Sentence examples for analytic solutions for from inspiring English sources

Explicit analytic solutions for the equilibrium conditions of one-stage symmetric systems are derived.

The numerical method is validated with analytic solutions for canonical problems.

Hence, here we provide new analytic solutions for the purification loops proposed.

Analytic solutions for the Airy wave are applied to set boundary conditions to generate water wave.

Note that all of these approaches propose analytic solutions for selected target designs, while our method numerically optimizes for phase patterns given arbitrary target designs.

Analytic solutions for the effectiveness factor are reported in all cases.

Approximate analytic solutions for generic quadratic and cubic non-linearities can be constructed.

The power of this formulation is demonstrated by analytic solutions for irreversible and nearly irreversible theories.

While, in general, polynomially complex, the inverse eigenvalue problem permits analytic solutions for small number of waveguides.

Thus, we find analytic solutions for the temperature profile and vapor and liquid pressure distributions along the pipe.

The corresponding power-series semi analytic solutions for the displacements and the internal forces of geocell reinforcement are also presented.