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Reply to "Its surveillance apparatus is (mostly) in order to monitor"

a) The aim of this paper is to clarify the fact that uniform asymptotic stability is equivalent to exponential stability for the half-linear differential system.

b) The purpose of this contribution is to clarify the fact that such algorithms need proper calculation of the update direction in undermodeled situations.

Do they respectively mean: The aim of this paper is in order to clarify ... and The purpose of this contribution is in order to clarify ... ?Or is "to clarify..." acting as an infinitival noun clause in both of them?

No, you cannot use "in order to" in those sentences. As I tried to explain to you in my previous post, "in order to" requires an action verb, but "to" will tend to sound more natural:

a.1) This paper has been written (in order) to clarify the fact that uniform asymptotic stability is equivalent to exponential stability for the half-linear differential system.

b.1) This contribution is provided (in order) to clarify the fact that such algorithms need proper calculation of the update direction in undermodeled situations.

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