Sentence examples for modified problems from inspiring English sources

Then, by using the truncation technique and the upper and lower solutions, we estimate a-priori bounds of modified problems.

To prove this result, we will need four lemmas and we will consider the following modified problems for (j = 0, 1, 2): begin{aligned} &x^{Delta}(t) + xbigl sigma(t bigr) in F_{j}bigl t,xbigl( sigma(t bigr bigr), quadDeltambox{-a.e.

We shall show that the sequence of modified problems (17) is such that each problem has a unique solution, which is uniformly bounded, together with its first and second order derivatives.

Consider the modified problem.

Step 1: The modified problem.

Let us consider the following modified problem.

Now we consider the slightly modified problem (1.3).

Then, we consider the following modified problem: (217).

In Section 3 we prove the existence of nodal solutions of the modified problem.

Then Problem (40) can be solved optimally by directly applying Algorithm 1 with the modified Problem P1 to check the feasibility.

The results demonstrate the effectiveness of the modified problem-oriented branch and bound algorithm in solving relatively large size cell formation problems.