{\\underline{k}}}{k!}", + "eb1a081de494ef41.png": "D(p||q)", + "eb20d9c5142e92c6.png": "{(w^{j})}^{1}", + "eb2e78a180cae1e4.png": "\\hbar\\frac{dk}{dt}=-eE", + "eb3d8a9563a4fccc.png": "max(|a|,|b|)", + "eb4c2d17d55a962d.png": "B_{\\rho}^{\\eta}", + "eb4c3999845c3e2e.png": "\\begin{matrix}C_{t3}&=&1.2\\\\ C_{t4}&=&0.5\\end{matrix}", + "eb4ce85af01655a6.png": "\\overline{X}_{i}", + "eb4faa61e4559473.png": "0+\\frac{4000}{100}=40", + "eb5555e745c7cff9.png": "\\frac{N_{\\nu}}{t}=\\Phi_{o}\\frac{\\lambda}{hc}", + "eb56f6f06f8aebbc.png": "|fix(M,Q_{i})|=(n/2)!^{2}", + "eb5d5984fffe3112.png": "\\int_{0}^{\\infty}x^{-x}dx", + "eb5e2dfca50ae2aa.png": "\\int_{0}^{1}F(x)dx=0", + "eb6277425e7aaa30.png": "i^{4n+2}=-1", + "eb666032ef59a9a8.png": "W_{1-2}=\\int PdV", + "eb775a614306e6b9.png": "(\\begin{matrix}i\\\\ u\\end{matrix})", + "eb7a456894cb208b.png": "f_{0}=\\frac{1}{2\\pi\\sqrt{LC}}", + "eb7dec7d596ac570.png": "\\Sigma_{i}=\\Sigma_{j},\\forall i,j", + "eb7ef9c9b303b39f.png": "\\int d\\Omega", + "eb80f6ee53ac2035.png": "(\\begin{matrix}0&-1\\\\ 1&0\\end{matrix})", + "eb8459fee199689d.png": "B=-13.1", + "eb885c4a185a5366.png": "M=[\\begin{matrix}0&1\\\\ -1&0\\end{matrix}]", + "eb8ca550c186b6c2.png": "\\frac{d\\phi}{dx}", + "eb8db3476b5d3f97.png": "|dr/dt|=\\sqrt{2}", + "eb8f1c8f50d6c16d.png": "q=-k\\frac{\\partial u}{\\partial x}", + "eb9522d0ce72e2aa.png": "\\frac{\\partial E}{\\partial t}", + "eb99ca12034fe23e.png": "Q(H)=\\prod_{i}Q_{i}(H_{i})", + "eba5938dbccc8079.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "eba6f076d6c1860c.png": "12^{2}+35^{2}=37^{2}", + "ebaf1ea8a1ed1eff.png": "p(\\cdot;\\theta+\\Delta)", + "ebb26806733127fe.png": "S_{k}=(\\begin{matrix}m\\\\ k\\end{matrix})\\frac{(m-k)!}{m!}=\\frac{1}{k!}", + "ebb30a3f57bdb3e4.png": "\\prod_{i\\in I}M_{i}/U", + "ebbca3246fbc5dbe.png": "U=(A^{T}A)^{1/2}A^{-1}", + "ebc635d05113f55b.png": "\\int_{X}||f||_{B}d\\mu<\\infty", + "ebc91c4b26633716.png": "Tr\\rho^{p}K^{*}\\rho^{1-p}K", + "ebccb3bdd5255aee.png": "(x^{5}-32)/(x-2)", + "ebd07e709cd1a6db.png": "DM(x1^{2^{|x|^{c}}})", + "ebd308ce2be88234.png": "\\alpha", + "ebd3d7cf8fa387c2.png": "s\\{\\begin{matrix}5\\\\ 3\\end{matrix}\\}", + "ebd521616f652ceb.png": "d\\theta_{j}(\\frac{\\partial}{\\partial\\theta_{k}})=\\delta_{jk}", + "ebd638b84b647c16.png": "=\\frac{1}{2}\\frac{m}{L^{3}}v^{2}[\\frac{y^{3}}{3}]_{0}^{L}", + "ebd875036f82a722.png": "(1+\\frac{0.129949}{12})^{12}-1", + "ebdb0dd58130570b.png": "\\frac{1}{(i\\omega-\\xi_{1})(i\\omega-\\xi_{2})}", + "ebe2a7effbc3ae7e.png": "(\\hat{x}\\hat{y})^{2}=\\hat{x}\\hat{y}\\hat{x}\\hat{y}", + "ebe484308f415764.png": "\\tilde{D}_{4}", + "ebe72d59798bcfd1.png": "S_{x}=x(H)", + "ebed251191fd658f.png": "\\sum_{n=0}^{\\infty}\\frac{1}{(-2)^{n}}", + "ebee5fde71a2c3f8.png": "MPC=\\frac{dC}{dY}", + "ebf81ab65c40ca56.png": "D^{\\prime}(R)", + "ebfb171c50d68c7d.png": "\\tilde{\\Gamma}", + "ec0564a69cdb118a.png": "P=exp(+\\beta Q)", + "ec067dad6493cf1e.png": "\\int_{a}^{b}f(x)dx", + "ec088131657f1e8b.png": "\\frac{\\partial c}{\\partial z}", + "ec0eb9c4a55a0d2c.png": "V=-Y=X", + "ec0ef8d3d8be1760.png": "u_{i}\\in[\\underline{u}_{i},\\overline{u}_{i}]", + "ec10bbfe9462c75b.png": "\\int_{A}(g-f)d\\mu=0", + "ec1169e3f96a6036.png": "2s-s=-2^{0}+2^{64}", + "ec22b9c52677961b.png": "\\hat{D}", + "ec24fd1a0afee6b6.png": "V_{\\theta}=\\frac{2n}{(n-1)^{2}}", + "ec2593f57f166ab6.png": "[\\begin{matrix}0&1\\\\ 0&0\\end{matrix}]", + "ec2df690ff96e10a.png": "{(f^{\\theta})}^{v}", + "ec35e3d60d1f68b7.png": "\\omega_{z}=\\frac{\\partial v_{y}}{\\partial x}-\\frac{\\partial v_{x}}{\\partial y}", + "ec38466293afbf9d.png": "\\sum_{q=0}^{N-1}\\zeta^{mq}", + "ec3cda7763e55c65.png": "g(x)=\\prod_{i}h(x_{i})", + "ec3dcceb30542352.png": "\\sqrt{\\pi}", + "ec3f81c53666e0c9.png": "\\tilde{A}_{3}", + "ec406ca52a7a0327.png": "H_{3}^{*}\\longrightarrow H+H_{2}", + "ec419e768e0c9f16.png": "s=\\int\\frac{dt}{r(t)}", + "ec43eed8afea4ac2.png": "\\prod_{i\\in I}X_{i}", + "ec4469562b5ea882.png": "P(T|F)=\\frac{P(T)}{P(F)}", + "ec46dbcdbc6e4091.png": "\\frac{dy}{dx}-y=x", + "ec5057b4b27dbef0.png": "\\Psi=(a\\Psi_{A}+b\\Psi_{B})", + "ec526a0af68af0dd.png": "\\langle N_{i}|i<\\omega\\rangle", + "ec5599349985280b.png": "\\frac{\\partial u_{i}}{\\partial x_{i}}=0", + "ec5f1f7f869bfaf0.png": "E=\\sqrt{\\sum P(n-X)^{2}}", + "ec5f4fc29b87a1d2.png": "\\tilde{O}(log^{3}n))", + "ec69e3d53a718336.png": "\\frac{d}{2}", + "ec7096d347a5e51b.png": "\\sqrt{\\frac{p}{\\rho}}", + "ec7280b8ae1244ae.png": "x\\notin C", + "ec72d9b8f5902db1.png": "q_{n+1}=p_{1}q_{n}+p_{n}q_{1}", + "ec772dcefbcc53bc.png": "\\tilde{A}_{3}", + "ec7a19f76bdf4279.png": "a_{n}\\notin O(2-\\epsilon)^{n}", + "ec7a815ca5917f74.png": "(\\begin{matrix}x\\\\ y\\\\ 1\\end{matrix})", + "ec7c24983f9c35a9.png": "\\langle f_{n},g\\rangle\\rightarrow\\langle0,g\\rangle=0", + "ec7f0d4fa49e7511.png": "r\\ge1+\\frac{2}{\\sqrt{3}}", + "ec84386ca5276544.png": "lnn\\#=n+o(n^{\\alpha})", + "ec86f65f157cbc02.png": "\\gamma=(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "ec8ba6b7766f4835.png": "k[\\overline{X}]", + "ec8d5abd6f87b96f.png": "\\overline{A}D", + "ec8f36a33e7b038f.png": "AI=I_{w}-I_{o}", + "ec9165348146564e.png": "g^{(c_{h})}", + "ec94b167aaf3b3e3.png": "\\tilde{\\phi}\\circ\\omega_{U}=\\omega_{V}\\circ\\phi", + "ec95c6d370d2d3a8.png": "[\\begin{matrix}2&2&4\\\\ 3&5\\end{matrix}]", + "ec976e6be505b3e2.png": "J_{l}^{\\delta}", + "ec9ab584e73a7092.png": "v=\\frac{dr}{dt}", + "eca190faa6b3a4ce.png": "E=\\int vidt", + "ecadf8dc80b54c78.png": "\\tilde{H_{i}}=\\varphi(H_{i})", + "ecb496a1cb52d660.png": "1^{\\prime}s", + "ecb5cf31b914345d.png": "\\Delta_{0}logf=-Kf^{2}", + "ecb7ca733b9c0a86.png": "(\\begin{matrix}1&1\\\\ -a&-c\\end{matrix})", + "ecbbb3d827eeefa3.png": "[\\begin{matrix}1&-sL\\\\ 0&1\\end{matrix}]", + "ecbe16e4900b7220.png": "R:=[\\begin{matrix}T&0\\\\ M&U\\\\ \\end{matrix}]", + "ecbe780d93afbf0e.png": "\\sum_{i}^{N}\\tau_{i}^{int}=0", + "ecc71033dea1f137.png": "N=1+\\prod_{p\\in S}p", + "ecc8dc3cc52a6f3e.png": "\\hat{h}_{k}", + "eccb534ba7817a93.png": "n_{x}\\times n_{y}\\le N^{0.6}", + "eccd8d9ae727b51d.png": "90=2\\times3^{2}\\times5^{1}", + "eccf28e0e9b2ba5b.png": "m=\\lceil n/2\\rceil-1", + "ecd42b897400070f.png": "(\\begin{matrix}6\\\\ 2\\end{matrix})=15", + "ecd4c3a65a8277cd.png": "(\\begin{matrix}a\\\\ b\\end{matrix})", + "ecd50fc6a0599d1b.png": "\\mu(\\pi)=\\frac{(dim\\pi)^{2}}{|G|}", + "ecd6c46ab716b7d2.png": "a=\\tilde{x}\\iff f(a)=f(\\tilde{x})", + "ecda03e4243b677e.png": "N=[\\begin{matrix}A&B\\\\ 0&C\\end{matrix}]", + "ece07137b9571d98.png": "\\overline{B}", + "eceedd127a98d348.png": "(\\eta K)_{X}=\\eta_{K(X)}", + "ecf127fb5bedf844.png": "A=\\int_{S}\\omega", + "ecf83ea5a903fc57.png": "\\frac{n}{2\\pi}sin\\frac{2\\pi}{n}", + "ecf8d52a8d4586d2.png": "(\\begin{matrix}6\\\\ 3\\end{matrix})", + "ecfa96fd6bbbbe35.png": "(-\\infty,-1/e]", + "ecfcc9d84c0dffd1.png": "\\overline{B}(x_{1},r_{1})\\subset W\\cap U_{1}", + "ed0209bfbe276356.png": "\\xi\\notin\\Omega", + "ed0c4204d5284043.png": "H=(\\begin{matrix}0&-i\\\\ i&0\\end{matrix})", + "ed0ef50f723bc306.png": "w_{-}=\\frac{c}{n}-v", + "ed14d451aced2f0e.png": "(\\begin{matrix}n\\\\ 0\\end{matrix})", + "ed29388a542882a7.png": "(\\begin{matrix}6\\\\ 4\\end{matrix})", + "ed2d06259e9cde21.png": "\\overline{X}", + "ed376477b39b1ed1.png": "y_{1i}-y_{0i}=\\beta_{i}", + "ed3d294c45d4ee09.png": "\\int dy=y", + "ed406b5575a590ec.png": "\\int zp(z|x)dz=x", + "ed43c7809c2ccef1.png": "BC\\overline{D}", + "ed44c943c3c9302d.png": "(I+2^{-n}M)^{2^{n}}", + "ed4b4e4096035563.png": "(\\frac{1}{6})^{i}(\\frac{5}{6})^{n-i}(\\begin{matrix}n\\\\ i\\end{matrix})", + "ed4b7cdd2553036e.png": "\\hat{H}=\\hat{H}(\\hat{P})", + "ed4bf89f7883f60f.png": "\\sqrt{\\pi}=\\pm\\sqrt{\\pi}", + "ed5130edca5eb082.png": "-\\sqrt{\\frac{1}{14}}", + "ed56fff2e3f8e673.png": "\\{A_{1},A_{2},\\cdot\\cdot\\cdot,A_{n}\\}", + "ed593b43ff3f7672.png": "B^{\\mu},W_{j}^{\\mu}", + "ed6130846fe39ce6.png": "b=\\partial v/\\partial x=-\\partial u/\\partial y", + "ed623613755a102e.png": "[\\begin{matrix}2&2&4\\\\ 3&5\\\\ 6\\end{matrix}]", + "ed6bea39892e3245.png": "\\hat{f}(x)", + "ed6e21ef61148d70.png": "|z|^{n}<\\epsilon", + "ed6eebb1023c0bb9.png": "g(x)=c+\\sum_{j\\in Q}x^{j}", + "ed732f083208877f.png": "E[\\epsilon|X]=0", + "ed784668bc873a19.png": "[\\begin{matrix}.7&0\\\\ .3&1\\end{matrix}]", + "ed7abbc91cc0cdf5.png": "g_{j}=1\\pm\\frac{g_{S}-1}{2l+1}", + "ed81725a6889d0af.png": "1+rx\\ge(1+x)^{r}", + "ed828b0f945c6940.png": "x^{p/q}=\\sqrt[q]{x^{p}}", + "ed8753afe547b86e.png": "\\tilde{h_{1}}\\leftarrow u_{1}^{z_{1}}remP", + "ed89f1a6e14d8da8.png": "\\frac{d}{da}", + "ed8cdb58812437e3.png": "\\tilde{z}", + "ed8d66be1eef625d.png": "{(\\begin{matrix}41\\end{matrix})}^{3}", + "ed96a8469e9c4753.png": "\\Delta(n)=O(\\frac{1}{n^{2}})", + "eda1c74d1c194254.png": "\\langle3,1+\\sqrt{-5}\\rangle", + "eda32b0644932cd2.png": "\\bigcup_{\\alpha\\in A}\\Sigma_{\\alpha}\\subset P", + "eda49b4d4743fc38.png": "\\sum_{n=1}^{\\infty}ln(a_{n})", + "eda9b36917563391.png": "(Ind(\\sigma),\\hat{V})", + "edab97249f68255f.png": "\\tilde{g}(a)", + "edb117db221c45b0.png": "\\frac{1}{N}\\frac{dN}{dt}=\\frac{ln(\\frac{1}{2})}{T_{1/2}}", + "edb14cd19a4ca411.png": "\\alpha_{z}(a):=f(z)", + "edb64420daf7c55c.png": "s,e,e_{v}\\in Z_{q}", + "edbb4a9d485500da.png": "E=\\gamma_{(u)}m_{0}c^{2}", + "edbbf099b8e2c20b.png": "\\underline{\\varphi(\\beta/\\alpha)}", + "edbc8948b0ef6932.png": "{(x_{n})}_{n\\in N}", + "edc89ba229c506ee.png": "(R_{3}-C_{0})^{2}=D_{0}", + "edc968f2b648c853.png": "x(\\underline{n})", + "edd1597a24c7d3c7.png": "Q=4\\pi sin(\\theta)/\\lambda", + "edd6f9dcd776ef6d.png": "E[X]=\\overline{X}", + "edd9c28059aa199b.png": "s\\{\\begin{matrix}6\\\\ 3\\end{matrix}\\}", + "eddeb81231d910c4.png": "A=\\frac{M}{\\rho}\\frac{n^{2}-1}{n^{2}+2}", + "eddfefc8f59e9b9a.png": "\\sum_{d|k}p_{n,d}=q_{n,k}", + "ede44b2a51925891.png": "\\Omega_{t}=R^{n}", + "ede55079d49db10b.png": "\\Delta V_{tc}=[\\frac{\\eta\\cdot I_{t}}{\\rho}]^{2/3}", + "edea646b197febe3.png": "(P_{j}(G))_{j\\ge0}", + "edf0606e6e17c97b.png": "\\hat{AB}", + "edfca8810293f0ad.png": "\\rho_{true}=\\frac{\\rho_{obs}}{C^{1/2}}", + "ee01627811b18815.png": "V_{R}=IR=C\\frac{dV_{C}}{dt}R", + "ee024bc16d11a75f.png": "\\prod_{i=1}^{n}X_{i}", + "ee02ea656f024961.png": "\\frac{4}{1326}\\approx0.00302", + "ee037bcdc82cfa31.png": "\\sum_{i=0}^{n}p_{i}(z)f^{(i)}(z)=0", + "ee0418543039f4a8.png": "\\alpha=\\gamma^{2}\\frac{v^{2}}{r}", + "ee0a68064ee6d304.png": "p=\\gamma(u)m_{0}u", + "ee0bc79ad00dc763.png": "\\zeta_{L}(s)\\}", + "ee0c538c5e46e02d.png": "\\phi_{e}\\notin F", + "ee0d5eb2a0dbf5f3.png": "E(m)\\in\\{0,1\\}^{n}", + "ee1647fdfdda9a6f.png": "R^{n}=\\cup_{i}P_{i}", + "ee239816242a31d5.png": "\\sum_{j=0}^{n}(\\begin{matrix}n\\\\ j\\end{matrix})(-1)^{j}(n-j)^{k}", + "ee2568258aee1e98.png": "B_{\\tilde{\\nu}}", + "ee2823cb9d7a9fe3.png": "A_{I}(\\vec{x})\\in R^{3}", + "ee2866a714b56135.png": "[\\begin{matrix}0&j^{T}\\\\ j&Q\\end{matrix}]", + "ee2aa782396a7600.png": "\\Delta t\\le2\\omega_{pe}^{-1}", + "ee2d9e15bd900135.png": "\\int e^{-x}cos(x)dx", + "ee2de9cb3c30f0d9.png": "X:(\\Omega,F,P)", + "ee2ebaa84298d6d0.png": "\\tilde{G}_{ij}=k(\\tilde{s}_{i},\\tilde{s}_{j+1})", + "ee2f41e0cfab79f8.png": "f_{0}(x)+u(4x)/4", + "ee386dc0d42f6199.png": "r\\{\\begin{matrix}p\\\\ q\\end{matrix}\\}", + "ee3f16c3b0a13eff.png": "z_{1}=f_{c}(z_{0})=c", + "ee4b0944fd253cdd.png": "\\mu-s\\le x\\le\\mu+s", + "ee4d86b56e60b523.png": "\\pi_{0},\\pi_{1}...\\pi_{K(x)}", + "ee5433039a44076c.png": "\\int_{0}^{x}f(x)dx", + "ee56685ea258cee4.png": "j_{s}=-\\frac{n_{s}e_{s}^{2}}{mc}A", + "ee5c24acf859e889.png": "f(\\langle x_{0},1\\rangle)", + "ee5ec9559ec27e80.png": "K_{1}^{a_{1}}...K_{n}^{a_{n}}", + "ee64d6af6439767a.png": "A,B=1,2,3", + "ee686ec54f962769.png": "\\int_{\\mathbb{R}}f(x-y)g(y)dy", + "ee6f25e20b056e7d.png": "L_{D}[\\rho_{S}(t)]=0", + "ee72f0979ae0039e.png": "F(h)=-\\frac{dU}{dh}", + "ee7332f0abc2a39d.png": "\\sum F=\\Delta m\\times\\frac{dy}{dt}", + "ee73cbd738d19694.png": "\\sqrt{B}", + "ee746e942bda8dd3.png": "\\sigma_{b}=P\\cdot\\hat{n}_{out}", + "ee7c42a5aa6808b8.png": "\\lambda_{1}\\ge\\frac{n}{n-1}\\kappa", + "ee7c8b8b433b00d7.png": "\\bigcup_{f\\in F}f(U)", + "ee807527d57c1e22.png": "Nu_{a}=\\frac{h_{a}D}{k}", + "ee82676289a8c1ea.png": "I(\\theta)=p_{i}(\\theta)q_{i}(\\theta)", + "ee83f1aff7ba9b20.png": "Base_{Sub}^{Super}", + "ee85047718693402.png": "q_{c,t_{n}}=q_{c}=q_{c,t_{0}}\\forall c", + "ee86477d7fa0849c.png": "\\tilde{u}\\in L^{2}(\\mathbb{R}^{n})", + "ee867e443214175c.png": "F_{X,Y}(x,y)", + "ee86d444641c9b2c.png": "P=\\frac{m_{7}v}{\\sqrt{8\\cdot\\frac{v^{2}}{x^{2}}}}", + "ee8e7cdd561cdbad.png": "Ix+=-Ix-", + "ee930ccbb9c5ded9.png": "(\\sqrt{\\frac{2}{5}},\\pm\\sqrt{6},0,\\pm2)", + "ee934a988085d1c4.png": "GH^{\\top}=P-P=0", + "ee95f4bdac728f2d.png": "<0.2W/cm^{2}", + "ee996d4ef850f90e.png": "qU=\\frac{1}{2}m(\\frac{d}{t})^{2}", + "ee9a041e62bfa32d.png": "0<4-2\\alpha-\\beta", + "eea12e448aebba94.png": "(X_{1}+\\cdot\\cdot\\cdot+X_{n})/\\sqrt{n}", + "eea657b21be77f63.png": "I_{B}=I_{C},I_{A}=0", + "eeababff4d15f454.png": "\\sqrt{dt}", + "eeb20d510b3b39ef.png": "[\\begin{matrix}Z&Q\\\\ 0&Q\\end{matrix}]", + "eebeabdaf81139b5.png": "Res(f^{\\prime}/f)=m", + "eebef09fbd91b272.png": "A[x]A[y]", + "eeccc2c59262e788.png": "\\overline{M}=\\frac{1}{I}\\sum_{i=1}^{I}E[n_{i}]", + "eed1a3ef109fadbe.png": "\\hat{K}_{G}", + "eedb60d48bade89c.png": "X\\equiv x_{\\overline{t}}^{q}mod\\psi_{l}(x)", + "eede5179b9d2cdaa.png": "(\\begin{matrix}1&0\\\\ 0&1\\end{matrix})", + "eee80f0371fe30e1.png": "e_{2}=(\\begin{matrix}0&-1\\\\ 1&0\\end{matrix})", + "eeec0df011cef968.png": "\\int u(x,t)d\\mu", + "eeefdc948f4a8d8f.png": "\\sqrt[n]{\\prod_{i=1}^{n}r_{i}}", + "eef15061969213da.png": "M=[\\begin{matrix}a&b-a\\\\ 0&b\\end{matrix}]", + "eef393d4cd8cb64b.png": "sys^{2}\\le\\frac{\\pi}{2}\\cdot area", + "eefe012095ba3fa5.png": "\\hat{e}=y-X\\hat{\\beta}", + "ef07d80ba6cd7270.png": "C_{v}=\\frac{\\hbar\\alpha\\omega}{16\\pi\\epsilon_{0}}", + "ef08fd54310cd823.png": "\\lambda_{j}-\\alpha\\mu_{j}", + "ef096b16e08ddc90.png": "max|x_{i}-m|", + "ef0c54a540e51a6a.png": "n=\\prod_{i=1}^{r}p_{i}^{a_{i}}", + "ef0de98cb5278751.png": "[\\begin{matrix}1&2&1234&4\\\\ \\end{matrix}]", + "ef110c5dd5d221f8.png": "GF(q)^{n}", + "ef183e4438a76bf6.png": "I", + "ef1ef085e1207146.png": "[\\begin{matrix}1&0\\\\ G&1\\end{matrix}]", + "ef20667c9bd7abaf.png": "\\epsilon(\\begin{matrix}n\\\\ 2\\end{matrix})", + "ef24d0f31d0692c9.png": "(8d)^{d}\\cdot15^{d\\cdot2^{2d+1}}", + "ef251a544bbdded0.png": "Set_{=\\emptyset}\\times Set_{=\\emptyset}", + "ef2f394e1dcd3bf8.png": "I^{m}M/I^{m+1}M", + "ef3390981bc99a85.png": "\\sqrt{2t}", + "ef366ea970c3ed49.png": "T_{n}=\\frac{a+1}{D^{2}-\\frac{b-1}{n}}", + "ef39650a8dd5f822.png": "f:\\{0,1\\}^{*}\\rightarrow Z_{n}", + "ef396980daada1ec.png": "\\frac{16}{5}\\times2=\\frac{32}{5}", + "ef3c25648b2a383b.png": "\\delta\\int2T(t)dt=0", + "ef439d8b7b2566ed.png": "[\\hat{q},\\hat{p}]=i\\hbar", + "ef50fd516e223c62.png": "((a),[c])\\notin I", + "ef536f067808eb14.png": "\\int fg=f(x)\\int g", + "ef5527927bb5b265.png": "(\\begin{matrix}7\\\\ 3\\end{matrix})=35", + "ef55767caadb00fa.png": "|x|\\le1,|y|\\le1", + "ef57b9f8bbef0ab6.png": "(\\begin{matrix}11\\\\ 4\\end{matrix})", + "ef591eefbcf58381.png": "\\gamma_{0}(q)=-\\psi(q)", + "ef5a86bce4a6a8d5.png": "{(\\omega^{\\zeta})}^{8}", + "ef5c6638e29adf94.png": "a^{2}=z(e^{z}-1)", + "ef7262ec282e8de9.png": "2^{n}(an+1)", + "ef72fabf1d3b85b2.png": "\\frac{dL}{dt}", + "ef758bb1081f14f0.png": "M=(Q,\\Gamma,\\delta,q_{0},g)", + "ef7a3d8545b2cfce.png": "\\sqrt{(}t)", + "ef847efe42c5cccf.png": "[\\begin{matrix}p&2\\\\ 2&q\\end{matrix}]", + "ef86de256ae0e9d4.png": "\\sqrt{-}4(3-\\sqrt{-}9)", + "ef86e882a36899c2.png": "j_{(z_{v})}", + "ef87e260356e9d8b.png": "lim\\int_{0}^{1}f_{n}=0", + "ef8ad3f8429a8afd.png": "\\int_{a}^{b}...", + "ef8f3d2d3f2fc6de.png": "RR_{ij}=\\frac{C_{ij}N}{P_{i}P_{j}}", + "ef984a3e414df320.png": "cp(z)=z^{n}\\overline{p(\\overline{z}^{-1})}", + "ef9a572f418c4c17.png": "\\sigma=\\sigma_{H_{2}O}\\times\\frac{m}{m_{H_{2}O}}", + "efa84a80261f93d8.png": "e^{\\gamma}\\cdot log_{|b|}(log_{|b|}(n))", + "efadd67f81b63470.png": "v_{x}=v_{xo}e^{-\\frac{k}{m}t}", + "efb00a984748ad6c.png": "\\int_{0}^{1}f(r)g(r)rdr", + "efbfc0181f4edd0c.png": "E_{\\beta\\gamma}={D^{\\alpha}}_{\\beta}F_{\\alpha\\gamma}", + "efbfcb41456bb17e.png": "\\mu(\\pi)=\\frac{(dim\\pi)^{2}}{|G|}", + "efc4de561320fb06.png": "Spec(\\oplus_{0}^{\\infty}I^{n}/I^{n+1})", + "efc5e44a52df57d6.png": "\\varphi_{i}(x)=(x,i)", + "efc8d621dc484bab.png": "\\int Ldt", + "efcda6d966896934.png": "h=(\\begin{matrix}1&1\\\\ 0&1\\end{matrix})", + "efd0f42a44673441.png": "(DR)^{2}\\le T\\le NR", + "efd194260b6fa65f.png": "\\frac{\\partial E}{\\partial w_{ji}}", + "efd92268b84dc5f0.png": "\\hat{\\alpha}>0", + "efdec4233449285a.png": "\\frac{\\partial^{2}z}{\\partial x^{2}}", + "efe04c1e54e410aa.png": "x", + "efe3075c48ef38c4.png": "\\alpha_{f}<<\\theta^{\\prime}", + "efe651ff0a0a820a.png": "\\hat{A}_{i}", + "eff0519907cf7887.png": "z^{3}-z^{2}-z-1=0", + "eff0dbe107254b71.png": "(\\begin{matrix}n+2\\\\ 2\\end{matrix})", + "eff590f527b5ed39.png": "\\hat{F}", + "effa6f6fa7bbe7ee.png": "(d,u,e,\\nu)_{L,R}^{i}", + "effd2a4e4bd759e6.png": "qU=\\frac{1}{2}m(\\frac{d}{t})^{2}", + "efff9e04598db560.png": "44+4\\sqrt{3}+4\\sqrt{6}", + "f00ba7ddbf731f61.png": "\\int xcos(y)dy", + "f0114e334b86f0d2.png": "s\\{\\begin{matrix}8\\\\ 4\\end{matrix}\\}", + "f012e26fe87df1d9.png": "(\\begin{matrix}4\\\\ 2\\end{matrix})", + "f015a55c37977977.png": "\\hat{1}", + "f01d15b42575a22b.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=0", + "f01ecddeb97c7d8c.png": "y^{\\prime\\prime}=f(t,y)", + "f021e7774acd344e.png": "MG", + "f02367597b8921d6.png": "\\sqrt{10}(4\\rho^{4}-3\\rho^{2})cos2\\theta", + "f026e7be13b63e44.png": "x=y\\pm\\sqrt{27-2y^{2}}", + "f02752c2486c213f.png": "\\psi_{BL,m}(t)", + "f02972467b485de0.png": "\\tilde{d}=1", + "f02b38a9d6f927f6.png": "x^{d}-1=\\prod_{m|d}\\Phi_{m}(x)", + "f044e30fbcaed4aa.png": "(\\begin{matrix}x&y\\\\ 0&z\\end{matrix})", + "f0460a50c30535e3.png": "\\hat{x}_{2}", + "f0468796e5c50ca6.png": "L=n_{l}-n_{\\overline{l}}", + "f04a953c756e3578.png": "y=0.5/\\sqrt{x}", + "f04cf00301313078.png": "\\hat{e}(s_{0})", + "f05034d881de80e2.png": "MPL=\\frac{\\partial F}{\\partial L}", + "f0506216a78a0a08.png": "\\tilde{\\nu}=0", + "f05480d93590e5de.png": "\\alpha\\le\\zeta_{1}=\\phi_{2}(1)", + "f05ee4eb3b019101.png": "i(E_{jk}-E_{kj})", + "f06092412576f834.png": "\\kappa(X,K_{X})=-1", + "f069bbb14186725d.png": "j=1,2,\\cdot\\cdot\\cdot,k-1", + "f06dc1cccb493eb7.png": "A=4\\pi r^{2}=\\pi d^{2}", + "f06f097d00558d82.png": "<10^{-6}", + "f06fcb4a7b8f753f.png": "V=|a\\cdot(b\\times c)|", + "f073d3bf602e4aa0.png": "|0|<|1|+|-2|", + "f07541e185c6ec4f.png": "(\\frac{a}{p_{1}})", + "f07976bbb2de4acc.png": "x=1+(-1)", + "f07d71b22b64d73b.png": "\\int sin(cos(x))dx", + "f07fe07ff214c89f.png": "ij=-ji=k", + "f080478e02490f0d.png": "Y=P_{x}\\cdot x+P_{y}\\cdot y", + "f082a11284801cfe.png": "\\sqrt{-3}", + "f08358ed31421424.png": "\\tilde{O_{P}}/O_{P}", + "f0877502fb8f0d68.png": "Q(\\frac{1}{T_{2}}-\\frac{1}{T_{1}})", + "f090758e37999a56.png": "M_{ij}=\\int v_{i}v_{j}dx", + "f091ea8c28bc9f0f.png": "\\tilde{w}=f(\\tilde{X},\\tilde{Y})", + "f095769b1c7e5ef4.png": "(\\begin{matrix}X\\\\ k\\end{matrix})", + "f09766a6ec2dd566.png": "\\frac{d}{dx}(x!)", + "f0a1e2f5b7b32a16.png": "G(r)\\sim exp(-r/\\xi)", + "f0a89f9f3b5891bf.png": "f(x)=\\int_{a}^{x}g(t)dt", + "f0a937bc1df32b9a.png": "Z:=(\\begin{matrix}x&dy\\\\ y&x\\end{matrix})", + "f0ab358c91571431.png": "S=\\int ds", + "f0af56bd3f2b5cef.png": "\\int_{0}^{\\infty}f_{a}dx", + "f0b0a0df2e79f2e3.png": "\\overline{X}_{n}=\\frac{1}{n}\\sum_{k=1}^{n}X_{k}", + "f0bf5cac3b04ca49.png": "\\int_{c}^{d}f(x)dx", + "f0c3d9574de52dae.png": "f^{*}\\omega_{N}|_{V}=\\omega_{M}|_{U}", + "f0d13ed8cfe56eb6.png": "2=\\{0,1\\}", + "f0d3c42ded154df4.png": "tr\\{\\begin{matrix}4\\\\ 3\\end{matrix}\\}", + "f0da2b23db3e2f43.png": "\\Pi_{i}=\\cup_{o\\in S_{i}}H_{o}", + "f0dce2c480d25955.png": "\\int dm=M", + "f0dd855c99e6fc5f.png": "A=(\\begin{matrix}0&1\\\\ -1&0\\end{matrix})", + "f0e94a00e38afb4c.png": "N_{\\alpha}^{l}", + "f0ec536428995672.png": "p_{(t_{1})}", + "f0ec5a7a0230371a.png": "\\tau_{\\alpha}^{p}", + "f0efb43e26ce1532.png": "t\\{\\begin{matrix}3\\\\ 3\\end{matrix}\\}", + "f0f0367abc836625.png": "-\\nabla^{2}u=f", + "f0f3d128d1aa303a.png": "E(\\overline{K})", + "f0f43f581bef28b2.png": "[\\begin{matrix}1&4&4\\\\ 3&5\\\\ 4&7\\\\ 6\\end{matrix}]", + "f0f79d168af3f596.png": "(\\begin{matrix}-1\\\\ 0\\end{matrix})", + "f0f98561f47bab0c.png": "D(f)=[\\begin{matrix}0\\\\ 0\\end{matrix}]", + "f0f9fb8f1372e3f6.png": "F_{21}RF^{-1}", + "f1041388d440cff8.png": "V_{w1}+U", + "f11e48b970e20418.png": "\\langle\\psi_{m}(t^{\\prime})|\\psi_{m}(t^{\\prime})\\rangle=1", + "f1266815dc4092ae.png": "\\int_{0}^{t}Z_{s}ds", + "f12748607c5fb6b4.png": "u_{i}^{\\prime}=1-u_{i}", + "f12d942cee4ec3e8.png": "x(v)+x(v^{\\prime})", + "f12e377413364011.png": "H=\\int\\rho hdV", + "f1354ccc976853ce.png": "\\frac{\\partial I}{\\partial x}", + "f1355576878628f9.png": "b=[\\begin{matrix}0\\\\ 1\\\\ 0\\\\ -1\\end{matrix}]", + "f1367a14203c2a92.png": "\\int vds", + "f137e8b19b095be3.png": "\\frac{dy}{dx}=-\\frac{1}{1+x^{2}}", + "f1492547ae84401d.png": "x", + "f1576435e7bb395c.png": "X=[x_{0}y_{0}V_{x}V_{y}]", + "f1580bfb655f7d89.png": "y\\notin FV(N)", + "f15aa1833a75fa0d.png": "m_{H}=\\sigma_{0}\\sqrt{2\\lambda}", + "f15e913c1980a0d8.png": "STA=\\frac{1}{n_{sp}}X^{T}y", + "f15e9dd656ed2134.png": "\\omega(\\delta,f^{(r)})", + "f15f96969ac11b4c.png": "F=\\frac{B^{2}S}{2\\mu_{0}}", + "f1630a260eb1a9dd.png": "\\epsilon^{T}\\Lambda^{T}\\epsilon=\\epsilon^{T}\\Lambda\\epsilon", + "f166dd5697c77d5d.png": "f(0,\\overline{u})=g(\\overline{u})", + "f169af424708adaa.png": "(-e^{\\frac{i\\pi}{N}})^{k}\\cdot W_{0}(k)", + "f17026a17cd015e3.png": "\\frac{\\partial V}{\\partial R}", + "f1739d0b60a7a2fb.png": "1/\\sqrt{1-(v/c)^{2}}", + "f175e6c12282ab33.png": "\\{\\sqrt{\\pi},2\\pi+1\\}", + "f17d4c915cf1b42d.png": "\\hat{O}", + "f189c3011d496ba3.png": "\\frac{df}{du}", + "f19384ca87d0c668.png": "R_{e}\\propto\\langle I\\rangle_{e}^{-0.83\\pm0.08}", + "f19c610fa7d83564.png": "|G(\\chi)|=\\sqrt{N}", + "f19deb0e0430c9e8.png": "z\\in-M_{j}M_{k}", + "f1a661f66a1f5478.png": "\\frac{\\partial^{2}T}{\\partial t^{2}}=\\frac{\\partial T}{\\partial x}", + "f1b03e84373df606.png": "\\tau=\\mu\\frac{du}{dx}", + "f1b6c44da10f8eaa.png": "g(x)\\int f(x)dx", + "f1d4eba1ced2de88.png": "V(P,e(P,u))=u", + "f1d636f3b140249c.png": "\\frac{1}{\\tau_{B}}=\\frac{V}{D}(1-p)", + "f1dcae8e6f084e1a.png": "x^{2}+q=px", + "f1de6cddfac3ad26.png": "\\underline{P}(Cl_{t}^{\\le})", + "f1e0dfc7b01b8985.png": "\\hat{T}_{\\pm2}^{(2)}=\\hat{a}_{\\pm1}\\hat{b}_{\\pm1}", + "f1e4f2a60de1c8cb.png": "(\\begin{matrix}u&&-v\\\\ v&&u\\end{matrix})", + "f1f07ef843a4affd.png": "\\int_{\\Omega}u_{j}u_{k}=0", + "f1f7f71210ffa8f4.png": "I\\models(a,b):R", + "f1f90824944c45b7.png": "\\frac{d^{2}w}{dz^{2}}=f(z)w", + "f1fe603b42c5c1bd.png": "\\alpha\\le\\zeta_{1}=\\phi_{2}(1)", + "f2076af6e0788a28.png": "\\mathbb{Z}", + "f214e3908e3f966f.png": "\\frac{1}{\\sqrt{d}_{u}}", + "f21909c3dbcfeb7b.png": "\\alpha s_{x}+\\beta s_{y}+\\gamma=0", + "f21a1a56fe05e8f7.png": "2x^{2}+y^{2}+8z^{2}=n", + "f21a5a7a60e6739c.png": "4\\times(\\begin{matrix}5\\\\ 2\\end{matrix})", + "f2201804a05cafb8.png": "C_{L}=C_{o}(f_{L})^{k-1}", + "f222303747d3302f.png": "\\sum|f(b_{k}^{\\prime})-f(a_{k}^{\\prime})|<\\epsilon", + "f22eacb71537e328.png": "H^{rot}=\\frac{1}{2}I\\omega^{2}=\\frac{L^{2}}{2I}", + "f233827015c3b8f1.png": "\\hat{S_{z}}", + "f23bf9b702ce69d6.png": "\\hat{e}_{z}", + "f23c6e0610941d13.png": "k=\\prod_{i=1}^{m}q_{i}^{n_{i}}", + "f23d82584752b976.png": "||x||_{\\infty}=max_{1\\le i\\le n}|x_{i}|", + "f23f183530492023.png": "Q=\\frac{X_{L}}{R}=\\frac{\\omega L}{R}", + "f2453e43dcb44b06.png": "[\\begin{matrix}1&sL\\\\ 0&1\\end{matrix}]", + "f24900090b4d07d7.png": "(b-1)u+Nv=1", + "f249b2c51b4c9058.png": "\\int_{0}^{T}PdX=nh", + "f24d6e2004fa104b.png": "\\overline{W}_{t}", + "f24fe31531af7c41.png": "D:\\phi\\mapsto\\frac{1}{i}\\phi^{\\prime}", + "f252e71254457413.png": "\\frac{d\\kappa}{dt}=\\frac{d^{2}\\theta}{dt^{2}}=2", + "f252fc08c80e4c0e.png": "M^{(\\chi_{\\nu})}", + "f2533eeae3fcc392.png": "e_{\\delta}^{\\alpha}", + "f253e2be0c5e2c98.png": "P_{e}^{(n)}\\rightarrow0", + "f25411b3a8bce816.png": "T=\\frac{\\pi}{\\sqrt{I}}", + "f258d3ceda5e95a5.png": "[\\overline{x}-\\frac{cs}{\\sqrt{n}},\\overline{x}+\\frac{cs}{\\sqrt{n}}]", + "f2645e95bcb7e28e.png": "\\hat{p}=0", + "f26c43c7a2df0af0.png": "z^{\\frac{1}{2}}=\\sqrt{z}", + "f26d8e787353ea0e.png": "|\\frac{big}{kets}\\rangle", + "f26ed39412ecef60.png": "-U(\\delta)", + "f26f63ffd125ff90.png": "y", + "f275944ac8fc1c27.png": "P(y|do(x))", + "f2792bf74dd05e2b.png": "1-e^{-e^{2.6-0.00024K}}", + "f27bdca33a0e9e4c.png": "\\hat{K}_{G}", + "f27f69712d1fbae9.png": "e^{+}e^{-}\\rightarrow\\gamma\\gamma\\gamma\\gamma", + "f282010810c53d46.png": "x=y=\\frac{i}{\\sqrt{2}}", + "f2832cd2140b9993.png": "\\Omega^{(d+2)}=d\\Omega^{(d+1)}", + "f2847a4d7df05422.png": "x=\\hat{X}", + "f285161f034700d3.png": "\\int_{0}^{1}f(x)dx", + "f285cae21211d6c9.png": "\\frac{\\partial f}{\\partial\\overline{z}}", + "f28af33c3571c8f8.png": "f(t,n)=\\sum_{i=0}^{n}(\\begin{matrix}t\\\\ i\\end{matrix})", + "f28b282e9609d1c2.png": "\\frac{dF}{dx}+2xF=1", + "f28e32886064b447.png": "PV=\\frac{1-e^{(-rt)}}{r}", + "f28f11e8cfdee4c2.png": "[\\overline{1}1\\overline{2}]", + "f2972913ce0ab8c9.png": "\\frac{\\partial u_{i}}{\\partial x_{i}}=0", + "f2a26d9cd56cb487.png": "a(mod\\Phi_{n}(q))", + "f2a57a05dbdeb151.png": "I(X_{1};X_{2})", + "f2a8f74187e72ce2.png": "[\\hbar]=M^{1}L^{2}T^{-1}", + "f2af397cd7951c04.png": "v\\notin N(T\\backslash S)", + "f2b179166d691ea5.png": "x_{0}0", + "f3e29dc84266e06e.png": "|Q_{0}|=|Q_{L}|=\\frac{P}{2}", + "f3e44145435eaa30.png": "\\{|A\\rangle,|B\\rangle,|C\\rangle\\}", + "f3f205896cd56f58.png": "K_{i}(\\tilde{M})", + "f3f2b95a3c47c8ed.png": "g(x)", + "f3f5ca3dabd29f8f.png": "\\tilde{w}", + "f3fd01eafcd8861c.png": "E[R]=\\sum_{i=1}^{n}R_{i}P_{i}", + "f400410c45a2ae7a.png": "|0\\rangle\\equiv|\\cdot\\cdot\\cdot,0_{\\alpha},\\cdot\\cdot\\cdot\\rangle", + "f403298e95e8c3df.png": "\\frac{|E(H)|}{|V(H)|-1}", + "f403483f8c37ff72.png": "\\hat{w}_{i}", + "f406a8a227c84f0a.png": "(c:a:a)\\cdot m:4_{2}\\cdot\\tilde{c}", + "f408fd0311d3c17a.png": "\\hat{D}(\\alpha)", + "f40bfad23351c407.png": "V=(\\begin{matrix}1&-1\\\\ 0&1\\end{matrix})", + "f41038558aea6a03.png": "\\overline{D}", + "f412ac38023ddb22.png": "\\sum k^{3}=(\\sum k)^{2}", + "f417bf5a9efd99c0.png": "\\partial C/\\partial Y_{d}=b", + "f41e242b1a5d9341.png": "\\frac{5\\sqrt{3\\pi}}{16}", + "f424f47d9d2f0f10.png": "x(\\underline{n})", + "f42a685c32c5d944.png": "\\langle f,\\varphi\\rangle=\\langle T_{f},\\varphi\\rangle", + "f42c079c0e588f14.png": "u=\\int u^{\\prime}dx", + "f42d2198563cd022.png": "\\nabla T_{m}=\\frac{\\Delta T_{m}}{\\Delta x_{stack}}", + "f42ef2e543ed4d87.png": "\\int d^{4}p/(2\\pi)^{4}", + "f43028a4a317e668.png": "A_{\\mu}\\rightarrow A_{\\mu}+\\partial_{\\mu}\\phi(x)", + "f431621e9d6dbcdf.png": "|A|=\\sqrt{A^{*}A}", + "f43478c3b7470f14.png": "E\\cap\\overline{E}=\\Delta\\otimes C", + "f4411cd8d9aba333.png": "\\{\\lambda_{n}(A)\\}_{n=1}^{N}", + "f4472b4fbec3f562.png": "\\frac{\\partial x}{\\partial\\theta}", + "f448778233dd94d0.png": "y=\\sqrt{1-\\frac{x^{2}}{4}}", + "f448f74cb5584578.png": "\\hat{a}_{i}", + "f44ab946ece5a8d7.png": "\\int_{a}^{b}f(k)dk", + "f4503fad9678c32d.png": "\\beta_{n}+n=-a", + "f45834462651c9a8.png": "=\\frac{T(t)\\times T^{\\prime}(t)}{2}", + "f45be6c955821a60.png": "(1-2t(n-1))", + "f45c7542c92f134e.png": "\\hat{t}<0", + "f45f769aa95f716e.png": "d=e^{-\\sigma\\sqrt{t}}=\\frac{1}{u}", + "f4630c34e693a02a.png": "d(v)d_{1}^{i}+\\cdot\\cdot\\cdot+d_{m}^{i}", + "f576061e7af47db0.png": "k=\\Omega(\\sqrt{nlogn})", + "f57b143d11c7a2dd.png": "(F^{+})_{+}", + "f58b3c2b21422b32.png": "AdS_{d+1}", + "f58ca712bae61b70.png": "(\\begin{matrix}p_{n-1}&p_{n}\\\\ q_{n-1}&q_{n}\\end{matrix})", + "f59299697fd15d95.png": "Z", + "f59ce7cf88e97fe0.png": "\\int Fdl", + "f59d6531e91160f0.png": "(\\begin{matrix}4\\\\ 3\\end{matrix})=4", + "f59e03543c974bbd.png": "\\tilde{m}", + "f5a561e5a7ea0320.png": "\\int\\sqrt{1+1/x}dx", + "f5a83c234c215d74.png": "\\gamma[t]\\in T(\\sigma[t])", + "f5ab20bf0a41187c.png": "F_{(\\lambda_{p})}", + "f5b26a1d19dd7fcc.png": "EL(\\Gamma)=w/h", + "f5b5a4fcff23a5bb.png": "S", + "f5b7528158cc53f0.png": "=k\\int_{R}^{\\infty}\\rho dr", + "f5bc68c63bf5c747.png": "\\tilde{c}_{i}\\equiv t_{i}modv^{-1}F^{-}", + "f5bd41aa882a967c.png": "Q_{r}=\\frac{\\prod(a_{j})^{\\nu_{j}}}{\\prod(a_{i})^{\\nu_{i}}}", + "f5bdde80ee7f375d.png": "F(r)=-\\frac{k}{r^{3}}", + "f5be40685f5410fa.png": "[\\begin{matrix}\\eta_{1}+1\\\\ \\eta_{2}+1\\end{matrix}]", + "f5c055b48507162d.png": "\\underline{x}^{k}", + "f5cad1f32e5c2b8c.png": "f(-x)=\\hat{\\hat{f}}(x)", + "f5df1670d0d04989.png": "\\frac{a_{1}}{1-\\lambda_{1}t}+\\frac{a_{2}}{1-\\lambda_{2}t}", + "f5e263ed6bf1ad2b.png": "u^{\\mu}=dx^{\\mu}/ds", + "f5e3d8d442814aa8.png": "J=(\\begin{matrix}0&I\\\\ -I&0\\end{matrix})", + "f5eee0c045c7155d.png": "P_{A}V=n_{A}RT", + "f5f7c29ef58595c3.png": "\\frac{\\partial\\sigma}{\\partial x}+f=0", + "f5f8c31832b1014c.png": "\\overline{q}_{tt}^{i}=0", + "f5fa387732259779.png": "\\gamma_{0}=[\\begin{matrix}0&1\\\\ 1&0\\end{matrix}]", + "f5fe3e88738b4399.png": "Z=tr\\{\\prod_{k=1}^{N}W_{k}\\}", + "f603e9506b2a8002.png": "\\int HdX", + "f60848eaffbcf835.png": "4^{n}/2n", + "f60935ae4d5a3eef.png": "(a,\\infty)=\\{x|x>a\\}", + "f612f3dbb169de69.png": "{(1+{(\\frac{x}{b})}^{-a})}^{-p}", + "f61635b20eccf589.png": "(\\begin{matrix}p&q\\\\ q&p\\end{matrix})", + "f61fa906c90bbcbc.png": "E_{k-1}e^{X_{k}}=Ee^{X_{k}}", + "f6355f07a6bd0ae4.png": "\\hat{C}", + "f6390573f1932e9d.png": "\\sum_{j=0}^{d-1}(\\begin{matrix}n\\\\ j\\end{matrix})(q-1)^{j}", + "f63aa793e8594d3f.png": "a=\\sqrt{n^{2}-m^{2}}", + "f63f2e028a7d8465.png": "\\int f\\ne1", + "f63fa687a8b4cc6a.png": "\\tilde{A}_{6}", + "f6410a1a8239645a.png": "I_{B}=I_{C},I_{A}=0", + "f6491210484bac7e.png": "|nm_{n}\\rangle", + "f6495e4bf06d9b02.png": "O(log|B|)", + "f64997c6c6abdaca.png": "G\\cong Z[b_{1},b_{2},...]", + "f64ab44814cbfc4e.png": "\\dot{\\partial}_{\\mu}=\\partial_{\\mu}", + "f652615d1912fea6.png": "\\tau=\\sqrt{t^{2}-x^{2}}", + "f652e93b175af6b4.png": "\\int f(x,y)dx", + "f659c6f50c9b9fcf.png": "m\\in F_{q}^{k}\\\\ \\{0\\}", + "f664831a4026a76d.png": "(\\begin{matrix}n\\\\ m\\end{matrix})", + "f6656518a7ca1b1e.png": "(\\begin{matrix}n-1\\\\ r-1\\end{matrix})", + "f6668fbd366c1984.png": "\\chi^{2}=\\sum\\frac{(O-E)^{2}}{E}", + "f67974f2b5260b3f.png": "\\overline{4}3m", + "f679e03d348f4cb8.png": "G=\\int_{0}^{T}k(t)x(t)dt", + "f67a618ec8f808ff.png": "\\prod_{i=a}^{b}f(1)", + "f67be959eda78302.png": "\\sqrt{\\lambda}", + "f67f05feb5aa64cc.png": "R(x)=2x^{2}+x-1", + "f681ebf0515e7802.png": "0.841T_{eff}", + "f68507e469e3cea8.png": "(\\begin{matrix}n\\\\ r\\end{matrix})", + "f6883050d51244ee.png": "\\overline{X^{i}}", + "f68acb90d566aa1f.png": "C_{X\\tilde{Y}}", + "f68c3b9431be005e.png": "\\sqrt{1}", + "f696e62611866116.png": "W_{i}^{*}=\\frac{Rgq_{bi}}{F_{i}u*^{3}}", + "f6990715678f0e7f.png": "y_{1i}-y_{0i}=\\beta_{i}", + "f69a362ea6f375d8.png": "(\\begin{matrix}1&0\\\\ 0&0\\end{matrix})", + "f69bd2accb02b806.png": "15*(\\begin{matrix}66\\\\ 8\\end{matrix})", + "f6a572915eed695a.png": "s=\\int ds", + "f6a9a14436a3b13e.png": "z_{1}=-1+i", + "f6a9b7794ec6a239.png": "\\tilde{x}\\sim F(\\tilde{x}|\\theta)", + "f6aa2e5db62cc7ef.png": "\\frac{\\partial}{\\partial c}P_{c}^{n}(c)", + "f6b1f39298c2222e.png": "u:\\underline{A}", + "f6b8fa2e68ce9f7a.png": "(\\begin{matrix}1&1\\\\ 1&0\\end{matrix})^{m}", + "f6b99a3bfb36eecf.png": "0.05H_{s}", + "f6b9b2dcde1c4c11.png": "a(x)=\\int f(x)dx", + "f6bb1a949a2e6d33.png": "[\\begin{matrix}1&sL\\\\ 0&1\\end{matrix}]", + "f6c507f37def1119.png": "\\tilde{p}_{P}", + "f6c8c417e8f2623c.png": "E=\\sqrt{\\sum P(n-X)^{2}}", + "f6c99b5be85c75f4.png": "\\hat{r}_{j}", + "f6cdd69b292107c3.png": "\\sqrt{17}", + "f6cf552412a2a846.png": "u_{xt}-(uu_{x})_{x}=u_{yy}", + "f6d6b479164c625e.png": "\\hat{V}_{s}", + "f6da25c1941340b7.png": "E_{p,m}=\\frac{1}{2}LI^{2}", + "f6e165b0f6ea4963.png": "v(t)=\\underline{e}(\\begin{matrix}v_{0}\\\\ -gt\\end{matrix})", + "f6e1845fce607f3c.png": "c_{g}=\\frac{1}{2}\\sqrt{\\frac{g}{k}}=\\frac{1}{2}c", + "f6f4b7c6f4d1acbc.png": "lim_{t\\rightarrow0}\\frac{\\Delta_{t\\Delta x}^{n}f}{t^{n}}", + "f6f4c50508c7f553.png": "\\Delta V_{tc}=[\\frac{\\eta\\cdot I_{t}}{\\rho}]^{2/3}", + "f6f91c16a9b23d3b.png": "\\tilde{g}_{33}", + "f6fd6cf6dbe78e99.png": "\\prod_{k=1}^{n}k^{k}", + "f701d336e5b0fcb6.png": "\\frac{n^{2}-3n+4}{2}", + "f7070d67feed8be7.png": "\\int_{E}\\varphi=\\infty", + "f70e12c15bf44329.png": "x_{i}|x_{1}\\cdot\\cdot\\cdot x_{i-1}x_{i+1}\\cdot\\cdot\\cdot x_{n}+1", + "f710463f1195b4aa.png": "\\langle\\phi|=\\langle\\psi|A^{\\dagger}", + "f7160e63a9f749af.png": "[-,BU]", + "f71691310d8a84d1.png": "a=tan(2/50)\\times g", + "f71ab19523af7438.png": "||Df^{-n}v||\\le c\\lambda^{n}||v||", + "f71f8cf4d6e14543.png": "a\\notin A", + "f73333cef40fec72.png": "H=\\frac{21}{4}-7", + "f7357d0691a65364.png": "(x^{l})^{m}\\equiv1(modn)", + "f739b8c9d8ec1f3c.png": "\\frac{\\partial Y}{\\partial r}", + "f7452491f515486f.png": "\\Gamma_{00}^{i}=U_{,i}", + "f74b0316cdc47a95.png": "Z=\\frac{X-E(X)}{Var(X)^{1/2}}", + "f74b89caa1d1d535.png": "\\langle X\\rangle=Tr(\\hat{X}\\rho)", + "f74e916d1aeef782.png": "(L_{f}|_{[m],S}", + "f751f6420cca51f0.png": "G(x)=F(a+bx)", + "f75465a36291888a.png": "S\\equiv\\frac{\\overline{D}}{\\sigma_{D}}", + "f755aedafbfd2abd.png": "0/0=0", + "f758d652a019b400.png": "(+\\alpha,-\\alpha)", + "f75ba8fe84964038.png": "A\\cdot B=A_{\\mu}\\eta^{\\mu\\nu}B_{\\nu}", + "f75f63d03a06d866.png": "||f||_{1}=\\int|f|d\\mu", + "f76ab1d343fdb126.png": "[\\hat{H},\\hat{L}_{z}]=0", + "f76b63124c20f1bd.png": "\\frac{\\partial L}{\\partial t}=0", + "f76d6e1bbf7fd647.png": "I^{I}=\\prod_{i\\in I}I_{i}", + "f76ed40279bbc5b7.png": "(A-\\tilde{\\lambda}_{*}I)", + "f76f5c97bb2937fa.png": "c=1/\\sqrt{\\mu_{0}\\epsilon_{0}}", + "f77287dad40b3e6d.png": "W=\\int_{a}^{b}PdV", + "f772ee3e35690c1f.png": "\\sqrt{19}", + "f7752781d9e155a1.png": "-\\frac{d^{2}}{dx^{2}}", + "f7772bb9ec9b75ed.png": "\\frac{\\partial(\\varphi f)}{\\partial x}+\\frac{\\partial(\\varphi g)}{\\partial y}", + "f777a4cd74a47691.png": "S=\\int_{0}^{T}E[s(t)^{2}]dt", + "f77954479044b596.png": "(\\begin{matrix}0&1\\\\ -1&0\\\\ \\end{matrix})", + "f77ae04f21a646e7.png": "T_{r}H=HT_{r}\\forall r", + "f77c933b121be4bf.png": "\\langle X\\rangle=Tr(\\hat{X}\\rho)", + "f77d1dcab64f6137.png": "y^{\\prime}(t)=\\alpha+\\frac{vy(t)}{c+vt}", + "f78f9474fb1db7ce.png": "S_{\\gamma\\delta}^{\\alpha}=S_{(\\gamma\\delta)}^{\\alpha}", + "f78fae6d9d4a1b4e.png": "p_{c}=\\frac{a}{27{b^{\\prime}}^{2}}", + "f7930b534029979b.png": "T^{*}T-TT^{*}", + "f7947990762929f6.png": "F_{y}=-T\\frac{y}{L}-Mg", + "f795555bd8735af8.png": "x=g^{-1}(y)=\\sqrt{y}", + "f79668f1a66c4b4f.png": "\\tilde{r}_{E}", + "f7988803993dfc28.png": "2.405\\sqrt{\\frac{g+2}{g}}", + "f7a357e83fd48d2f.png": "L=(\\begin{matrix}\\chi\\\\ \\chi^{\\prime}\\end{matrix})", + "f7a96f8261effbcb.png": "V=\\frac{16\\pi h-\\pi h^{3}}{3}", + "f7affb0738561861.png": "r^{-l_{1}}+r^{-l_{2}}", + "f7b7ad58ef29c4b6.png": "|x-\\sum_{n=0}^{N}x_{n}|\\rightarrow0", + "f7cedc08f77efce0.png": "\\overline{126}_{H}", + "f7d04919dd829702.png": "f^{\\prime}(x)=-2xe^{-x^{2}}", + "f7d410d7c835ba71.png": "\\frac{dE_{2}}{dE_{1}}=-1", + "f7d8ae13e11c66dd.png": "H=m-am^{(b-1)}", + "f7dc253729c96e66.png": "\\tilde{\\chi}(t)=\\tilde{\\rho}(t)R_{0}", + "f7edfa86c61d085d.png": "p_{\\lambda}^{\\epsilon}", + "f7eeec48470e6f90.png": "F=\\pi_{*}O_{\\tilde{X}}/O_{X}", + "f7efaf772ebb0e5a.png": "(\\begin{matrix}1&1\\\\ 0&1\\end{matrix})", + "f7f53a2f6ba63a63.png": "\\frac{a}{2}+\\frac{a}{6}(\\sqrt{2}-1)", + "f7f863a798efc152.png": "j(G(j\\omega)-G(j\\omega)^{*})", + "f7fd016d491e39b0.png": "\\hat{K}(n)", + "f8045e6a2278f2b4.png": "(\\begin{matrix}1&1\\\\ 1&-\\end{matrix})", + "f80d4209a68f8902.png": "(\\int f)^{3}", + "f80f2d387936e77f.png": "\\langle\\psi_{m}(t^{\\prime})|\\psi_{m}(t^{\\prime})\\rangle=1", + "f8121220a2c877da.png": "2K_{||}+K_{\\perp}", + "f81215d56b877495.png": "\\int y(t)dt", + "f814c5bb2b47f35a.png": "g(x)=\\int_{0}^{x}f(t)dt", + "f817e2a458955027.png": "p\\notin(0,1)", + "f818e15611eea61a.png": "\\neg(", + "f82885bb2ba69efb.png": "\\hat{C}_{1}", + "f82b043f3ffccaf9.png": "\\varphi_{cb}(a)=a^{b-c}", + "f82d4a247b7e2387.png": "f(u)=\\beta_{1}+\\beta_{2}e^{-u}", + "f8394fca28f64ba1.png": "\\pi_{n}=p_{1}(\\pi_{n-1})", + "f83d31f27a6ff392.png": "(\\begin{matrix}2n\\\\ n\\end{matrix})", + "f83d474c5a6138b3.png": "\\tilde{P}(X_{1},...,X_{n-1})", + "f83dc3019406a6da.png": "dx=\\frac{-2u}{(u^{2}-1)^{2}}du", + "f84d71ae904940d2.png": "I_{x}=I_{y}=\\pi r^{3}t", + "f84dacba2a6fd309.png": "\\tilde{\\epsilon}_{ij}", + "f84f73616c09b1f4.png": "\\int(\\int f(r)dv)dr", + "f85006da0d790e48.png": "v=(n_{1},n_{2}\\cdot\\cdot\\cdot n_{m})", + "f852e20b72665a98.png": "P(e^{\\prime})=\\{a_{1},b_{4}\\}", + "f8537dba676971ef.png": "\\frac{dV}{dr}", + "f856fe9b0abae2f2.png": "\\dot{w}=\\frac{\\partial w}{\\partial x}", + "f8592be040e85cd0.png": "\\overline{h_{i}}=h_{i}^{*}", + "f85aa6b849634408.png": "(\\pm\\frac{(\\varphi+1)}{2},\\pm\\frac{1}{2},0)", + "f85d948e70bab4e3.png": "\\tilde{c}(\\Pi)", + "f8657d810f831bbd.png": "A(0,u_{k},v_{k})", + "f86a6eafd659e82e.png": "\\psi(\\Omega^{\\Omega^{2}+\\Omega2+\\psi(0)})", + "f86c7fe700d1f6de.png": "l_{(l_{\\psi})}", + "f870f5b627e53349.png": "G(\\xi_{n}^{(N,j)})", + "f872881d47b687b4.png": "\\int p(x)f(x)dx=-H", + "f879347c5805ca2f.png": "S^{DIFF}(S^{n})=\\Theta^{n}", + "f87be793e7764c35.png": "\\tilde{c}(\\Pi)", + "f87de7742b76e5fe.png": "e_{a}:=e(f_{a}):=e_{a}^{\\mu}\\partial_{\\mu}", + "f8814da1e69cb27c.png": "A\\cup B\\in\\bigcap F", + "f88a56ec8faf2e3f.png": "\\int_{C}=0", + "f895d2965948178b.png": "(\\begin{matrix}1&1\\\\ 1&0\\end{matrix})^{m}", + "f897fa5804e0208a.png": "\\int xrdx=\\frac{r^{3}}{3}", + "f89cac39d7406b3f.png": "\\tilde{S}_{i}", + "f8a3391cebc47d7c.png": "\\tilde{X}", + "f8a3e64488e95d92.png": "Z=tr\\{\\prod_{k=1}^{N}W_{k}\\}", + "f8a678a845c8d894.png": "=\\sqrt{7}", + "f8b169096200c886.png": "\\frac{db}{dt}=\\frac{1}{3}", + "f8b3f5fce4422ce9.png": "\\tilde{G}", + "f8b5d36d9d54d0d0.png": "B(r)=-c^{2}", + "f8c48e877fc3e58b.png": "\\alpha^{\\prime}f=0\\cdot f=0", + "f8c4a27a6ae383d7.png": "\\hat{A}", + "f8c56318d8560e52.png": "x/3=x/4+x/12", + "f8c8b5ad79efc77a.png": "\\epsilon_{\\circ}=8.85\\times10^{-12}F/m", + "f8ca0659d168b5c6.png": "\\langle\\langle-1,...,-1\\rangle\\rangle", + "f8cad403b41254b7.png": "0.3<\\frac{M_{1}}{M_{2}}<20", + "f8d18c86934edc04.png": "log_{2}(26^{n^{2}})", + "f8d4062218ba979c.png": "F=G\\frac{Mm}{r^{2}}", + "f8e0611b6d83c2c1.png": "C_{\\beta}(s)=[\\begin{matrix}1&0\\\\ s&1\\end{matrix}]", + "f8e4741db73c2586.png": "\\tilde{\\delta}_{i}", + "f8ef8d83504008b8.png": "x\\mapsto\\prod_{i=1}^{n}w_{x}(i)", + "f8f6bcb6671d9c83.png": "\\sum_{j=0}^{n}(\\begin{matrix}n\\\\ j\\end{matrix})(-1)^{j}(n-j)^{k}", + "f8f7a84582d15af9.png": "\\frac{\\epsilon_{x}}{\\beta_{x}}+\\frac{\\epsilon_{y}}{\\beta_{y}}+\\eta_{s}\\frac{\\epsilon_{z}}{\\beta_{z}}", + "f8fc8578656dc854.png": "\\frac{\\partial f}{\\partial\\overline{z}}=0", + "f8fe8cb9b5c9a1ee.png": "\\vec{v}=k(\\phi/s)\\hat{\\phi}", + "f906dbada030f5dc.png": "f(t)=L^{-1}\\{F(s)\\}", + "f90e13b9060fd773.png": "AB", + "f92aaf9053b2b4ff.png": "\\overline{F}(x)=o(1/x)", + "f92bb5db89a62d03.png": "R/Z\\cong S^{1}", + "f92d25f7bbae7b0f.png": "\\overline{B}(x_{1},r_{1})\\subset W\\cap U_{1}", + "f92e56b915615fdc.png": "S^{n}\\subset R^{n+1}", + "f9334de0d102067b.png": "var(T)=\\frac{2n(\\sigma^{2})^{2}}{(n+2)^{2}}", + "f93b7b7cdbc7687f.png": "\\mu_{4}=(k)(k+2)", + "f9420246bb88c746.png": "\\psi", + "f94ba676d56575da.png": "\\frac{\\partial\\theta_{e}}{\\partial z}>0", + "f950bcbdb6fac455.png": "\\tilde{V}", + "f950f52c075f7dc7.png": "\\delta[\\rho-\\hat{\\rho}]", + "f95131f656097e1d.png": "\\int_{0}^{L}F(x)dx", + "f95b0545b6520d87.png": "\\overline{n}_{8}", + "f96003bc107fd301.png": "(\\begin{matrix}n+r-1\\\\ r\\end{matrix})", + "f960883acb4ab116.png": "\\sigma(\\tilde{\\nu})", + "f96332e4c0e95881.png": "(x_{0}+1,y_{0})", + "f965581ee29ff09c.png": "[\\hat{Y},\\hat{I}_{\\pm}]=0", + "f96a035fee2114d0.png": "\\Pi_{\\omega}^{\\delta}", + "f96a52e02de6b8d8.png": "\\int_{0}^{\\infty}x^{-x}dx", + "f96d25dabd2d63b2.png": "\\phi(\\tilde{\\nu}-\\tilde{\\nu}_{0})", + "f9735cc0226b936d.png": "L_{3}+-4L_{2}\\rightarrow L_{3}", + "f97f79221b444478.png": "(\\begin{matrix}m\\\\ 3\\end{matrix})", + "f98128ced0c058d3.png": "K=\\frac{V}{A_{p}L}", + "f983b34e9592e74d.png": "f=\\sqrt{h^{2}+(a+b)^{2}}", + "f983e08c68400800.png": "L=10\\cdot0.5=5", + "f98af37b864f23f5.png": "\\tilde{A}_{7}", + "f98ea68e9d89e4d0.png": "\\epsilon_{\\circ}=8.85\\times10^{-12}F/m", + "f991750ec5ab9059.png": "\\lambda_{n}=(\\begin{matrix}n\\\\ 2\\end{matrix})\\frac{1}{N}", + "f991fbbefb88fd76.png": "(-1,0,0)", + "f996b9020096c98f.png": "\\int\\sqrt{x^{2}+a^{2}}dx", + "f99b6975f781782b.png": "(\\begin{matrix}1&1\\\\ 1&-\\end{matrix})", + "f99e01df1ee2abe1.png": "g(\\tilde{x})", + "f99f01c7aa345e05.png": "\\overline{P}(Cl_{2}^{\\le})=Cl_{2}^{\\le}", + "f9a44faecdff360d.png": "\\int_{0}^{1}g_{n}=1", + "f9a9028cbf89e123.png": "P^{(\\phi_{\\sigma})}", + "f9aa09d962d4b161.png": "\\frac{d^{k}f}{dx^{k}}(x)=0", + "f9acbc2ea4068369.png": "a\\sqrt{D}", + "f9b53924e619375e.png": "2+\\sqrt{2}+\\sqrt{6}", + "f9bc2814b267a965.png": "\\int_{A}f=\\int_{[-a,a]^{n}}\\tilde{f}", + "f9bc618d434c60da.png": "q=(\\begin{matrix}a&b\\\\ c&d\\end{matrix})", + "f9bdb3f58f44640c.png": "[\\frac{n}{m},\\frac{k}{m},\\frac{d}{m}]_{q^{m}}", + "f9be0fc81393634d.png": "s_{a}^{*}(t)\\cdot e^{j2\\pi f_{0}t}", + "f9bfaa6481341b5d.png": "\\sqrt{a\\pm b\\sqrt{c}}=\\sqrt{d}\\pm\\sqrt{e}", + "f9c0b9be427c9828.png": "\\sqrt{2}r", + "f9c4762045d4fa4c.png": "S_{k}(x-1)", + "f9c821ccee566544.png": "\\langle g_{1},g_{2},...,\\rangle", + "f9c99fd65a8b2dad.png": "\\hat{s}", + "f9ccab93721abc60.png": "\\int_{a}^{b}f(x)d_{h}x", + "f9d33655e05455ba.png": "S=F(\\mu)+L(\\mu)", + "f9e2502fdc45b443.png": "T^{t}=e^{t\\frac{d}{dx}}", + "f9e2ee6039d21575.png": "\\sqrt{\\nu}", + "f9e3e7dd52966777.png": "(\\begin{matrix}p\\\\ i\\end{matrix})", + "f9e3ff572c3de304.png": "\\sqrt[12]{2}:1", + "f9e5718397fdfbde.png": "(\\begin{matrix}n\\\\ k\\end{matrix})", + "f9e6073a8e64ec0d.png": "\\int\\frac{dC}{1-C^{2}}", + "f9f9fbd662aed3a0.png": "=arctan\\frac{5}{12}", + "f9fa5240357fc045.png": "\\dot{v}_{2}=\\frac{1}{C}\\frac{v_{1}-v_{2}}{R}", + "f9fe1dc1c3257ae5.png": "\\frac{d\\Phi_{B}}{dt}=-EMF", + "f9ff65bd69ff1009.png": "(\\tilde{\\rho},\\tilde{V})", + "fa03ea1ee99aeefd.png": "\\sqrt{\\pi}", + "fa0a0fde411c97ec.png": "A(i)>A(j)", + "fa0f519def25a140.png": "B\\backslash A=\\{x\\in B|x\\notin A\\}", + "fa10954966d9b295.png": "W_{s}=\\int_{1}^{2}\\sigma_{s}dA", + "fa160bdeab47c5f3.png": "lim_{h\\rightarrow0}\\frac{h}{h}=1", + "fa18c7285beb2cb8.png": "rect(\\frac{t-u}{\\Delta_{t}})", + "fa19a66cda0e277b.png": "(CH_{2}(COOH)_{2})", + "fa1ae048bc7a91ce.png": "y", + "fa1c8af7f394ccb2.png": "T_{2}=T_{1}e^{\\mu_{s}\\beta}", + "fa1de2d9de0b2b36.png": "\\hat{A}(t)", + "fa24311321d96d51.png": "\\tilde{t}", + "fa25f835343c3717.png": "e^{\\frac{-1}{x^{2}}}", + "fa26310bef7d4a6f.png": "angle(x_{1}):=\\theta", + "fa2a47421a27a5e2.png": "\\forall i:V_{i}(P_{i})\\ge w_{i}", + "fa2b0e06a78486be.png": "\\overline{AB}\\cong\\overline{DE}", + "fa2ea4176db42b31.png": "\\eta_{Carnot}=1-\\frac{T_{cold}}{T_{hot}}", + "fa494e427888d232.png": "O(log|B|)", + "fa4d1c97077326af.png": "[\\begin{matrix}1&4&4\\\\ 3&5\\\\ 4&7\\\\ 6\\end{matrix}]", + "fa4d742b8ba07e43.png": "1-(1-p)^{k}", + "fa532fddba6467bb.png": "\\int\\frac{1}{x}dx", + "fa5b611a8a937f09.png": "s\\{\\begin{matrix}p\\\\ 2\\end{matrix}\\}", + "fa5b82f5462ce73e.png": "\\hat{f}(3)", + "fa6089b10e5df17c.png": "\\partial_{y}=\\frac{\\partial}{\\partial y}", + "fa611cdf71fcad93.png": "\\hat{6}", + "fa635043f22a116b.png": "p_{1}=p(x_{0}+\\Delta x)", + "fa667aca2152b47f.png": "V_{ind}=-\\frac{d\\phi}{dt}", + "fa706d70282bff74.png": "Y_{0}\\approx1/\\sqrt{S}", + "fa806b860701e429.png": "g(Q-I)=0", + "fa838445d38f7f65.png": "i=-\\frac{dq}{dt}", + "fa8573c29b64f3f9.png": "r^{\\prime2}+(r\\theta^{\\prime})^{2}=1", + "fa85d58296e26b4a.png": "\\{0,1,...,2^{32}-1\\}", + "fa88a5d5cbaabf84.png": "cos(\\omega_{0}n)u[n]", + "fa95f075c013b18e.png": "\\frac{1}{\\sigma_{i}+n\\lambda}\\sim\\frac{1}{\\lambda n}", + "faa19bee7c461b03.png": "f(x):=\\int_{0}^{x}\\omega", + "faaa4686bf51cecf.png": "y(x)=\\int g(x)dx", + "fab3f7013a486f5b.png": "\\delta\\vec{x}(t)\\approx H\\cdot\\delta\\vec{x}_{0}", + "fab76662334c1590.png": "x^{\\prime}=\\sqrt{\\frac{-z}{x}}", + "fabcbfa76a668371.png": "P_{ij}=\\tilde{P}_{ij}logn/n", + "fac22fb7bcc2aae3.png": "[\\begin{matrix}1&0\\\\ -sC&1\\end{matrix}]", + "fac338e902c12544.png": "\\hat{y}_{+}", + "fac473e43eabeb1a.png": "Z=\\sum_{j}g_{j}\\cdot e^{-\\beta E_{j}}", + "fac98fcdb29c7ec0.png": "\\delta[\\rho-\\hat{\\rho}]", + "faca8dd73ee582db.png": "GA", + "facb5a68e6d0ee92.png": "10^{0}a\\}", + "fcff60c033ca5dc8.png": "NSE_{i}=h_{i}^{t}\\times G", + "fd0291100467c83e.png": "(\\begin{matrix}1&0\\\\ 0&1\\end{matrix})", + "fd05dff7331cc370.png": "O_{i}>2\\cdot E_{i}", + "fd062c1c75ed27f0.png": "\\tilde{K}_{\\pm}", + "fd082668e85f1084.png": "\\int f(x,y)dx", + "fd132aefe7c8b1be.png": "(\\mu_{ab}(t))\\in\\Gamma_{S(t)}", + "fd15a1b20ea97253.png": "-tr(\\gamma^{\\sigma}\\gamma^{\\mu}\\gamma^{\\nu}\\gamma^{\\rho})(4)", + "fd1a9285650a5331.png": "PSL_{2}(Z[i])", + "fd264ad1a280ee6c.png": "(x_{0}+1,y_{0})", + "fd2d7cf46646b700.png": "V_{i}^{\\prime}=\\sum_{j=1}^{3}a_{ij}V_{j}", + "fd2f7f622a40c804.png": "B=\\int_{0}^{b}e^{x}dx", + "fd348c143a7f71a1.png": "\\tilde{W}", + "fd3af42ae6bff997.png": "S=\\sum_{k=0}^{\\infty}9*10^{k}", + "fd4323a8e421f8fc.png": "k([\\overline{x}])=i^{r-1}([y])", + "fd4637fd882a2258.png": "\\hat{\\mu}=\\frac{\\sum_{i}x_{i}}{n}", + "fd46d444a7fa6f09.png": "\\tilde{\\phi}(xU)=\\phi(x)", + "fd47764c967931ad.png": "\\gamma_{1}=\\gamma_{2}\\in]0,1[", + "fd49183df5f6350b.png": "2^{k-1}+k", + "fd584711a1ad1c52.png": "cf(\\prod A/D)", + "fd58ea70432bb0d7.png": "\\frac{7}{9}\\le\\frac{A_{1}}{A_{2}}\\le\\frac{9}{7}", + "fd5a0f7b81a48474.png": "\\langle r,a|r^{3},a^{2},arar\\rangle", + "fd5dd04273e58e83.png": "\\gamma=lim_{\\epsilon\\rightarrow0}\\frac{lnf(\\epsilon)}{ln\\epsilon}", + "fd5fa10b703985a9.png": "-1/\\phi", + "fd6183f2c2b48f0a.png": "V_{p\\times p}=[v_{1},...,v_{p}]", + "fd63859dbb4463d1.png": "[\\begin{matrix}x^{\\prime}\\\\ y^{\\prime}\\end{matrix}]", + "fd65daaf6aab6db7.png": "\\tilde{D}_{\\eta}", + "fd6667938960ff38.png": "\\sqrt{n}\\in\\mathbb{Z}", + "fd7fafb93c5f3202.png": "inf_{x>0}logx=-\\infty", + "fd7ffeb7972d262a.png": "L^{-1}=\\int_{0}^{t}()", + "fd83de32f15457b0.png": "f(a)=lim_{n\\rightarrow\\infty}f_{n}(a_{n})", + "fd8f3af429452e9d.png": "-\\sqrt{s}", + "fd91ddfbedde687a.png": "\\alpha_{k}^{2}+\\beta_{k}^{2}>9", + "fd94f00feb5b94c4.png": "\\sum_{k=1}^{i}\\frac{A}{i}k=\\frac{A}{2}(i+1)", + "fd9dc59d96ba9fcc.png": "\\sqrt{a^{2}+b^{2}}=c", + "fda35876e5ee1c7a.png": "\\mathbb{G}", + "fda3b7d708289d22.png": "f_{p}^{D}(x)=(\\frac{1-x}{x})^{p}", + "fda5ce354ef925f3.png": "|\\omega_{i}|=q^{1/2}", + "fdafb634ed5c9dbf.png": "\\sigma_{8}^{w}", + "fdb0994a9ec85536.png": "p=\\prod_{i=1}^{n}p_{i}", + "fdb49e2d5f0b718e.png": "\\frac{-e^{-ikr}}{4\\pi r}", + "fdb6b354c5094bfa.png": "\\sum_{n=0}^{\\infty}x_{1}^{n}x_{2}^{n}", + "fdb83b031670aa9e.png": "\\int_{0}^{x}1dt=x", + "fdbf43936b239461.png": "p(x)=\\prod_{j}(1-xX_{j})", + "fdcc91ab2e656b54.png": "\\int r^{2}dm", + "fdcd6d753a47e572.png": "\\frac{d^{2}u}{dy^{2}}=\\frac{1}{\\mu}\\frac{dp}{dx}", + "fdd4806e3edcf5b3.png": "2cos(\\frac{2\\pi}{7})", + "fdd61f75a72da3d4.png": "2log_{2}n\\ll k\\ll\\sqrt{n}", + "fdd890922195692c.png": "P^{(\\phi_{\\sigma})}", + "fddf3b32dc67ed10.png": "\\hat{S}^{2}", + "fde0e24a73c59f8a.png": "\\{\\begin{matrix}5\\\\ 5/2\\end{matrix}\\}", + "fde185dbe37ac9c6.png": "\\hat{x}_{i}", + "fdee9a64435764b8.png": "\\overline{\\omega}=exp(-i2\\pi/3)", + "fdeed3576f494d9e.png": "lim_{x\\rightarrow0}f^{-1}(x)=-\\infty", + "fdf2342ea0c041da.png": "1-\\frac{2}{4}=0.5=50\\%", + "fdf8d3ce300d0ab1.png": "\\frac{1}{2}", + "fdff1c3738b24087.png": "\\langle\\hat{T}\\rangle", + "fe01977f946bba3e.png": "\\frac{\\partial y}{\\partial x}", + "fe05d42b59327bc4.png": "\\overline{O_{R}P}", + "fe1136a6df8e7318.png": "\\int\\phi dx", + "fe15e9668dc16d01.png": "\\overline{x}", + "fe1c60b459733b80.png": "D=\\prod_{i=1}^{K}d_{i}", + "fe23daa46a9d1dd7.png": "\\tilde{0}", + "fe2556eb55c51862.png": "-N_{c}^{2}-1", + "fe2785f6d66828bd.png": "M_{ij}=\\int v_{i}v_{j}dx", + "fe27a0456da8ee1c.png": "dy/dx=e^{-3x}/y^{3}", + "fe2b5bfefe2f59ad.png": "\\underline{P}X=\\{O_{1},O_{2}\\}\\cup\\{O_{4}\\}", + "fe2c7fa141a2ec06.png": "(=\\hat{\\beta}\\hat{\\alpha})", + "fe32c1e9cc4373e4.png": "\\int(u-v)dx", + "fe340e3380d794ae.png": "-na^{n}u[-n-1]", + "fe3795e2f097e7f8.png": "K_{k}(\\tilde{M})", + "fe3f90731bb990a9.png": "\\sqrt{\\gamma}", + "fe43aa54e725cdd8.png": "E_{W}=\\frac{1}{2}w^{T}w", + "fe4b2b335254c501.png": "E=1-\\frac{T_{Low}}{T_{High}}", + "fe57e0f7052dc3e2.png": "d_{1}=[\\begin{matrix}x&y\\\\ \\end{matrix}]", + "fe581afe47ac794c.png": "\\{\\begin{matrix}3\\\\ 3\\end{matrix}\\}", + "fe5b5dba52e881ac.png": "[\\begin{matrix}1&0\\\\ 0&3\\end{matrix}]", + "fe5cad3d9e8a94a0.png": "I=\\prod_{i=1}^{n}P_{i}^{a_{i}}", + "fe6991426e8a3f53.png": "1\\vee3\\iff|+\\rangle", + "fe6e8c88ea647f41.png": "\\{\\lambda_{n}(A)\\}_{n=1}^{N}", + "fe705dabfacc7ec9.png": "C_{i}=E_{K}(C_{i}^{\\prime})\\oplus2^{i}L", + "fe787bfb568fe1c4.png": "\\sum_{k=1}^{m}f(P_{k})m(C_{k})", + "fe7d567ac33eb28a.png": "\\hbar^{2}l(l+1)/2mr^{2}", + "fe7e1fe93033bdc8.png": "-\\sqrt{5}", + "fe7eece69975cbe1.png": "(\\begin{matrix}n\\\\ k\\end{matrix})=\\prod_{p}p^{b(p,n,k)}", + "fe938af2c772a57a.png": "\\frac{\\partial y}{\\partial t}+A\\frac{\\partial y}{\\partial x}=0", + "fea406a2c88aa7ca.png": "|\\hat{f}|", + "fea77c0816ad00ad.png": "\\sum_{m}|u_{m}|^{2}<\\infty", + "fea83783df5f1fca.png": "\\hat{t}", + "fea89e9072b602b5.png": "-\\triangle_{S}(\\triangle_{S}+2)", + "feaf33366e335e70.png": "\\hat{\\zeta}_{0}(\\omega)", + "feb3d6bd67b32379.png": "H=\\sum_{k}E_{k}a_{k}^{\\dagger}a_{k}", + "feb41bac9c9fcde3.png": "A\\overline{B}", + "feb4ffaeab789dcb.png": "ta_{jj}+(1-t)a_{kk}", + "feb5f45badd329da.png": "B=3(\\int_{0}^{a}e^{x}dx)", + "feb94fe04657c5b3.png": "\\mu(\\varphi^{-1}B)=\\nu(B)", + "feb97fe5ebd63734.png": "\\frac{\\partial\\eta}{\\partial y}>0", + "febc9957b00aef89.png": "O_{X,x}\\otimes\\kappa(f(x))", + "febe4bd94e1ae123.png": "\\frac{d}{2}", + "fec32e3edb5517a2.png": "\\int_{Z}i^{*}\\alpha", + "fec3e6809905efa4.png": "(\\begin{matrix}7\\\\ 3\\end{matrix})=35", + "fec525b55c5c99ec.png": "\\lambda", + "fec6f0c58488e6ee.png": "\\hat{f_{j}}", + "fecacbd04ac860fa.png": "y^{2}=x^{3}-px-q", + "fed50ffd1f8ae39d.png": "cos\\theta_{o}=-\\frac{v}{c}", + "fed667c56bcff5f2.png": "\\tilde{E}=E\\times\\mathbb{Z}_{n}", + "fed885d5270ab858.png": "\\int_{0}^{1}f(x)dx", + "fedbb69279356ade.png": "1-\\sum_{j=1}^{m}P_{ij}", + "fedf8c549f02810a.png": "\\prod_{i=0}^{k-1}(x-i)^{n}", + "fee0d37cf19dc9f9.png": "\\overline{r_{0}}=r\\cdot\\hat{r}", + "fee104ef0f682c46.png": "e^{\\int f(x)dx}", + "fee42c88ef5b3fce.png": "L[y]=\\int_{a}^{t}ydt", + "fee4fe5c9004de09.png": "R_{ij}=|R_{i}-R_{j}|", + "fef285930b19f377.png": "2\\cdot(\\begin{matrix}12\\\\ 4\\end{matrix})=990", + "fef92687f1775dbc.png": "|\\overline{AJ}|=\\frac{2}{\\pi}r", + "fefea4872d14fdd5.png": "(\\begin{matrix}x&y\\\\ -y&x\\end{matrix})", + "ff00434611b63a6b.png": "\\langle\\psi|E_{A}\\psi\\rangle", + "ff02acc68dfe3b17.png": "\\overline{x}(t)", + "ff038390f81f0037.png": "\\int_{X}p(x)dx=1", + "ff054c314c610b40.png": "\\sum_{L}L^{2}4^{-2L}e^{-4\\beta L}", + "ff05bd139cf9ff85.png": "c=r-\\frac{1}{T}ln(\\frac{F}{S})", + "ff0863d529e07ea0.png": "\\overline{f}=\\hat{f}", + "ff1103cbdc515e7e.png": "4-2\\sqrt{3}", + "ff19efcb582a5281.png": "\\int_{\\Omega}u_{j}u_{j}=1", + "ff1a694d815934b3.png": "0^{\\prime\\prime}", + "ff1b3bdb8dda926b.png": "(\\begin{matrix}p\\\\ k\\end{matrix})", + "ff1d6c3bca3b1517.png": "\\epsilon=2\\nu\\langle E_{ij}E_{ij}\\rangle", + "ff1e44e12a8992ea.png": "T(E,eV,r)", + "ff28c54bf32c7369.png": "P_{\\beta}(\\sigma)=\\frac{e^{-\\beta H(\\sigma)}}{Z_{\\beta}}", + "ff2914f63ecff101.png": "F=\\rho^{SV}", + "ff2980e7a65c1b46.png": "d=v_{0}t_{d}cos(\\theta)", + "ff2bc4d00a547239.png": "x_{2}=b+\\sqrt{b^{2}-c}", + "ff2d7685234b6c2d.png": "\\frac{5\\pi}{12}(75^{\\circ})", + "ff2da0a35b3522c2.png": "(\\frac{m^{*}}{n})=(\\frac{n}{|m|})", + "ff3baa5ac9d9921e.png": "PB-C=\\sqrt{\\gamma}Q", + "ff3c5289abc9bdc6.png": "[a^{\\prime},b^{\\prime}]", + "ff42a21b2621c19c.png": "\\int_{A}(g-f)d\\mu=0", + "ff44bf6f1a961efe.png": "F[y]=\\int_{E}ytdt", + "ff452c17ebbf7e06.png": "b_{k}|k>0", + "ff497a786ad8d16b.png": "O((n/\\sqrt{\\epsilon})logn)", + "ff571f7b66d74f51.png": "L=\\epsilon\\dot{M}c^{2}", + "ff5a972110407fb2.png": "m_{B}/m_{A}B", + "ff5e8faada060671.png": "\\frac{n}{2\\pi}sin\\frac{2\\pi}{n}", + "ff5ff025c9148db8.png": "\\hat{f}(n)", + "ff6112b4c936a2d8.png": "(j-1,j,j+1)", + "ff6f758fde6fed27.png": "0", + "ff7079803d2a25d2.png": "(\\begin{matrix}0&-1\\\\ 1&0\\end{matrix})", + "ff75876c9ac8f3b4.png": "\\frac{dC}{dt}", + "ff7606e8c78140ca.png": "-\\sqrt{3}", + "ff81817f534a78b1.png": "b(t)=b1\\times e^{\\frac{-t}{\\tau}}", + "ff8d694a4ce69527.png": "\\dot{Y}=\\alpha(v-s)Y", + "ff8db4b36504dcde.png": "G^{1/2^{m}}", + "ff9027578122fe3a.png": "pd_{R}k=gl.dimR", + "ff9b301d535b8325.png": "t(t+1)(t-1)=0", + "ff9eebb45f414fcd.png": "8\\sqrt{3}", + "ffa032b3fbcff7fa.png": "g(x)=c+\\sum_{j\\in Q}x^{j}", + "ffa078db7d6a4e76.png": "d_{\\hat{K}}", + "ffa52917b9e75a9b.png": "-\\sqrt{\\frac{1}{10}}", + "ffa7ed32aff9f53b.png": "K_{G}(X)^{\\wedge}\\cong K(X_{G})", + "ffaa161d5abe5006.png": "[\\begin{matrix}c&s\\\\ s&c\\end{matrix}]", + "ffb6aab5a77153c7.png": "-\\sqrt{x}", + "ffba18891cc01fcd.png": "R_{t}=a\\phi^{-m}S_{w}^{-n}R_{w}", + "ffba5add450daa5c.png": "Q(x_{1},...,x_{n})>0", + "ffc4c5802f680c07.png": "\\hat{8}", + "ffc62c07ab3096ee.png": "(\\begin{matrix}7\\\\ 2\\end{matrix})=6\\times\\frac{7}{2}=21", + "ffc7df7a286a7f8c.png": "\\frac{a}{a+b}+\\frac{b}{a+b}=1", + "ffc9d37d827a406d.png": "C_{E_{2}}^{J}=-\\epsilon_{1}^{1}\\epsilon_{2}^{3}/D", + "ffcb805407ffd4c5.png": "\\int_{D}f\\Delta g=0", + "ffcb809bfe7c1c00.png": "\\sqrt{2}+1", + "ffd674f7a14df6ec.png": "c=\\sqrt{a^{2}+b^{2}}", + "ffd8b4a1471c8f02.png": "J=[\\begin{matrix}0&I\\\\ -I&0\\end{matrix}]", + "ffdc89c482fbeb22.png": "f^{*}(x)=e^{\\frac{xf^{\\prime}(x)}{f(x)}}", + "ffe2da40ef72af8e.png": "d=\\frac{i}{1+i}\\approx i-i^{2}", + "ffe341c05fa5de66.png": "[\\begin{matrix}1\\\\ 0\\end{matrix}]", + "ffe488ef8dc9bbfd.png": "dh=h_{x}dx+h_{y}dy", + "ffe91c1e27f33aab.png": "\\int y^{2}dv", + "ffec2b5d8b7ee5ef.png": "\\sqrt{17}", + "ffeff0bdcfd6fab1.png": "\\sigma_{j}^{2},j=1,2,...", + "fff178e576aa12aa.png": "E^{*}\\rightarrow\\hat{E}^{-}", + "fffc7b9718ed14e5.png": "\\pi_{0},\\pi_{1}...\\pi_{K(x)}" +} \ No newline at end of file diff --git a/valid/valid_images/00000b332dcd6fe5.png b/valid/valid_images/00000b332dcd6fe5.png new file mode 100644 index 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