User:Hakeem.gadi/philtl

${\displaystyle \mathrm {d} (\mathbf {V_{x}} ,\mathbf {V_{y}} )={\sqrt {(f_{y1}-f_{x1})^{2}+(f_{y2}-f_{x2})^{2}+(f_{y3}-f_{x3})^{2}}}}$

${\displaystyle \mathrm {d_{\sigma }} (\mathbf {V_{x}} ,\mathbf {V_{y}} )={\sqrt {\left({\frac {f_{y1}-f_{x1}}{\sigma _{1}}}\right)^{2}+\left({\frac {f_{y2}-f_{x2}}{\sigma _{2}}}\right)^{2}+\left({\frac {f_{y3}-f_{x3}}{\sigma _{3}}}\right)^{2}}}}$

${\displaystyle \sigma _{f_{c1}}={\sqrt {\frac {(f_{c1_{1}}-E(V_{c1}))^{2}+(f_{c1_{2}}-E(V_{c1}))^{2}+\dots +(f_{c1_{20}}-E(V_{c1}))^{2}}{n}}}}$

${\displaystyle \sigma _{f_{c1}}={\sqrt {\frac {(2-2.15)^{2}+(2-2.15)^{2}+(2-2.15)^{2}+(2-2.15)^{2}+(3-2.15)^{2}+(2-2.15)^{2}+(2-2.15)^{2}+\dots +(2-2.15)^{2}}{20}}}}$

${\displaystyle \sigma _{f_{c1}}={\sqrt {\frac {(-0.15)^{2}+(-0.15)^{2}+(-0.15)^{2}+(-0.15)^{2}+(0.85)^{2}+(-0.15)^{2}+(-0.15)^{2}+\dots +(-0.15)^{2}}{20}}}}$

${\displaystyle \sigma _{f_{c2}}={\sqrt {\frac {(f_{c2_{1}}-E(V_{c2}))^{2}+(f_{c2_{2}}-E(V_{c2}))^{2}+\dots +(f_{c2_{20}}-E(V_{c2}))^{2}}{n}}}}$

${\displaystyle \sigma _{f_{c2}}={\sqrt {\frac {(1-1.15)^{2}+(1-1.15)^{2}+(1-1.15)^{2}+(1-1.15)^{2}+(1-1.15)^{2}+(1-1.15)^{2}+(1-1.15)^{2}+\dots +(1-1.15)^{2}}{20}}}}$

${\displaystyle \sigma _{f_{c3}}={\sqrt {\frac {(f_{c3_{1}}-E(V_{c3}))^{2}+(f_{c3_{2}}-E(V_{c3}))^{2}+\dots +(f_{3_{20}}-E(V_{c3}))^{2}}{n}}}}$

${\displaystyle \mathrm {d_{\sigma }} (\mathbf {E(V_{c})} ,\mathbf {V_{new}} )={\sqrt {\left({\frac {f_{new1}-E(V_{c1})}{\sigma _{f_{c1}}}}\right)^{2}+\left({\frac {f_{new2}-E(V_{c2})}{\sigma _{f_{c2}}}}\right)^{2}+\left({\frac {f_{new3}-E(V_{c3})}{\sigma _{f_{c3}}}}\right)^{2}}}}$

${\displaystyle \mathrm {d_{\sigma }} (\mathbf {E(V_{z})} ,\mathbf {V_{new}} )={\sqrt {\left({\frac {f_{new1}-E(V_{z1})}{\sigma _{f_{z1}}}}\right)^{2}+\left({\frac {f_{new2}-E(V_{z2})}{\sigma _{f_{z2}}}}\right)^{2}+\left({\frac {f_{new3}-E(V_{z3})}{\sigma _{f_{z3}}}}\right)^{2}}}}$

${\displaystyle sum={\frac {1.0}{0.5}}+{\frac {1.1}{1.5}}+{\frac {1.2}{2.5}}+{\frac {1.3}{3.5}}+{\frac {1.4}{4.5}}+\dots +{\frac {2.0}{10.5}}}$

${\displaystyle Class(f_{1},f_{2},f_{3},f_{4},f_{5},f_{6})={\begin{cases}C_{1}&{\text{if }}0\leq Prog_{i}(f_{1},f_{2},f_{3},f_{4},f_{5},f_{6})<10000\\C_{2}&{\text{if }}10000\leq Prog_{i}(f_{1},f_{2},f_{3},f_{4},f_{5},f_{6})<20000\\C_{3}&{\text{if }}30000\leq Prog_{i}(f_{1},f_{2},f_{3},f_{4},f_{5},f_{6})<40000\\C_{4}&{\text{if }}40000\leq Prog_{i}(f_{1},f_{2},f_{3},f_{4},f_{5},f_{6})<50000\end{cases}}}$

${\displaystyle y={\begin{cases}3x-7&{\text{if }}x=-3\\5x^{2}&{\text{if }}x=2{\text{ or }}x=5\\x-4x^{3}&{\text{if }}x=-4{\text{ or }}x=4\end{cases}}}$

${\displaystyle \mathbf {A} ={\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{13}\\a_{31}&a_{32}&a_{33}\\\end{bmatrix}}}$

${\displaystyle y={\frac {1}{1!}}+{\frac {2}{2!}}+{\frac {3}{3!}}+\cdots +{\frac {n}{n!}}}$

${\displaystyle f(n)=\sum _{i\mathop {=} 1}^{n}n^{\frac {1}{i}}}$

${\displaystyle f(N)=\prod _{i\mathop {=} 1}^{N}7^{\frac {1}{i}}=7\times 7^{\frac {1}{2}}\times 7^{\frac {1}{3}}\times 7^{\frac {1}{4}}\times \cdots \times 7^{\frac {1}{N}}}$