Sentence examples for deduce the solution from inspiring English sources

First, the theory of elastic wave propagation is used to deduce the solution of free field ground motion on the axis of tunnel under incident SH wave without considering the existence of the tunnel.

In [40], the author discussed the controllability of fractional control systems with control delay, and only used the Mittag-Leffler function to deduce the solution.

Once these are deduced, the solution comes out of the expression at the bottom, which needs to be evaluated using the "redefined" operations.

KD independently deduced the solution for the stillbirth crossover phenomenon.

The differential form of single-phase seepage equation and the analytical solution for pressure diffusion equation are adopted to deduce the analytical solution for shape factors in transient pressure diffusion equation.

The queuing theory and convex optimization are used to deduce the optimal solution in this framework theoretically.

Finally, we deduce the exact solutions of the combined ZK-mZK equation via the semi-inverse variational principle.

We conclude the paper by applying this fact to deduce the existence of solution for the three algorithms mentioned at the beginning of this section.

As an application, we obtain a procedure which allows to easily deduce the existence of solution for the recurrence equation of certain algorithms.

Thus by Theorem 4.3 we deduce the uniqueness of the solution of our integral equation.

Laminated theory was employed to deduce the closed-form solutions to static stress and natural frequency.