Sentence examples for the solution define from inspiring English sources

In particular, a Lie algebraic criterion is presented that implies that all finite-dimensional projections of the solution define random variables which admit a density.

where ϕ is the solution defined above.

Figure 2 Error curves for the solution defined from (20) Figure 3 Error curves for the solution defined from (21).

By a direct computation, it follows that the solution defined by (2.2) satisfies (2.1).

Figure 5 Error curves for the solution defined from (23), respectively from (24).

The control is the trace on the fixed endpoint of the solution defined in the cylindrical domain.

Therefore, we choose to have the solution defined on the same mesh of elements at every timestep.

We regard the solution defined above with such a step-like contrast structure as being smoothly connected by two pure boundary solutions:, and,.

That is, some functional in terms of a norm of the solution defined in the sense of Theorem 2.1 satisfies a differential inequality that necessarily implies that such norm blows up in finite time.

To this end, we again consider the solution defined by and, if necessary, always without loss of generality, we can replace by and by since the solution has a finite derivative the interval.

Note that each equation given in each of (a), (b) and (c) is not equivalent since our method requires knowledge of the fractional derivatives or integrals of the solution defined at zero as well.