Sentence examples for cases for the problem from inspiring English sources

We now discuss two special cases for the problem.

In order to obtain accurate results from CBR, effective retrieval and matching of useful prior cases for the problem is essential, but it is still a controversial issue to design a good matching and retrieval mechanism for CBR systems.

The following results will generalize this basic consequences to the CF case for the problem (1.1 - 1.3 1.1 - 1.3

Prove a base case for the problem.

Several structural results for special cases of the problem are derived and studied.

Furthermore, the numerical results for different particular cases of the problem are presented.

Numerical results for different particular cases of the problem are presented graphically.

In this case, for example, the problem {There are 3 apples/… apples were added/There are 7 apples.} satisfies the requirement.

In such cases, constraints for the problem cannot be expressed only in terms of the design variables; that is, they are implicit functions of the design variables.

For the general case of the problem (1.1 - 1.2), we can directly employ the classical augmented Lagrangian method proposed by [6].

BP converged for all proteins in the PDB dataset and for almost all cases for the hGH hGHR problems; in any event, the sum product marginals at termination were utilized to predict the positional marginal amino acid probabilities (Equation 9).