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The phrase "acceleration of the progress" is correct and usable in written English.
It can be used when discussing the speed or rate at which progress is being made in a particular context, such as a project or initiative.
Example: "The acceleration of the progress in renewable energy technologies is crucial for combating climate change."
Alternatives: "speeding up progress" or "enhancement of progress".
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The State of the World's Children 1981-1982 advocathe the rapid acceleration of the development progress for the world's poorest billion people in order to significantly improve the lives of their children by the end of the twentieth century.
It may be hypothesized that the decrease in PAL expression before inoculation facilitates nematode infection, whereas the high level of PAL at 5 and 15 DAI reflects acceleration of the infection progress promoted in the OE root.
The aftermath led to an acceleration in the progress of suffrage in Britain – and, two years later, to the formation of the Manchester Guardian.
The strategic plan, in emphasizing equity and by focusing on the most disadvantaged and excluded children, families and communities, aims to support the acceleration of progress towards the fulfilment of the rights of all children.
This led to a dramatic acceleration of the process.
However, the reasonable uncertainties (derived from exploring a novel field and the exponential acceleration of scientific progress) require the adoption of a cautious and comprehensive approach to the subject.
UNICEF played a leadership role in consultations on the post-2015 development agenda, advocating for the inclusion of children, equity, sustainability and the acceleration of progress on the current Millennium Development Goals.
He argued that the acceleration of technological progress had led to "the edge of change comparable to the rise of human life on Earth". This thesis has long struck a chord here in Silicon Valley.
The rapid acceleration of technological progress, they say, has greatly widened the gap between economic winners and losers the income inequalities that many economists have worried about for decades.
The gay liberation movement sprung up around the Stonewall Riots in 1969, but the acceleration of gay rights progress in the last 10-15 years is astounding.
The new figures contain new perspectives on issues such as the acceleration of progress in some regions, differences between poor and rich countries, the number of children at risk if goals are not met, and much more.
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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