Sentence examples for thus for large from inspiring English sources

Thus, for large enough (lambda>0), it is necessary that (Vert y_{lambda} Vert geqGamma).

Thus, for large enough (t>0), (p_{2}hleq y(t)leq h).

Thus, for large i, we have λ 1 ( μ i, τ i ) < 0, which contradicts the assumption.

Thus for large strains, Poisson's ratio decreases for the AC strain and increases for the ZZ strain with the increasing strain.

The results of the multi-objective optimization show that the tray holdups and diameter values of the columns strongly influence the control properties; thus, for large values of the tray holdups and diameters, the control properties were better.

Thus, for large, well-established firms, partnering with and/or later acquiring smaller biotech companies provides a viable option to committing a firm's R&D investment capital to internal development programs (Ahn, Meeks, et al., 2010).

Thus, for large-scale democratic movements to have enough energy to get off the ground, certain psychological and cultural building blocks are required.

Thus, for larger perturbations, the initial rise of s grows faster with the size of the perturbation than the increase in the final steady state.

Thus, for large-scale datasets, traditional hierarchical clustering methods quickly arrive at a bottleneck in terms of computational time and memory usage.

Then for sufficiently large,, and thus for sufficiently large, we have Consequently, we obtain, that is, (2.14).

Distributed algorithms are scalable and thus attractive for large networks.