Sentence examples for problem has been obtained from inspiring English sources

The solution to this multi-objective optimization problem has been obtained using a New Hybrid Method.

The exact (in quadratures) solution of this problem has been obtained.

Exploiting the robust formulation (3) and the cost function template (9), the following robust optimization problem has been obtained: (14).

Because of existence of an eccentric vacant defect on the plate, the anti-symmetric problem has been obtained.

An approximate solution of the problem has been obtained by the Ritz method, which employs functions based upon the static deflection of polar orthotropic plates.

Based on initial FEM analyses, a better understanding of the problem has been obtained and a tool was developed that can assist in the design of more robust stacks.

For the case of small deviations from equilibrium, analytical solutions of the diffusion problem have been obtained.

The explicit solutions for this flow problem have been obtained by means of the homotopy analysis method, which exhibits the exponentially decaying behaviors at far field.

Although solutions for this problem had been obtained as far back as 1908 by Blasius [1], the problem is still of great interest to many researchers as can be seen from the several recent studies [2 5].

Systematic and satisfactory results on the weak solutions to the Cauchy problem to the fractional porous medium problem have been obtained, including the existence, uniqueness, comparison principle, and regularity to the suitable weak solutions.

Optimal solutions for this problem have been obtained for the UPA schemes, and novel quasi-optimal algorithms have been proposed for the APA strategies, exhibiting complexities that are linear in the number of resource units and users.