Sentence examples for be given as below from inspiring English sources
In terms of the reduced displacement functions appearing, the following conditions in (35) will be given as below: begin{aligned} &w^{left( k right)} left( {y,z} right) = 0 hfill & bar{C}_{12}^{left( k right)} L + bar{C}_{22}^{left( k right)},v_{,y}^{left( k right)} + bar{C}_{23}^{left( k right)},w_{,z}^{left( k right)} = 0quad {text{at}};{text{y}}, pm,{text{b}} hfill end{aligned}.
Details of this scheme are given as below, and a pictorial description of this scheme is given in Fig. 12. Fig. 12 Channel model of Scheme 3. Channel model for Scheme 3 at the phase associated with ({mathcal {L}}={i_{1}, ldots, i_{L}}).
It then jumps to this state with probability (q_{ij}) or remains in the current state i with probability (1 - q_{ij},) where (q_{ij}) is given as below: begin{aligned} q_{ij} = {left{ begin{array}{ll} min left( frac{ p_{ji} }{ p_{ij} }, 1 right) & text { if } p_{ij} > 0, 1 & text { if } p_{ij} = 0. end{array}right.
The entire spectrum of solid carbonaceous materials like coals, lignite, all types of biomass material, and char to residue-derived fuels have been considered in derivation of present correlation which is given as below: HHV=0.3536FC+0.1559VM−0.0078ASH (MJ/kg) (where FC 1.0 91.5% fixed carbon, VM 0.92 90.6% volatile matter and Ash 0.12 77.7% ash content in wt% on a dry basis).
The detailed steps of the PSO algorithm is given as below: Step 1 Initialize parameters and population.
The CNFs were synthesized in a tube furnace via the WA-CVD method at 800°C as reported earlier[39]; however, a brief description is given as below.
As a result, the inner objective function is given as below: {displaystyle begin{array}{l}min f=sum limits_{i=1}^NBig{{P}_{ES}(i)+{P}_L i -{P}_G(i)- kern0em frac{sum limits_{i=1}^Nleft[{P}_L(i)-{P}_G(i)right]}{N}Big}^2end{array}} (4).
The activation of output layer is given as below: begin{aligned} hat{x}_{l}=f(W_2 a_h+B_2), end{aligned} (3)where the (hat{x}_{l}^{(i }in {R^m}) is output vector, a nonlinear approximation of input vector (x_{l}^{(i)}).
