Sentence examples for conditions for a solution from inspiring English sources

We know that one of the conditions for a solution to exist is that (M x)) is a convex set.

Necessary and sufficient conditions for the existence of a nonoscillatory bounded solution are more rare because it is much more difficult to find necessary and sufficient conditions for a solution of higher order equations.

Then, by Theorem 8, necessary conditions for a solution are begin{aligned}& tilde{c}^{Delta}(t)=-deltatilde{c}bigl sigma(t)bigr), end{aligned} (13) begin{aligned}& f(0)=-deltatilde{c}bigl sigmad{aligned} (14) Solving (13) (see t bigrm 2.74 in [26]) wend{alignedlde{c}(t)=c_{0}e_{circleddashdelta}(t,0), quad c_{0}=tilde{c}(0).

They provided necessary and sufficient conditions for a solution of a set-valued problems and some existence results for solutions of set-valued optimization problems and a generalized vector (mathbb{T} -inequality problem under T} -inequality of cone-convexity for set-valued maproblem

This is a necessary but not sufficient condition for a solution.

In cases (i) and (iii), the previous proposition givesnecessary and sufficient condition for a solution to be recessive.

We develop an architecture based on successive nested polygons and present a necessary and sufficient condition for a solution in this architecture to be feasible.

Moreover, I got a sufficient condition for a solution of stochastic differential equation to belong to the class Vh, and showed that solutions of stochastic differential equations have their densities in a special case by using the class Vh.

Given this assumption and the fact that only one SU is allowed to transmit in a given band, the problem has no solution when N<Q. Thus, a first trivial necessary condition for a solution to exist is that N≥Q.

For application to optimal transportation, the function B has the form B ( ·, u, p ) = | det c x, y | ρ ρ ∗ ∘ Y ( ·, p ) (4.3 where ρ and ρ ∗ are positive densities defined on Ω and Ω ∗ respectively, satisfying the mass balance condition ∫ Ω ρ = ∫ Ω ∗ ρ ∗, (4.4 which is a necessary condition for a solution u for which the mapping T u = Y ( ·, D u ) is a diffeomorphism.

Hence, the existence of a spanning arborescence in G is a necessary but not a sufficient condition for a solution to the VAFFP.