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The phrase "smaller time period" is correct and usable in written English.
You can use it when referring to any timeframe that is shorter or more limited than another timeframe. For example, "I need to get this project done within a smaller time period, so I will need some extra help."
Exact(2)
The Education Department data cover a smaller time period, reporting tuition from the academic year that began in the fall of 2009, but calculating increases from 2006 to 2008.
In a smaller time period, Apple has sold more than half a billion iOS devices, including more than 100 million iPads.
Similar(58)
The duration of the trials varied considerably but did not necessitate dividing the meta analysis into smaller time periods with separate meta-analyses for each period.
However, our diary-based "gold standard", is not validated by interviews and likely biased by under reporting of locations with smaller time periods.
In a small time period ( left[ {t,t + Delta t} right) ), there are some conclusions.
On the contrary, to transfer huge files it would be better to exploit paths with broad bandwidth, even if available only for a relatively small time period [53].
The slope of the i-v curve at a small time period is the same, R0−1, in both cases whereas the slope on return sweep depends on the window function.
The 'If' value of the study area is 1.29 which specifies that the low infiltration capability and causes more water flow in small time period during the rainfall season (Bhatt and Ahmed 2014).
The first part is a small time period during which the base station is kept silent to allow for noise variance estimation at the receiver as it was already explained.
Indeed, the direct method for recording blood pressure depends on the catheterization of arterial vessels that are functional during a small time period.
Although a relatively small time period, gaps of approximately 15 days would be expected to lead to significantly lower serum levels of palivizumab [ 23].
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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