Sentence examples for solution let us from inspiring English sources

To show that model (2) has a positive global solution, let us firstly prove that the model has a positive local solution by making a change of variables.

To obtain a positive solution, let us construct a cone K by K = { x ∈ Q : x ( t ) ≥ e ( t ) x ( s ), t, s ∈ I } (2.2).

For a feasible solution, let us choose (gamma _{i} = frac {1}{binom {k-1}{l-1}}) when L i ⊆K∗, and γ i =0 otherwise, which we can easily check whether it satisfies the first and second constraints of (15).

Before proving that the successive updates of the proposed method converge to the optimal solution, let us establish the relationship between primal and dual variables in the subproblems with the following proposition.

To look for conditions under which it is negative (i.e. the s.o.c. is satisfied for an interior solution), let us multiply the previous expression by (e_{T}) and subtract from it the f.o.c.

In our article, we are going to study the large time asymptotic behavior for the solution of (1.1) and (1.2) by comparing it to the Barenblatt-type solution, let us give some details.

"MoPub's native ads solution lets us control the whole ad experience – from setting minimum price floors and prioritizing direct advertisers over house ads to blocking certain ad categories and limiting how often a user sees a creative," Feng said.

To prove the existence and uniqueness of viscosity solutions, let us see the following main hypotheses first.

end{aligned} (3.1) Before computing the solutions, let us state explicitly the limitations that RL, considered as an order 2 polynomial on (D^{2}), that is, (RL x)=a x^{2}+b x +c), has no negative roots implies.

Since we are looking for nodal solutions, let us consider the so-called nodal Nehari set mathcal{N}_{epsilon}^{pm}= bigl{ v intilde{H}; v^{pm}neq0 mbox{ and } I_{epsilon}' v v^{pm}= 0bigr}.

In order to describe further these solutions, let us consider their energy at the time t + that we denote by k 1, k 2, k 3, with ℓ ∗ < k 3 < k 2 < k 1 < ℓ 0. Let us define the points H i as { H i } = O ( P + ) ∩ Γ k i for i = 1, 2, 3.