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The main properties of this class of substitute problems are discussed, especially the 'dual decomposition' data structure which enables the use of very efficient special purpose LP-solvers.
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Hence, in order to get robust optimal decisions, the structural optimisation problem with random parameters must be replaced by an appropriate deterministic substitute problem.
Hence, in order to get robust maximum load factors, the structural analysis problem with random parameters must be replaced by an appropriate deterministic substitute problem.
In order to get reliable/robust optimal designs with respect to random parameter variations, by using stochastic optimization methods, the original random structural optimization problem must be replaced by an appropriate deterministic substitute problem.
Job Availability & The Substitute Problem.
According to research published this week (see article), the basic technique of substituting problem-free mitochondria has now been tested in a laboratory and the researchers seem confident that, given the green light, they could bring a healthy child into the world.Most of a child's genes would come from the couple it would learn to call mum and dad.
Notwithstanding this, the next proposition allows substituting Problem 1 for Problem 2 without resort to such assumptions: Constraints (9)–(10) are equivalent to constraints(6)–(7) within the set of all candidate trajectoriesq that come to be well-behaved.
Substituting into problem (2.4), we see that problem (2.4) equals the linear programming problem (2.7).
But palm oil is high in saturated fats, so health advocates argue that using it substitutes one problem for another.
These critics argue, she writes, that "tattooing shifts the focus of women's issues from society to the self; that tattooed women are empowered only in their minds; and that women who find solace in tattoos are no different from women for whom shopping and exercise are substitutes for problem-solving".
As shown in Table 14, it excludes/includes just one driver ("method can be split" is substituted by "problem with hierarchy").
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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