otherwise stated (⟨ij⟩ becomes ⟨IJ⟩ in Dutch, and digraphs marking eclipsis in Irish, are capitalised on the second letter, i.e. ⟨mb⟩ becomes ⟨mB⟩). Contents: ...

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}}}...

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...

) = ∑ j W i j a j ( l ) {\displaystyle x_{i}^{(l)},\quad a_{i}^{(l)}=f(x_{i}^{(l)}),\quad x_{i}^{(l+1)}=\sum _{j}W_{ij}a_{j}^{(l)}} where x {\displaystyle...

Contents A B C D E F G H I J K L M N O P Q R S T U V W X Y Z See also References Alfa Brouwerij, Schinnen Amstel Brouwerij, Amsterdam Bavaria Brouwerij...

{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...

_{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)...

∣ i = 1 , 2 , … , m ) ∣ j ∈ J + ⟩ } ≡ { t b j ∣ j = 1 , 2 , … , n } , {\displaystyle A_{b}=\{\langle \min(t_{ij}\mid i=1,2,\ldots ,m)\mid j\in J_{-}\rangle...

Bremen: 2 cities Berlin: 1 city Hamburg: 1 city Contents A B C D E F G H I J K L M N O P Q R S T U V W X Z Städte (Alle Gemeinden mit Stadtrecht) nach...

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...

×14, T ×13, A ×6, E ×6, I ×6, O ×6, U ×6, Á ×1, À ×1, Ã ×1, Ạ ×1, Ả ×1, Ă ×1, Ắ ×1, Ằ ×1, Ẳ ×1, Ặ ×1, Ẵ ×1, Â ×1, Ấ ×1, Ầ ×1, Ẩ ×1, Ậ ×1, Ẫ ×1, É ×1, È...

{\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...

ISBN 978-1-107-02414-4. vonHoldt BM, Shuldiner E, Koch IJ, Kartzinel RY, Hogan A, Brubaker L, et al. (7 July 2017). "Structural variants in genes associated...

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...

{\displaystyle C_{ij}} in terms of M k {\displaystyle M_{k}} : [ C 11 C 12 C 21 C 22 ] = [ M 1 + M 4 − M 5 + M 7 M 3 + M 5 M 2 + M 4 M 1 − M 2 + M 3 + M 6 ] . {\displaystyle...

entries of B {\displaystyle B} that compose its i , j {\displaystyle i,j} minor matrix M i j {\displaystyle M_{ij}} as ( a s t ) {\displaystyle (a_{st})}...

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...

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...

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...

is of the form χ : G → G m {\displaystyle \chi :G\to \mathbb {G} _{m}} . Contents:  !$@ A B C D E F G H I J K L M N O P Q R S T U V W XYZ See also References...

(m\vert E(x))}{\partial x_{j}}}=\sum _{i}^{K}H_{ij}\left[{\frac {m_{i}}{E_{i}}}-1\right]} Note that H j i T = H i j {\displaystyle {H}_{ji}^{T}=H_{ij}}...

k L j l ′ − δ i l L j k ′ − δ j k L i l ′ + δ j l L i k ′ ] {\displaystyle [L'_{ij},L'_{kl}]=i[\delta _{ik}L'_{jl}-\delta _{il}L'_{jk}-\delta _{jk}L'_{il}+\delta...

{\displaystyle {\Big |}\sum _{i,j}M_{ij}\langle S_{i},T_{j}\rangle {\Big |}\leq K_{G}} for all vectors Si, Tj in the unit ball B(H) of a (real or complex) Hilbert...

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...

transform each cell, a i j {\displaystyle a_{ij}} of A {\displaystyle A} , to be the product of a local term weight, l i j {\displaystyle l_{ij}} , which describes...

\\u_{m}v_{1}&u_{m}v_{2}&\dots &u_{m}v_{n}\end{bmatrix}}} Or, in index notation: ( u ⊗ v ) i j = u i v j {\displaystyle (\mathbf {u} \otimes \mathbf {v} )_{ij}=u_{i}v_{j}}...

{q}}_{j}\right)={\frac {m}{2}}\sum _{i,j}a_{ij}{\dot {q}}_{i}{\dot {q}}_{j}} ∑ k = 1 n q ˙ k ∂ L ∂ q ˙ k = ∑ k = 1 n q ˙ k ∂ T ∂ q ˙ k = m 2 ( 2 ∑ i , j a i j q ˙ i...

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...

Cambridge, MA: Aiken Computation Laboratory A proof can be found in the Appendix B of Kondratyuk, L. A.; Krivoruchenko, M. I. (1992). "Superconducting quark matter...

\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...