Proof Corollary 5.1 should be applied to the coefficients α = 1 / p, β = 1 / q, γ = r and the points a = x p, b = y q, c = z.
Proof Corollary 5.1 should be applied to the coefficients α = p, β = q, γ = r and the points a = 1 + x, b = 1 + y, c = 1 + z. □.
If the strict inequality in conditions (18), (20), (21), (22), and (24) is replaced by equality, then the conclusions of Theorems 4, 5, 6, and Corollary 2 should be changed from global asymptotic stability to stability.
Theorem 3.3 (or, equivalently, Corollary 3.4) should be compared with Theorem 2.2 of [6] (valid for the case where ψ does not depend on t and the set Y is bounded), where the function g is assumed to be continuous in all variables.
The corollary to manufacturing should be self-evident.
As a corollary, genetic results should be confirmed in different populations [ 11].
That corollary, of which we should be reminded from time to time, is this: popular entertainment from Hollywood is – to greater or lesser extent – propaganda.
Corollary to that spending should be higher employment and incomes, as well as higher consumption patterns for clothing, shelter, technology and communications.
To assess current state of affairs, we presented postdocs, principal investigators, academic leaders, workforce analysts, and funders with a summary of the latest statistics (see our Policy Papers below) before asking them to respond both to the big question and to its corollary: If so, what should be done to remedy the situation?
If we go on increasing the intrinsic growth rate of the species as (r_{1}(t)=0.40+0.02sin(t)), (r_{2}(t)=0.48+0.03cos(t)), while the values of other parameters are the same as above, then one can calculate that (b_{1*}= b_{2*}=0.01>0) at this time, which satisfies the condition of Corollary 2.3, then system (4) should be persistent in the mean almost surely by this corollary.
