Sentence examples for problems are used from inspiring English sources

Two standard problems are used to validate the method.

Two dimensional, multi-material test problems are used to compare the solution methods.

The space asymptotic solutions for both the direct and adjoint problems are used as trial functions.

Stochastic versions of standard Rayleigh Bènard convection problems are used to evaluate the approach.

Weighted CSP (Constraint Satisfaction Problems) are used to model and to solve constraint optimization problems.

These test problems are used to evaluate the performance of our algorithm.

Several potential problems are used to establish the validity of the coupled method.

Two well-known suites of benchmark functions and five engineering problems are used as case studies.

Linear and non-linear vibration problems are used to demonstrate the applications.

Five test problems are used as the first case study to generate the true Pareto front.

Two realistic, albeit hypothetical example problems are used to demonstrate the capability of the model.