Sentence examples for substituting the condition from inspiring English sources

Substituting the condition (iv) in Theorem 19 by the condition that X is ordered complete, we can get the following result.

Now, we consider a new set of real functions, say Θ. Precisely, we modify the set Ψ by substituting the condition (psi_{3}) by another condition.

Substituting the conditions as in Eqs.

Remark 3.2 Compared with [16], we substitute the condition that F is positively homogeneous by the condition (iii), when F u,x,.) is C-explicitly quasiconvex.

He imposed two of the Arrovian conditions, universal domain and the Pareto criterion, but substituted the condition of minimal liberty for the other two (non-dictatorship and independence of irrelevant alternatives).

By substituting the initial condition we obtain (33).

Substituting the initial condition in (7) we obtain.

Substituting the initial condition, we obtain C= biggl(frac{sqrt{2}}{2}-frac{sqrt{6}}{4} biggr p_{1}.

Substituting the semiunitary condition (18) back into (15), the error under optimal training is (19).

end{aligned} Substituting the initial condition, we obtain C= biggl(frac{4sqrt{2}}{3}-2 biggr)p_{1}+ biggl(4- frac{8sqrt {2}{{3} biggr).

Upon substituting the boundary condition ϕ| s=l/2 = 0 into (10) we obtain ( F=sqrt{frac{P}{E_1I}}cdot frac{l}{2}, ) from which the value m for every particular load P could be unambiguously found.