To this end, we note that the integral identity (6.20) leads to the corresponding energy equality ∫ Ω [ | ∇ z θ | 2 − 1 2 V θ ( x ) z θ 2 ] d x = 〈 F ∗ f θ, z θ 〉 H − 1 , H 0 1.
The Gini coefficient is equal to begin{aligned} G_mathrm{in}=A/(A+B), end{aligned}where A is the area between the line corresponding perfect equality and B is the area under the Lorenz curve.
The highest q parameters were obtained as the solubility parameters of dye and polymer approached equality corresponding to the maximum dye polymer affinity.
Moreover, it is clear that x ⋆, which denotes the vector of optimal dual variables corresponding to the equality constraints A T λ=w, yields the optimal rate vector r ⋆.
However, if we use periodic boundary condition, this dependence disappears and we obtain that starting from one cell, the probability of invasion is (3) where r ≡ r B / r A. It can be shown that ≤ ρ, with the equality corresponding to neutral mutants, r = 1.
As it is used in this paper, in Equations 4 and 5, and the corresponding ones, the equalities stand if n → ∞ and n in the summation means the truncation.
The model's assertion about mutation rates implies six different equalities, corresponding to the six possible pairs among the four codons.
This criterion, under the present circumstances, states that the model is ordinary stable if the restriction h 4 - 1 6 1 - b h 2 + 3 2 b 1 - b ≥ 0 (51). is satisfied where the equality is corresponding to the marginal stability state.
For the given value of, if the solution of (23a)–(23d) satisfies (23c) with equality, the corresponding solution represents a valid power partitioning and this value of corresponds to twice a weighted sum of achievable rates.
In more details, it is unstable in the domain 0 < x < 1.0667 while it is stable in the domains 1.0667 ≤ x < ∞ where the equality is corresponding to the marginal stability state.
