Sentence examples for solutions are derived for from inspiring English sources

General solutions are derived for the solute concentration by successive implementation of finite Hankel and Laplace transforms assuming different sets of boundary conditions and linear sorption kinetic process.

Closed-form solutions are derived for these cases.

Analytical solutions are derived for their self-equilibrium analysis.

Explicit solutions are derived for the mutli-stage cracking process.

Real fundamental solutions are derived for each eigenvalue distribution.

The complete exact solutions are derived for the full sub-diffusive fluid flows.

The closed-form solutions are derived for these two types of problems, using Fourier series.

Explicit solutions are derived for mirror geometries of CY threefolds with hyperbolic singularities.

Analytical solutions are derived for the various transport models, wherever possible.

Closed-form solutions are derived for the non-dimensional boundary value problem.

Analytical solutions are derived for steady-state situations to validate the general numerical approach.