Sentence examples for extend the solution to from inspiring English sources

In order to extend the solution to a maximal interval we can apply the Theorem 2.3 [[14], p. 97].

In some cases, it is desirable to extend the solution to the interval [ 0, N ], see Remark 2.1 hereafter.

This procedure can be repeated to extend the solution to the entire interval [0, T] in finitely many steps.

With the help of (11) we then can extend the solution to the interval ( q a, q b ) provided ( q a, q b ) ∩ ( a, b ) = ∅.

This procedure can be repeated to extend the solution to the entire interval in finitely many similar steps, thereby completing the proof for the existence and uniqueness of mild solutions on the whole interval.

If we extend the solution to (1.6) to the interval by symmetry, we get a solution to the same problem (1.6) with the condition at, substituted by a condition at, Conversely, symmetric solutions to this latter problem are solutions to the original problem (1.6).

Now we need estimates which allow us to extend the solutions to the whole interval ([0, T]) and pass to limit as (mrightarrowinfty) and (epsilonrightarrow0). Hence, uniform estimates with respect to m and ϵ are needed.

Note that despite the fact that the case n = 2 is solved in the previous section, the new material presented below extends the solution to all the cases.

It also considers the problem of minimizing a cost function or performance measure; then extends the solution to problems with equality constraints.

This approach takes into account the a priori structural constraints of the synthesis problem, analytically extending the solution to the subdomain of synthesis as well as finding the tolerances for small perturbations of the objective functional.

This article extends the solutions to the prediction problem for factorizable real random signals to the class of improper complex-valued random signals.