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Exact(28)
In other words, the optimal objective value of problem (AP) is less than or equal to the optimal objective value of problem (DCLFP).
Let E E denote the objective value of problem (4) with given ρ.
For convenience, let τ to be the target value of problem (8) and problem (9).
The maximum objective value of problem (7), R(τ ms ), is obtained only when the equality in (7a) holds.
Then, the optimal value of problem (41) is given by p ⋆ = inf α n p ( α n ).
However, the optimal value of problem (15) is infinite, and this problem does not have an optimal solution.
Similar(31)
Although there has been some concern about the value of problem-based learning, over and above lecture-based learning, in terms of knowledge acquisition [ 3], there have been a number of studies conducted in a variety of countries which indicate that PBL does not disadvantage students [ 4- 8].
It is clear that, sometimes decision of using substitution and simultaneous ordering is not affordable and it depends on values of problem parameters, so we analyzed this too.
By a direct calculation, we get that the solution u satisfies the periodic boundary value condition of problem (2.1).
Let denote the optimal values of problems and, respectively, that is.
In addition, the global optimal values of problems (P) and (Q) are equal.
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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