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Exact(6)
Figure 2 Exact and approximate solution of the example.
The respective exact solution of the example is found using a commercial solver (CPLEX).
This prevents the learner from merely duplicating the characters and symbols that compose the text and solution of the example.
Figure 2 shows a graphical representation of the exact solution and, for m = n = 15, the approximate solution of the example.
In addition, our Theorem helps to explain why the solution of the example above satisfies the standard conditions (11)–(13) despite not being piecewise differentiable.
A nonlinear limit-state function example was provided to validate the accuracy and efficiency of the hybrid algorithm by comparing the algorithm's solution with the exact solution of the example.
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Open image in new window Figure 2 The convergence of the sequence { v ̂ p ( t ) } Open image in new window to the exact solution of Example 2. Example 3. The third example, is the following integral equation: u ( t ) = e t sin ( e t ) − ∫ 0 t e s + t cos ( u ( s ) ) ds, 0 ≤ t ≤ 0. 74.
Moreover, Fig. 3 illustrates the optimal solution of the examples after the grand coalition (i.e. S 15 = {1, 2, 3, 4}) and demonstrates that each customer is allocated to which depots.
A simple application of the solution to the example problem of a clamped strip subject to tension is calibrated and the results found used to infer the slip and separation lengths.
Numerical solutions of the example are given in Table 2 and Figure 2.
Also, Figure 5 shows the exact and the approximate solution of this example.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com