The phrase 'is given as below' is correct and can be used in written English.
It is typically used to introduce a list or description of items that appear later in the sentence. For example: "The list of tasks is given as below: 1) Clean the windows 2) Vacuum the carpets 3) Dust the furniture".
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 formal definition of the 0-1 knaproblemroblem is given as below.
Hence the related transportation problem with enhanced flow is given as below.
Hence the related transportation problem with restricted flow is given as below.
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.
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}}).
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}.
Let f Δ 1 denote the time scale partial derivative with respect to t 1 and let f Δ 2 denote the time scale partial derivative with respect to t 2. Definitions of these partial derivatives are given as below [2, 3].
MO sequences are given as below.
Hence, NDT is given as shown below.
