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The phrase 'for subsequent generations' is correct and usable in written English.
It is typically used to describe something that will have an impact on, or be relevant for, future generations. You could use it, for example, in the following sentence: "This legislation will have a positive impact on the environment for subsequent generations."
Exact(46)
A crossover rate of 80% was used to generate new docking solutions for subsequent generations, and one solution from each generation was propagated to the next generation.
A mutation rate of 0.02 and a crossover rate of 0.8 were used to generate new docking trials for subsequent generations.
A mutation rate of 0.02 and a crossover rate of 0.8 were used to generate new docking trials for subsequent generations, and the best individual from each generation was propagated over the next generation.
We are manufacturing rather than solving problems for subsequent generations.
His achievement became the chief model for subsequent generations.
Progress was slow, and assimilation rates for subsequent generations varied by ethnicity.
Similar(12)
CB conducted labwork for subsequent generation of the Myzostoma EST-library at the MPI for Molecular Genetics in Berlin Germanyy).
The resulting gel-purified products were then cloned into expression vector pFB-Neo for subsequent generation of stable cell lines.
Unambiguously mapped and unique reads were kept for subsequent generation of binding profiles and calling of peaks using MACS with an fdr < 0.05 [ 61].
Lactate metabolism includes energy-consuming shuttling processes to transport lactate from astrocytes to neurons for subsequent generation of pyruvate via lactate dehydrogenase and further processing in the citric acid cycle and mitochondrial respiratory chain [ 13].
Jo March and her sisters would become vital role models for many subsequent generations of American woman.
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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