end{aligned} Inserting the above three inequalities into (4.1), we get the desired conclusion immediately.
Inserting the above arguments into (22), we obtain begin{aligned} lim_{jtoinfty}bigl| U^{ k)+}-U^bigr| =0.
So inserting the above computations into (77) and (78), we get (60) and the first formula of (62).
Now, inserting the above estimates for s into (2.24), using (2.19), and taking be small enough, we get (2.37).
In order to compute (mathfrak {A}) we simply insert the above presented system and network parameters into (24) – (27) and (34).
Inserting the above recurrence relation into equation (6), we get the following recurrence relation for the extended Mittag-Leffler's function.
Inserting the above estimates into (2.6) and (2.7), and summing up the results and using the Gronwall inequality, we arrive at biglVert (u,b bigrVert _{L^{infty}(0,T H^{2})}+Vert uVert _{L^{2}(0,T;H^{2+alpha}+Vertrt bVert _{L^{2}(0,T;H^{2+beta}leqeq C.
Gene drives' primary function in a population is to insert the above mentioned molecular "scissors" along with the gene mutation into the desired part of the DNA, where the "scissors" cut the corresponding gene on the chromosome within the genome and substitute it with the mutated gene.
end{aligned}Inserting the above equation into (4), the canonical partition function of the model can be written as begin{aligned} Z_{t,M}(p,q =sum _{n_1=0}^{t-M}sum _{i=0}^{n_1} left( {begin{array}{l} {n_1} i end{array}} right) left( {begin{array}{l} {t-n_1-2} M-2 end{array}} right) frac{q^i}{p^{n_1}}.
Given the distribution of population, the growth function of populated locations and the largest population size, we insert the above expressions of P s,t), l(t), and n(t) as shown in Eq. 4, Eq. 5 and Eq. 6 into Eq. 3. Then we have GP ( t ) = ∫ 1 a ∗ t b + c ( ( φ ∗ s - λ ) ∗ ( η ∗ t ε ) ∗ s ) ds = ηφ t ε 2 - λ [ ( a ∗ t b + c ) 2 - λ - 1 ].
