Sentence examples for additional assumption is needed from inspiring English sources

An additional assumption is needed.

To establish the superlinear convergence of Algorithm 1, the following additional assumption is needed.

We now show an equivalent backward system of Problem A. In order to do this, one additional assumption is needed: (H3.3): There exists (alpha>0), and for each (tin[0,T]), (x,x'inmathbb{R}^{n}) and (u_{1},u_{2}inmathbb{R}^{ntimes d}), biglvert sigma bigl t,x,x',u_{1} bigr) - sigma bigl t,x,x',u_{2} bigr) bigrvert geq alpha vert u_{1}-u_{2}vert.

None of these additional assumptions is needed in this paper.

This contrasts with the other incomplete networks, where additional assumptions are needed.

In order to recover the original sources, additional assumptions are needed.

All investigations on the two time scales show that much of the analysis is analogous but, at the same time, usually additional assumptions are needed in the discrete case in order to overcome the topological deficiency of lacking connectedness.

Of course, some additional assumptions are needed depending on the considered boundary conditions, that is, we assume (1.3) and (1.5) for the Dirichlet case, (1.7) and (1.8) for the Neumann case, or (1.10) for the periodic case.

Because counterfactual outcomes are not observed, additional assumptions are needed for inference.

Additional assumptions are needed and various models have been proposed to predict long-term changes.

According to this scenario, some additional assumptions are needed to explain the absence of periodicity of the nucleotide variability in the nonCGI-TSSs.