Sentence examples for extend the solutions from inspiring English sources

To extend the solutions globally we build on an idea due to Colliander, Holmer and Tzirakis.

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.

It is possible to extend the solution on the right of to some where the solution will assume the value.

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.

Now we need to extend the solution ϕ of equation (3.1) to the domain ((-infty,xi^)) and ((xi^,+infty)).

Thus, z ( x ) can be used to extend the solution y ˆ ( x ) on [ 0 ; a 2 ].

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 ) = ∅.

Next, we extend the solution of RC-MCSB problem to our target problem and present a novel and efficient bottom-up solution.

Then, the same idea is in turn applied to extend the solution of a reduced matrix eigen-decomposition problem to approximate the eigenvectors of an SPSD matrix.