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long Tail Keywords (2 words) rank correlation correlation coefficient sidebar hide kendall rank point pairs |
long Tail Keywords (3 words) kendall rank correlation rank correlation coefficient move to sidebar accounting for ties zundark talk contribs section about handling 25 june 2024 |
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wikipedia free encyclopedia displaystyle tau rho binom xnyn xiyi xjyj xixj yiyj frac textnumber concordant pairstextnumber discordant pairs pairsn choose over sum ijoperatorname sgnxixjoperatorname sgnyiyj textstyle mathbb cdots beginalignedetau eleftleft ilinn right ielifrac ijelilj leftsum ijelieljsum ivliright ijelieljfrac ivlirightleft ielinn ivlirightendaligned etau elifrac eli nto infty zafrac asqrt vartau ancnd sqrt rsin leftfrac aright adelta xdelta ydelta delta ijxixjyiyj ncsum leq ijleq ijin afrac enc nprdelta prdelta beginbmatrixxyendbmatrixbeginbmatrix endbmatrix beginbmatrixzwendbmatrix beginbmatrix beginbmatrixz endbmatrixin beginbmatrixfrac rfrac rendbmatrixa theta arctan sin arightsin xiyixjyj ncndn bfrac ncndsqrt beginalignedn ititi jujuj nctextnumber pairsndtextnumber pairstitextnumber tied values itextthtext group ties first quantityujtextnumber jtextthtext second quantityendaligned cfrac mtau nfrac beginalignednctextnumber pairsrtextnumber rowsctextnumber columnsmminrcendaligned zancnd zbncnd beginarraycclvfrac vtvu vtsum vusum endarray ncnd oncdot log onlog ymathrm left sysymathrm symathrm mymathrm mcdot cdot icon wikimedia foundation powered mediawiki
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https://wikimedia.org/api/rest_v1/media/math/render/svg/24ec973d9d76826ce30b51f8ef4f420c5d1ab900 height: height attribute not set width: width attribute not set description: {\textstyle x,y} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b22205dc81df5e6d1b049d10f1fcc74b43d4719c height: height attribute not set width: width attribute not set description: {\displaystyle r=\sin {\left({\frac {\pi }{2}}e[\tau _{a}]\right)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/28cd39e5390bdb423eeeea7b448d2aa3ac721896 height: height attribute not set width: width attribute not set description: {\textstyle a^{+}:=\{(\delta x,\delta y):\delta x\delta y>0\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/301c478b69aaa5cc70e7860ec6f45285e5014ba8 height: height attribute not set width: width attribute not set description: {\textstyle \delta _{i,j}:=(x_{i}-x_{j},y_{i}-y_{j})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8f9dcb350bb8fb6a28ddc4aebfb5c4b03ce8784f height: height attribute not set width: width attribute not set description: {\textstyle \mathbb {r} ^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/11e933a1407459ffdf310977cab9bdd487b0fbb3 height: height attribute not set width: width attribute not set description: {\textstyle n_{c}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/05f5936f99567019f2664f6e37ea3e591e2089aa height: height attribute not set width: width attribute not set description: {\textstyle \delta _{i,j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7599cf40276a4004f7c02f67d19cafd53d065377 height: height attribute not set width: width attribute not set description: {\textstyle a^{+}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4244b436450c0f82f516b19d556160efcd0bb0ca height: height attribute not set width: width attribute not set description: {\textstyle n_{c}=\sum _{1\leq i |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a8f52cfbf13424564280394156ed2d0843278489 height: height attribute not set width: width attribute not set description: {\displaystyle e[\tau _{a}]={\frac {4}{n(n-1)}}e[n_{c}]-1={\frac {4}{n(n-1)}}\sum _{1\leq i |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/47f05bc790250ac866dc5baad18f801bb6463269 height: height attribute not set width: width attribute not set description: {\textstyle (x_{i},y_{i})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b3a9e1af6f92055bae1c9dfe6a67ba2387a8147c height: height attribute not set width: width attribute not set description: {\displaystyle e[\tau _{a}]=2pr(\delta _{1,2}\in a^{+})-1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5560ac89ce7bf0852b516dc542b7c34873b0d055 height: height attribute not set width: width attribute not set description: {\textstyle \tau _{a}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0e1eb0a056c17b19c82d8f6af7be841fff70c53e height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{bmatrix}x\\y\end{bmatrix}}={\begin{bmatrix}1&r\\r&1\end{bmatrix}}^{1/2}{\begin{bmatrix}z\\w\end{bmatrix}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e58095a4ba3d8e38614954c35b53691855778423 height: height attribute not set width: width attribute not set description: {\textstyle (z,w)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8ba5fba4401807f728f465bad533de4631c6c4e height: height attribute not set width: width attribute not set description: {\displaystyle \delta _{1,2}={\sqrt {2}}{\begin{bmatrix}1&r\\r&1\end{bmatrix}}^{1/2}{\begin{bmatrix}(z_{1}-z_{2})/{\sqrt {2}}\\(w_{1}-w_{2})/{\sqrt {2}}\end{bmatrix}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c5e0d64c8270b9cce4c4b8fefd005c916736ade5 height: height attribute not set width: width attribute not set description: {\textstyle {\begin{bmatrix}(z_{1}-z_{2})/{\sqrt {2}}\\(w_{1}-w_{2})/{\sqrt {2}}\end{bmatrix}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0496e0fbc2d62df7524fb6e62273eb48a2f9db17 height: height attribute not set width: width attribute not set description: {\textstyle \delta _{1,2}\in a^{+}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8f872cefaedca53de40d667c8de1a588d27956a9 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{bmatrix}(z_{1}-z_{2})/{\sqrt {2}}\\(w_{1}-w_{2})/{\sqrt {2}}\end{bmatrix}}\in {\frac {1}{\sqrt {2}}}{\begin{bmatrix}1&r\\r&1\end{bmatrix}}^{-1/2}a^{+}={\frac {1}{2{\sqrt {2}}}}{\begin{bmatrix}{\frac {1}{\sqrt {1+r}}}+{\frac {1}{\sqrt {1-r}}}&{\frac {1}{\sqrt {1+r}}}-{\frac {1}{\sqrt {1-r}}}\\{\frac {1}{\sqrt {1+r}}}-{\frac {1}{\sqrt {1-r}}}&{\frac {1}{\sqrt {1+r}}}+{\frac {1}{\sqrt {1-r}}}\end{bmatrix}}a^{+}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b090610627f68b86b1725883741642c984868a10 height: height attribute not set width: width attribute not set description: {\textstyle (1,0),(0,1)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fdff67a2a803cfb3723f7061c3fb1e621c8feb18 height: height attribute not set width: width attribute not set description: {\textstyle ({\frac {1}{\sqrt {1+r}}}+{\frac {1}{\sqrt {1-r}}},{\frac {1}{\sqrt {1+r}}}-{\frac {1}{\sqrt {1-r}}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c1c4ff779ac8323e90aeabd312b699863f34464d height: height attribute not set width: width attribute not set description: {\textstyle ({\frac {1}{\sqrt {1+r}}}-{\frac {1}{\sqrt {1-r}}},{\frac {1}{\sqrt {1+r}}}+{\frac {1}{\sqrt {1-r}}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a11744bd71a5eb6efe4f28e12ca57f874d82658c height: height attribute not set width: width attribute not set description: {\textstyle \theta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6084bd4241ccf482f32905c0fead5d2877a9263f height: height attribute not set width: width attribute not set description: {\displaystyle \theta =\arctan {\frac {{\frac {1}{\sqrt {1+r}}}-{\frac {1}{\sqrt {1-r}}}}{{\frac {1}{\sqrt {1+r}}}+{\frac {1}{\sqrt {1-r}}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ec68c19d74fb0a2504bfa2a8edf509c785672b34 height: height attribute not set width: width attribute not set description: {\textstyle \pi +4\theta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8e6c01fdecbb5620eeb7034568ff23208c381826 height: height attribute not set width: width attribute not set description: {\displaystyle pr(\delta _{1,2}\in a^{+})={\frac {\pi +4\theta }{2\pi }}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5c2f1df1feb4d05666cd6635b862ed980c328aa7 height: height attribute not set width: width attribute not set description: {\displaystyle \sin {\left({\frac {\pi }{2}}e[\tau _{a}]\right)}=\sin(2\theta )=r} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3d14568bac3f906aa9b0f69bf7a23f014eaf2322 height: height attribute not set width: width attribute not set description: {\displaystyle \{(x_{i},y_{i}),(x_{j},y_{j})\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a4e90e70df81dd461038b628870de3cf7dfa0cc7 height: height attribute not set width: width attribute not set description: {\displaystyle x_{i}=x_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c76b272c0b580ff78ef288b775f89cfdcd64d1f4 height: height attribute not set width: width attribute not set description: {\displaystyle y_{i}=y_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b9876858a88642f0d63904ec0f49878cf8e25e11 height: height attribute not set width: width attribute not set description: {\displaystyle \tau _{a}={\frac {n_{c}-n_{d}}{n_{0}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/623dc495686a64be200683a70cf583c01c6957c3 height: height attribute not set width: width attribute not set description: {\displaystyle \tau _{b}={\frac {n_{c}-n_{d}}{\sqrt {(n_{0}-n_{1})(n_{0}-n_{2})}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5a8a56a9c95a4e79cdd35c7ad72b7268c61f228a height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}n_{0}&=n(n-1)/2\\n_{1}&=\sum _{i}t_{i}(t_{i}-1)/2\\n_{2}&=\sum _{j}u_{j}(u_{j}-1)/2\\n_{c}&={\text{number of concordant pairs}}\\n_{d}&={\text{number of discordant pairs}}\\t_{i}&={\text{number of tied values in the }}i^{\text{th}}{\text{ group of ties for the first quantity}}\\u_{j}&={\text{number of tied values in the }}j^{\text{th}}{\text{ group of ties for the second quantity}}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a6e20146fb295492a88f8598eee20b3b381da3b1 height: height attribute not set width: width attribute not set description: {\displaystyle \tau _{c}={\frac {2(n_{c}-n_{d})}{n^{2}{\frac {(m-1)}{m}}}}=\tau _{a}{\frac {n-1}{n}}{\frac {m}{m-1}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/64497370c6603a616cbf7f6cc22c0fbd3099e4ca height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}n_{c}&={\text{number of concordant pairs}}\\n_{d}&={\text{number of discordant pairs}}\\r&={\text{number of rows}}\\c&={\text{number of columns}}\\m&=\min(r,c)\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/11731a38f68af9d93f99720aec639ab965aad824 height: height attribute not set width: width attribute not set description: {\displaystyle \tau _{a}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e88ac18f02494d162dc967abe5823e722e563e85 height: height attribute not set width: width attribute not set description: {\displaystyle z_{a}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fdc43162e79997b83b635f3d6792af28dd4f622c height: height attribute not set width: width attribute not set description: {\displaystyle z_{a}={n_{c}-n_{d} \over {\sqrt {{\frac {1}{18}}v_{0}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/80f93129bd40980c3460b8bc2fea0c94c03b9268 height: height attribute not set width: width attribute not set description: {\displaystyle v_{0}=n(n-1)(2n+5)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ad81fb943b9b74ad72d5cab88767faa9730999c4 height: height attribute not set width: width attribute not set description: {\displaystyle -|z_{a}|} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0ecafb5c12559387f111abaf664d2235c0a0573f height: height attribute not set width: width attribute not set description: {\displaystyle z_{b}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8360a39672c98a2b406ae3d99eb30531703ed043 height: height attribute not set width: width attribute not set description: {\displaystyle \tau _{b}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/de4ae21cfcfb63a84c3791e9d3e118666ff66d25 height: height attribute not set width: width attribute not set description: {\displaystyle z_{b}={n_{c}-n_{d} \over {\sqrt {v}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/74fff77b9666911c553dc6851209142a4dfa3633 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{ccl}v&=&{\frac {1}{18}}v_{0}-(v_{t}+v_{u})/18+(v_{1}+v_{2})\\v_{0}&=&n(n-1)(2n+5)\\v_{t}&=&\sum _{i}t_{i}(t_{i}-1)(2t_{i}+5)\\v_{u}&=&\sum _{j}u_{j}(u_{j}-1)(2u_{j}+5)\\v_{1}&=&\sum _{i}t_{i}(t_{i}-1)\sum _{j}u_{j}(u_{j}-1)/(2n(n-1))\\v_{2}&=&\sum _{i}t_{i}(t_{i}-1)(t_{i}-2)\sum _{j}u_{j}(u_{j}-1)(u_{j}-2)/(9n(n-1)(n-2))\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/72ea85ed42f09e7e4b5dd8bdd479a4156bc17321 height: height attribute not set width: width attribute not set description: {\displaystyle n_{c}-n_{d}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6cd9594a16cb898b8f2a2dff9227a385ec183392 height: height attribute not set width: width attribute not set description: {\displaystyle o(n^{2})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9ee17d0db6ada2cc1ab80c22b6b6d349272acd66 height: height attribute not set width: width attribute not set description: {\displaystyle o(n\cdot \log {n})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4 height: height attribute not set width: width attribute not set description: {\displaystyle x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d height: height attribute not set width: width attribute not set description: {\displaystyle y} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9d2320768fb54880ca4356e61f60eb02a3f9d9f1 height: height attribute not set width: width attribute not set description: {\displaystyle o(n\log n)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7dd5b2a59aefd6e04e81166dfd687e0073cbddd7 height: height attribute not set width: width attribute not set description: {\displaystyle s(y)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2801749c08b7128e0f9d78cbf11c6c013e93c258 height: height attribute not set width: width attribute not set description: {\displaystyle n_{c}-n_{d}=n_{0}-n_{1}-n_{2}+n_{3}-2s(y),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5d35ab39fc1af104a61e369bf3b6065e3612a5f7 height: height attribute not set width: width attribute not set description: {\displaystyle n_{3}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ee784b70e772f55ede5e6e0bdc929994bff63413 height: height attribute not set width: width attribute not set description: {\displaystyle n_{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/840e456e3058bc0be28e5cf653b170cdbfcc3be4 height: height attribute not set width: width attribute not set description: {\displaystyle n_{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bd7f1ba0f7c401d26d5b79bdd5e36ef3e79d5da6 height: height attribute not set width: width attribute not set description: {\displaystyle y_{\mathrm {left} }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6bd9c3d7aabc5284301d154dad11a666438901d6 height: height attribute not set width: width attribute not set description: {\displaystyle y_{\mathrm {right} }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/79fb02d1694d20615d7b9fa19340a5d1503f16e3 height: height attribute not set width: width attribute not set description: {\displaystyle s(y)=s(y_{\mathrm {left} })+s(y_{\mathrm {right} })+m(y_{\mathrm {left} },y_{\mathrm {right} })} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0eaacd3dc84de8d35a65f670bb50accc5032a283 height: height attribute not set width: width attribute not set description: {\displaystyle y_{\mathrm {left} }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/086dea952df4578900e941ca5b1c869c02bc00dd height: height attribute not set width: width attribute not set description: {\displaystyle y_{\mathrm {right} }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6398ef7fe528d15fcfe8840b915857833db48ec9 height: height attribute not set width: width attribute not set description: {\displaystyle m(\cdot ,\cdot )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8b61e3d4d909be4a19c9a554a301684232f59e5a height: height attribute not set width: width attribute not set description: {\displaystyle t_{i}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/86f8d397f4684f948df846413e6d62b009718724 height: height attribute not set width: width attribute not set description: {\displaystyle u_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ebfd3cc015f62a31a2bf80260f53aefa7049d6b7 height: height attribute not set width: width attribute not set description: {\displaystyle \tau _{c}} |
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https://login.wikimedia.org/wiki/special:centralautologin/start?type=1x1 height: 1 width: 1 description: no alt description found |
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http://en.wikipedia.org/static/images/footer/wikimedia-button.svg height: 29 width: 84 description: wikimedia foundation |
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http://en.wikipedia.org/w/resources/assets/poweredby_mediawiki.svg height: 31 width: 88 description: powered by mediawiki |
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