Sentence examples for any corresponding solution from inspiring English sources

More generally, if T C1(R)→C(R) and A1,A2 C(R)→C(R) are operators satisfying the generalized Leibniz rule equationT(f⋅g)="(Tf)⋅(A1g)+(A2f)⋅(Tg),f,g∈C1(R), and some weak additional assumptions, the operators A1 and A2 are of a very restricted type and any corresponding solution T has the formTf(x)="(c(x f′(x)|f(x)|p(x)sgn(f(x))+d(x ln|f(x)||f(x)|p(x)+1){sgnf(x)}.

Assume that and is a corresponding solution of problem (2.13), (1.10).

Moreover, according to recent theoretical results, for any initial condition the corresponding solution to Burgers' equation must converge to a constant as t → ∞.

If Failure counters of any solutions exceed Limit, the corresponding solution is abandoned, and scout bee is triggered.

Therefore, for any feasible q d, the corresponding solution of subproblem (P2-1) can be obtained by solving the following equivalent transformed optimization subproblem (18): begin{array}{l}underset{P_s,{P}_d}{ max}kern0.5em {eta}_{d,mathrm{S}mathrm{E}}left {P}_s,{P}_dright -{q}_d{P}_{d,{P}_dright -{q}_d{P}_{ds,mathrm{total}}left {P}_sthrm{t}.kern0.5em {C}_3,{P}_dright5end{array} (18).

In addition, by Lemma 4, for any initial condition φ ⋅ ≼ α λ, the corresponding solution satisfies x φ t ≼ x α λ t for all t ∈ T 0, +.

The corresponding solution algorithm is further discussed.

The technological difficulties and corresponding solution were proposed.

The corresponding solution is considered as the initial basic feasible solution of the original problem.

Furthermore, each interviewee's dialogue contains a phrase which can be interpreted as a method to extract a letter (or letters) from the corresponding solution word.

The wave-maker region for these eigenvectors is shown to be located close to the attachment line by computing the corresponding solution to the adjoint eigenvalue problem.