Sentence examples for be rewritten as left from inspiring English sources

Since (S t)+I t)+R t)equiv1), system (1) can be rewritten as left { textstylebegin{array}{l} left.

We remark that the limiting problem can be rewritten as: left{ begin{array}{ll} u_{t}- text{div} left(g:(|nabla u|) nabla uright) -f leq 0, qquad |nabla u|leq lambda, left u_{t}- text{div} left(g:(|nabla u|) nabla uright) -fright)(|nabla u|-lambda)=0, end{array} right.

where the SINR constraints in (8) can be rewritten as: left(1+frac{1}{lambda gamma_{k}}right) |boldsymbol{h}_{k}^{H}boldsymbol{w}_{k}|^{2} geq left|left[ begin{array}{c} boldsymbol{h}_{k}^{H} boldsymbol{W} sigma_{k} end{array} right] right|^{2}, ~forall k. (9).

Assuming that (S t)+N t)=1), this equation system can be rewritten as left { textstylebegin{array}l} N t)[gamma S t)^{2}-gamma m S t)+beta_{2}]=0, -N t)[gamma S t)^{2}-gamma m S t)+beta_{2}]=0.

Therefore, Eq. 1 can be rewritten as left(frac{1}{2{m}_{perp } z)}{overset{frown }{p}}_{perp}^2+frac{1}{2{m}_z z)}{overset{frown }{p}}_z^2+varphi (z right psi (z)=Epsi (z) (2 where ϕ z) represents the potential energy along z axis.

When the influence of the windings' resistances are neglected, and assuming that the winding leakage reactance for each tap of ET secondary winding is (X_{0}), the equivalent impedances can then be rewritten as: left{ begin{array}{l} Z_{text{eq}} = {text{j}}x_{text{eq}} hfill Z_{T} = {text{j}}T^{2} X_{0} hfill n_{T} = N_{text{E1}} / TN_{T} ) hfill end{array} right.

Eq (9) can be rewritten as: tau left( x right) = frac{{phi_{ss} }}{4} cdot frac{{dsigma_{ss} }}{ds} cdot frac{ds}{dx} (10 where ds/dx is defined as the strain in the stainless steel, since the strains developed within the concrete are ignored due to their negligible values when compared to the strains developed in the stainless steel.

Hence, (14) can be rewritten as begin{aligned} left( 1-rho right) left( 1-upsilon -frac{1}{pi ^H_k+pi ^A_k} right) left( h_k+a_kright) end{aligned} which, apart from the irrelevant effect of (1-rho ), coincides with the desired maximizing function.

As far as the m th inverter (1≤m≤n) is considered, (1) can be rewritten as I_{2,m} left( s right) = G_{{rm cs},m} (s)I_{{rm ref},m} left( s right) - Y_{{rm cs},m} U_{rm pcc} left( s right) (6).

Then, the covariance matrix E{A A H} in (27) can be rewritten as begin{array}rcl@ E left{{boldsymbol A} {boldsymbol A}^{mathrm{H}}right} = {{boldsymbol R}^{boldsymbol K}}otimes left[ {{boldsymbol r}_{1}^{mathrm{T}} }, {{boldsymbol r}_{2}^{mathrm{T}} }, ldots, {{boldsymbol r}_{L}^{mathrm{T}}} right]^{mathrm{T}}.

Therefore, the objective of the optimization problem (2) can be rewritten as: min_{Z,E} left| Z right|_ + gamma left| E right|_{1} (3).