Sentence examples similar to substitute condition from inspiring English sources

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.

For the blank in (1)′ we may substitute various conditions that undermine J.

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.

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).

Moreover, instead of depicting the explicit formula of (Sigma _{1}), we will try to find the other conditions to substitute the boundary value condition.

Substituting the conditions as in Eqs.

The characteristic equation analysis is achieved by substituting input conditions into variables UI, R and Otx in Eq. (1).

Substituting these conditions in the Langevin equation, equation (18), we obtain physical insight into the shortcomings of the conventional heuristic method.

We mentioned previously that the relation of deformation equivalence is a good general substitute for the condition that two manifolds belong to the same connected (resp.: irreducible) component of the moduli space.

His rationale was that one could substitute an untreatable condition for a treatable one - malaria being treatable with quinine.