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The phrase "a small expectation that" is correct and usable in written English.
It can be used when expressing a minor hope or belief regarding a future event or outcome.
Example: "I have a small expectation that the project will be completed on time, despite the challenges we are facing."
Alternatives: "a slight hope that" or "a modest belief that".
Exact(1)
As part of a liberal, feminist, grammar-nerd circle of friends, I had a small expectation that we would all see "they" as a positive thing; what I didn't expect was fights to break out on my Facebook feed.
Similar(59)
For procurements over $2,500 but under $100,000, the acquisition is reserved for small businesses, unless there is a reasonable expectation that small businesses could not provide the best scientific and technological sources consistent with the demands of the proposed acquisition for the best mix of cost, performance, and schedules.
A less sympathetic observer might recall that neoconservative foreign policy thinking has all along indulged a romance of the ruthless — an expectation that small numbers of people might be able to play a decisive role in world events, if only their ferocity could be unleashed.
This reflects an expectation that short reads will be unable to resolve small, but presumably abundant, repeats.
If its nested position among hyphal fungi is correct, the unicellular thallus of Olpidium may have evolved by reduction from hyphae, contradicting an intuitive expectation that the smaller structure would predate the larger one.
College classes may only represent a small part of the week, with an expectation that academic hours are instead spent independently.
Report authors Gus Van Harten and Pavel Malysheuski point out that the "legitimacy" of the ISDS concept "appears to depend in part on an expectation that it benefits smaller businesses, not just large multinationals and the super wealthy".
Furthermore, there is no evidence that the neurons in human PVH nodules lack FLNa, and, the percentage of heterotopic neurons is usually small despite the expectation that, assuming random X-inactivation, ∼50% of neurons in the heterozygous PVH patients should lack FLNa [9].
Our results are consistent with the expectation that a small percentage of exomes will result in identification of an incidental finding under the ACMG recommendations.
First, it seems to have created an expectation that all totalitarian regimes were hollow at the core and would crumble with a small push from outside.
This phenomenon corresponds to our expectation that a smaller radius should be chosen at a point with high curvature so that smoothing effect can be reduced.
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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