Sentence examples for be obtained as left from inspiring English sources
(12 Setting k_{1} = left[ {B times frac{alpha }{2}} right],quad k_{2} = left[ {B times left( {1 - frac{alpha }{2}} right)} right], (13 the bootstrap confidence interval can be obtained as left( {bar{X} - omega_{{ k_{2} )}} frac{S}{sqrt n },quad bar{X} - omega_{{ k_{1} )}} frac{S}{sqrt n }} right), (14 where (bar{X}) and S are the mean value and standard deviation of the sample x, respectively.
According to Eqs. (33) and (38), the full tensor permeability expression of single fracture group in fractured media can be obtained as left[ k right] = k_{{{text{fr}}0}} left[ {1 - left( {{p mathord{left/ {vphantom {p {p_{1} }}} right.
The neutral currents on both the grid and load side iSN, iLN can be obtained as: left{ begin{aligned} i_{text{SN}} &= 0 hfill i_{text{LN}} &= i_{text{La}} hfill end{aligned} right.
It is clear that the covariance of the term (mathcal {K}) can be obtained as (left |Delta _{mathbf {G}_{overline {t},i}}mathbf {W}_{i}Delta _{mathbf {F}_{i,overline {t}}}right |^{2}).
It can be obtained as: left{ begin{aligned} S_{c1} = frac{1}{2}S_{c} + Delta S_{pe} hfill S_{c2} = frac{1}{2}S_{c} - Delta S_{pe} hfill end{aligned} right.
Likewise, for the proposed Phillips-Heffron model of CC-VSC, the corresponding equivalent inertia K J, equivalent synchronizing coefficient K S, and equivalent damping coefficient K D can be obtained as: left{ begin{array}{l} K_{text{J}} = J hfill K_{text{S}} = k_{text{i}} U_{text{g}} cos theta_{0} hfill K_{text{D}} = k_{text{p}} U_{text{g}} cos theta_{0} hfill end{array} right.
If the number of sampling points is m, then the normalized equal-interval amplitude scale is obtained as (left{ {A_{i} } right} = left( {1,, frac{m - 1}{m}, ldots,, frac{m - i + 1}{m}, ldots,, frac{2}{m},, frac{1}{m}} right)), (i = 1,, 2, ldots,, m).
The mutual coherence [3] of Θ t can be obtained as follows: mu left({varTheta}^tright triangleq underset{begin{array}{c}hfill ine jhfill hfill 1le i,jle Nhfill end{array}}{ max}frac{left|{theta}_i^T{theta}_jright|}{{leftVert {theta}_irightVert}_2{leftVert {theta}_jrightVert}_2}, (12 where θ i is the column vector of Θ t.
Similarly, the Katz receive centrality of node I can be obtained as (K_{i}^{r} left( alpha right) = left[ {left( {I - alpha A^{T} } right)^{ - 1}.1} right]_{i}).
The generator matrix (GM) can be obtained as (mathbf {G} = left [mathbf {I}_{K}~mathbf {H}_{u}^{T}mathbf {H}_{p}^{-T}right ]), where I K is an identity matrix of dimension K×K, and the matrix (mathbf {H}_{p}^{-T}) is the well-known inverse transpose of (18).
By multiplying the MTTRj by the number of breakdowns calculated in Eq. (1), the total repair time for machine j, T j (t), can be obtained as follows: T_{j} left( t right) = frac{{t_{j} times {text{MTTR}}_{j} }}{{{text{MTBF}}_{j} }}.
