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The phrase "availability to engage" is correct and usable in written English.
It can be used when discussing someone's readiness or willingness to participate in an activity or conversation.
Example: "I appreciate your availability to engage in this important discussion about our project."
Alternatives: "willingness to participate" or "readiness to engage".
Exact(5)
Indeed, the literature has shown that combining teaching with another job might reduce teachers' availability to participate in school meetings, as well as their availability to engage in additional school activities with colleagues (Maninger et al. 2011; Parham and Gordon 2011).
The younger age group may have been more likely to be working and have other competing role demands limiting their availability to engage in an interview.
The binding of 4E-BP1 to eIF4E is regulated by phosphorylation; 4E-BP1 hyperphosphorylation decreases this binding, increasing eIF4E availability to engage the cap initiation complex eIF4F.
Allocation of the GPs to the study groups was made randomly in most settings, through assigning a unique code to each GP, with the exception of Cyprus, where allocation was based on the GPs' availability to engage in the intervention.
By displaying availability to engage in talk about the topic proposed through a topic initiating practice, the participants in examples 1 3 make a bid for a topical line to be generated and, thus, make relevant for their interlocutors to either accept or reject the bid.
Similar(55)
Other factors previously shown to modify weight include accessibility to foods with high caloric density, availability of opportunities to engage in physical activity, and lack of public awareness of overweight health hazards [ 32, 33].
In particular, actual definitions of patient engagement do not fully consider the emotional (feeling) and cognitive (thinking) components of this experience, which, in our findings, appear to be crucial in understanding patient availability and capacity to engage in self-care.
Nevertheless, quasi-experimental designs can be an approachable option for populations such as children with autism whose cognitive abilities and availability to participate and to engage in testing and activities are variable.
While there has been a growing availability of material resources to engage with e-textiles, there has been very little work to date on researching and developing tools specifically to support an e-textile craft: tools that cater to the specific challenges that arise from the merging of distinct disciplines.
Consequently, the availability of cognitive resources to engage non-threat goals and task demands is decreased.
The literature on parental involvement however tends not to disaggregate gender, and makes assumptions about the availability of mother's time and willingness to engage in such programmes.
More suggestions(15)
access to engage
possibility to engage
availability to mobilize
availability to encourage
availability to cooperate
availability to undertake
availability to begin
capabilities to engage
capability to engage
availability to deploy
offer to engage
ability to engage
willingness to engage
provides to engage
available to engage
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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