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The phrase "a special solution by" is correct and usable in written English.
It can be used when referring to a unique or tailored answer or method provided by someone or something.
Example: "The project was successful thanks to a special solution by our engineering team that addressed the client's specific needs."
Alternatives: "a unique solution from" or "a tailored answer by".
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(See [1].) In the nonautonomous case with constant delays, it has been proved by Pituk [2] that the value of the limit can be characterized in an implicit formula by using a special solution of the adjoint equation to (1.4) and the initial values.
They are ebonized with steel wool that was marinated overnight in a special solution of vinegar.
PFS is a special solution for special problems.
When "Lawrence" was last restored, in 1988, some of these flaws could be disguised by "wetgate printing," a process of dousing the print in a special solution.
Both of them are score functions which are the criterions for a special solution.
Dr. Sandell said that the process used a scrubber with a special oxidizing solution developed by Carrier.
Meanwhile, aussieBum has introduced tighty whities dipped in stress-busting elixirs of either ginseng or vitamin C; after 15 washes, the briefs must be resoaked in the special solution, also sold by aussieBum.
However, for the side effects of the one-step method such as by-product, special solution environment seem more fatal which severely restricts the application scope of nanofluids.
The organic smoke is created by a special glycol solution and reduces visibility to less than one foot.
By employing an iterative perturbation method the special solution is obtained for the fractional order model.
Additional verification is performed by comparison with a special analytical solution, and the dynamic stability analysis of pipes conveying fluid.
More suggestions(16)
a mild solution by
a temporary solution by
a unique solution by
a complete solution by
a simultaneous solution by
a sparse solution by
a weak solution by
a Final solution by
a stable solution by
a bacterial solution by
a proper solution by
a false solution by
a joint solution by
a successful solution by
a nontrivial solution by
a detailed solution by
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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