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The phrase "significantly constrained" is correct and can be used in written English.
It describes a level of restriction or limitation that greatly impacts the situation. Example: The company's financial resources were significantly constrained, causing them to limit their production and marketing efforts.
Exact(38)
Harley says film distribution is "significantly constrained in Australia by the monolithic structure of exhibition", pointing to the decades-long suburban multiplex duopoly of Hoyts and the Greater Union-Village Roadshow-Birch Carroll and Coyle combine.
To be eligible, homeowners must have been trying to rebuild but found that they were "significantly constrained" by the pre-storm values of their homes.
Therefore, the secondary throughput would be significantly constrained, and the secondary system would suffer from a long latency.
However, the performance of currently available transducers for HI and SHI is significantly constrained by their limited bandwidth.
Significantly constrained attachment of Bacillus sp. bacteria on the surfaces of the Cu-containing coatings was observed, suggesting their excellent antifouling performances.
However, frequency domain watermarking for a coding DNA sequence is significantly constrained because the transformation and inverse transformation must be performed while completely conserving the amino acid sequence.
Similar(22)
Defeating Isil at its source will significantly constrain Isil's reach into the west".
Because capital is more mobile than labor, competition among governments significantly constrains how capital is taxed.
Some quite basic seismic observations will significantly constrain compositional and structural models of Mars' interior.
Lower rates of car ownership significantly constrain immigrants' daily activity space.
These requirements significantly constrain the functional form that the artificial viscous force can have.
Related(13)
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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