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The phrase "a deep influence of" is correct and usable in written English.
It can be used when discussing the significant impact or effect that something has had on another thing, such as a person, idea, or culture.
Example: "The artist's work reflects a deep influence of classical music, which shaped her creative style."
Alternatives: "a profound impact of" or "a strong effect of".
Exact(2)
The related electrical resistance between the Pt electrodes was 36 kΩ and 35 GΩ, respectively, revealing a deep influence of the FIB exposure contamination, which reduces the resistance of about a six-order of magnitudes in this case.
Our data demonstrate a deep influence of age on the short-term variability of repolarization phases, and tend to suggest that only QTVI is able to characterize temporal myocardial repolarization lability in patients with CHF regardless of aging.
Similar(58)
Seyed Khalil created a musical group that still exists, the Baba Taher Ensemble, named for a classic Persian mystical poet whose verses have left a deep influence on the development of Iranian music.
To many infectious diseases, age has a deep influence on the rate of disease spread in a population, especially the contact rate [ 2, 20].
This complexity exerts a deep influence on the design of these interventions, and the methodology, the measurements, the analysis and the results of these initiatives.
In areas such as apoptosis, nervous system, ageing, etc. other articles and authors have had a deep influence on our knowledge of worm development.
Thermal treatment of systems with supported hexachloroplatinic acid has a deep influence on the final form of the metal (its oxidation state).
The dependence of the microstructure versus graphene content is expected to have a deep influence on the dielectric properties of the composites.
For Chungyalpa — who was working as a field conservationist for the World Wildlife Fund WWFF) at the time — that moment was a stirring reminder of the deep influence of religious traditions on human behavior.
Nowhere in Brazil is the deep influence of three and a half centuries of slavery so obvious, from the color of people's skin to the color of the food (often orange, from the ubiquitous use of dendê, or red palm oil); from the deep influence of the African-derived religious traditions of candomblé to the musical beats of axé and samba.
He is certainly right to stress the deep influence of Marcel Duchamp, whom he aptly characterizes as "a high priest of the irrelevant".
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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