g^{ij}g^{kl}+\mu \left(g^{ik}g^{jl}+g^{il}g^{kj}\right)\\&+\alpha \left(a^{i}a^{j}a^{k}a^{l}+b^{i}b^{j}b^{k}b^{l}+c^{i}c^{j}c^{k}c^{l}\right)\end{aligned}}}...

C i j k l ε k l ⇌ ε i j = S i j k l σ k l {\displaystyle \sigma _{ij}=C_{ijkl}\,\varepsilon _{kl}\,\rightleftharpoons \,\varepsilon _{ij}=S_{ijkl}\,\sigma...

{T}}\mathbf {A} \right)=\operatorname {tr} \left(\mathbf {B} \mathbf {A} ^{\mathsf {T}}\right)=\sum _{i=1}^{m}\sum _{j=1}^{n}a_{ij}b_{ij}\;.} If one views...

following an overhaul, individual J-22s can be approved to perform a further 1,000 flight hours. IJ-22 Orao 1 26 dedicated reconnaissance aircraft.[citation needed]...

j=1}^{n}c_{ij}x_{ij}&\colon &&\\x_{ij}\in {}&\{0,1\}&&i,j=1,\ldots ,n;\\\sum _{i=1,i\neq j}^{n}x_{ij}={}&1&&j=1,\ldots ,n;\\\sum _{j=1,j\neq i}^{n}x_{ij}={}&1&&i=1...

{\partial {\widetilde {x}}^{b}}{\partial x^{k}}},} so that R i j {\displaystyle R_{ij}} define a (0,2)-tensor field on M {\displaystyle M} . In particular, if...

as C l C l ∗ C l | n l ⟩ = ( 2 μ E l n + F l ) C l | n l ⟩ = ( 2 μ H l + 1 + G l ) C l | n l ⟩ , {\displaystyle {\begin{aligned}C_{l}C_{l}^{*}C_{l}|nl\rangle...

_{i=1}^{m}|a_{ij}|^{2}\right)^{1/2}} The L 2 , 1 {\displaystyle L_{2,1}} norm as an error function is more robust, since the error for each data point (a column)...

j}^{\rm {(DM)}}=\mathbf {D} _{ij}\cdot (\mathbf {S} _{i}\times \mathbf {S} _{j})} . In magnetically ordered systems, it favors a spin canting of otherwise...

f_{ij}^{\;\;k}\kappa ^{jl\cdots m}+f_{ij}^{\;\;l}\kappa ^{kj\cdots m}+\cdots +f_{ij}^{\;\;m}\kappa ^{kl\cdots j}=0} where f i j k {\displaystyle f_{ij}^{\;\;k}}...

written as a ⋅ b = ∑ i , j = 1 n a i δ i j b j = ∑ i = 1 n a i b i . {\displaystyle \mathbf {a} \cdot \mathbf {b} =\sum _{i,j=1}^{n}a_{i}\delta _{ij}b_{j}=\sum...

of any smooth curve γ : [a, b] → M as L ( γ ) = ∫ a b F ( γ ( t ) , γ ˙ ( t ) ) d t . {\displaystyle L(\gamma )=\int _{a}^{b}F\left(\gamma (t),{\dot {\gamma...

{\displaystyle [{\hat {x}}_{i},{\hat {p}}_{j}]=i\hbar \delta _{ij},} where δ i j {\displaystyle \delta _{ij}} is the Kronecker delta. This relation is attributed...

L 2 , L x ] = [ L x 2 , L x ] + [ L y 2 , L x ] + [ L z 2 , L x ] = L y [ L y , L x ] + [ L y , L x ] L y + L z [ L z , L x ] + [ L z , L x ] L z = L...

{\displaystyle y_{ij}=\mu +\tau _{i}+\mathrm {B} (x_{ij}-{\overline {x}})+\epsilon _{ij}.} In this equation, the DV, y i j {\displaystyle y_{ij}} is the jth...

L 21 T L 31 T 0 I L 32 T 0 0 I ) = ( D 1 ( s y m m e t r i c ) L 21 D 1 L 21 D 1 L 21 T + D 2 L 31 D 1 L 31 D 1 L 21 T + L 32 D 2 L 31 D 1 L 31 T + L...

Then M i j = b ( i ) ⋅ b ( j ) {\displaystyle M_{ij}=b^{(i)}\cdot b^{(j)}} where the dot product a ⋅ b = ∑ ℓ = 1 k a ℓ ∗ b ℓ {\textstyle a\cdot b=\sum...

t ) ) ( d d t x j ∘ γ ( t ) ) d t . {\displaystyle L=\int _{a}^{b}{\sqrt {\sum _{i,j=1}^{n}g_{ij}(\gamma (t))\left({\frac {d}{dt}}x^{i}\circ \gamma...

a 1 n b p q ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮ a m 1 b 11 a m 1 b 12 ⋯ a m 1 b 1 q ⋯ ⋯ a m n b 11 a m n b 12 ⋯ a m n b 1 q a m 1 b 21 a m 1 b 22 ⋯ a m 1 b 2...

if vertex  v i  is incident with edge  e j , 0 otherwise. {\displaystyle B_{ij}=\left\{{\begin{array}{rl}\,1&{\text{if vertex }}v_{i}{\text{ is incident...

(ℓ) and spin (s) angular momentum of the electrons: B ≡ B el = B el ℓ + B el s . {\displaystyle \mathbf {B} \equiv \mathbf {B} _{\text{el}}=\mathbf {B}...

= ( l + d l ) / b − ( l − d l ) / b l t = 2 d l l t b = 1 r b = s t r a i n   g r a d i e n t b {\displaystyle \rho _{g}={\frac {(l+dl)/b-(l-dl)/b}{lt}}=2{\frac...

{1}{Z}}\sum _{h}e^{\sum _{ij}W_{ij}^{(1)}\nu _{i}h_{j}^{(1)}+\sum _{jl}W_{jl}^{(2)}h_{j}^{(1)}h_{l}^{(2)}+\sum _{lm}W_{lm}^{(3)}h_{l}^{(2)}h_{m}^{(3)}},} where...

^{k}}_{ij}\mathbf {u} _{k}.} Explicitly, in terms of the metric tensor, this is ω i k l = 1 2 g i m ( g m k , l + g m l , k − g k l , m + c m k l + c m l k...

\otimes |\psi _{i}\rangle \in S_{\nu }(H\otimes H)} , and a i j = ν a j i ∈ C {\displaystyle a_{ij}=\nu a_{ji}\in \mathbb {C} } is a complex coefficient, etc...

drop Δ p = p b − p a {\displaystyle \Delta p=p_{b}-p_{a}} is in units ( P a ) {\displaystyle \mathrm {(Pa)} } , and L {\displaystyle L} is the length...

_{1j}]^{T}=\left[\sum _{i=s}^{L-1}\sum _{j=t}^{L-1}i{\frac {P_{ij}}{\omega _{1}}},\sum _{i=s}^{L-1}\sum _{j=t}^{L-1}j{\frac {P_{ij}}{\omega _{1}}}\right]^{T}\\\mu...

}}^{f}=\mathbf {A} {\boldsymbol {\Sigma }}^{x}\mathbf {A} ^{\mathrm {T} }} reads Σ i j f = ∑ k n ∑ l n A i k Σ k l x A j l . {\displaystyle \Sigma _{ij}^{f}=\sum...

23 S 24 S 25 S 26 S 13 S 23 S 33 S 34 S 35 S 36 S 14 S 24 S 34 S 44 S 45 S 46 S 15 S 25 S 35 S 45 S 55 S 56 S 16 S 26 S 36 S 46 S 56 S 66 ] {\displaystyle...

using a least square fit by minimizing the residuals. This results in C = L i j m i j m k l m k l . {\displaystyle C={\frac {L_{ij}m_{ij}}{m_{kl}m_{kl}}}...