Sentence examples for required for solutions from inspiring English sources

For an illuminating treatment of Book Three, see Bos (2001), Chapter 27. 2. This is not to say that these more complicated curves were required for solutions to these problems.

"We have no evidence of it working yet and until we have evidence of it working; it is hard to push it strongly as a policy" IT2 The multidimensional context of suicide and the intersectoral action required for solutions highlights the sensitivity of policy to the conflicting interests of each sector.

We discuss the minimum number of boundary conditions required for solution uniqueness and illustrate this with numerical examples.

This suggests an important overlap between Descartes' three classes of geometrical problems and Pappus's three classes, which, recall, were separated based on the types of curves required for solution: Planar problems are solvable by straightedge and compass, solid problems by conics, and line-like problems by more complicated curves that have an "inconstant and changeable origin".

This result indicates that a high degree of immobilization is required for protein solutions to accurately model tissue.

Workload balancing among cells tends to increase CMS processing costs, and hence the use of multiobjective optimization methods is required for CMS solutions that are optimal and feasible.

The contact time required for Cu II) solutions with initial concentrations of 10, 30 and 50 mg L−1 to reach equilibrium was 10 min (Fig. 5).

The resulting operator entails subsidiary computations (solutions of pressure Poisson and convection diffusion subproblems) that are similar to those required for decoupled solution methods; however, in this case these solutions are applied as preconditioners to the coupled Oseen system.

A decomposition technique is applied in order to reduce the computational effort required for the solution of the monolithic model, thus facilitating the solution of realistic industrial problems of moderate scale.

We detail the interfaces, protocols, operation and extensions required for our solution.

The computer time required for the solution was considerably less than in earlier models.