The phrase "aforesaid equation" is correct and usable in written English.
It can be used in formal or legal contexts to refer back to an equation that has been previously mentioned in the text.
Example: "In the analysis, we will refer to the aforesaid equation to derive the necessary conclusions."
Alternatives: "previously mentioned equation" or "aforementioned equation".
Alternatively, finite difference numerical model can be used to utilize the aforesaid equation (Bansal [2013]).
Thus, finite difference numerical model can be used to utilize the aforesaid equation (Bansal [2013]).
Using Descartes' rule of signs, we find that there is exactly one sign change of the equation: Lambda^{2Malpha}+bigl(a_{s}^{alpha}(1+ alpha_{1}H_{0})+c_{s}^{alpha}bigr Lambda ^{Malpha}+a_{s}^{alpha}(1+alpha_{1}H_{0})c_{s}^{alpha} 1-R_{s})=0 (9) for (R_{s}>1), thus there is exactly one positive real root of the aforesaid equation for which the argument is less than (frac{pi }{2M}).
Using Descartes' rule of signs, we find that there is exactly one sign change of the equation: Lambda^{2Malpha}+bigl(a_{r}^{alpha}(1+ alpha_{1}H_{0})+c_{r}^{alpha}bigr Lambda ^{Malpha}+a_{r}^{alpha}(1+alpha_{1}H_{0})c_{r}^{alpha} 1-R_{r})=0 (15) for (R_{r}>1), thus there is exactly one positive real root of the aforesaid equation for which the argument is less than (frac{pi }{2M}).
In last few decades the area related to the existence theory of solutions/positive solutions of the aforesaid equations has been got much attentions from researchers.
The RANS equations were solved using the aforesaid four equations transition turbulence model and the fully turbulent SST k ω model.
In the same line, he also obtained the aforesaid stability for the evolution equations [24].
In the first step of the aforesaid approach, the following system of linear equations is solved to determine the damping factors and the frequencies: {displaystyle sum_{m=0}^M}a(m)xleft n-mright)=0, n = M, M+ 1,dots, N- 1 (7).
In fact, as discussed in Section 3.2, the running time of computing of the aforesaid algorithms is the solution to the recurrence equation T ( n ) = { c if n = 1, a T ( n b ) + h ( n ) if n ∈ N b.
It is reckoned that these results may play an important role in the theory of difference equations, and are useful in many practical problems in the aforesaid fields.
The aforesaid coatings have great industrial applications.
