The phrase "associated with the solution" is correct and usable in written English.
It can be used when discussing elements, factors, or components that relate to or are connected with a particular solution to a problem.
Example: "The variables associated with the solution must be carefully analyzed to ensure accuracy in the results."
Alternatives: "linked to the solution" or "related to the solution".
Finally, the limitations associated with the solution are discussed.
These will take a back seat to the good feelings associated with the solution of a very important but secondary problem.
This approach is able to overcome most of the difficulties associated with the solution of mixture design problems.
The surface grains of the Cu2O film showed shape evolution associated with the solution pH and the orientation.
It is shown that this extension can reduce the computational costs associated with the solution of these problems.
Development of next-generation stochastic multiscale models whose parameters can be learned from available clinical data under uncertainty constitutes a research challenge made more difficult by the high computational cost typically associated with the solution of these models.
This is seen by comparing the amount of "wall heating" associated with the solutions to Noh's shock reflection problem computed in each reference frame.
To examine the specific hardware performance and trade-offs associated with the solutions presented here, the architecture is first verified in Matlab for the image parameters.
We are concerned with the existence of uniform attractors for the process associated with the solutions of the following non-autonomous p-Laplacian equation: u t − Δ p u + | u | p − 2 u + f ( u ) = g ( x, t ), ( x, t ) ∈ Ω × R. (1).
Define real subsets A : = [ b 1 − a, ∞ ) and B : = ( − ∞, b a − 1 ] of empty intersection whose Euclidean distance is D = 2 b 1 − a ≥ 0 and consider maps S, T : ( − ∞, b a − 1 ] → ( − ∞, b a − 1 ] being associated with the solutions of both dynamic systems which fulfil the necessary condition of Lemma 2.1 d ( x, S x ) ≤ d ( x, T x ) everywhere in their definition domain.
