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The phrase "uniquely characterized" is correct and usable in written English.
You can use it to describe a particular person, place, or thing that stands out from the others. For example, you could say, "The town of Cambridge is uniquely characterized by its rich history and unique architecture."
Exact(58)
Due to the Wick expansion property, a quasifree state is uniquely characterized by its covariance matrix.
Wireless sensor networks are uniquely characterized by tight energy and bandwidth constraints.
Each tile algorithm is uniquely characterized by its sequence of reduction trees.
Therefore, areas must be determined such that each of them is uniquely characterized by mean/distribution pair.
Thus, A(e j ω ) can be uniquely characterized by θ A : A({e^{jomega }}) = e^{jtheta_{A} omega)}.
These terminated dendrimers are uniquely characterized by exhibiting blue fluorescence emissions (λexc = 370 nm, λmaxem = 440 nm).
Uniquely characterized connectives are sometimes spoken of as implicitly defined, but there are definite risks involved in the latter usage see Došen and Schroeder-Heister (1985).
A ray in a 2D space is uniquely characterized by three parameters: two for the location of its origin, and one for its direction.
Consequently, the decision regarding which method should be used may be difficult, especially if the accuracies of different approaches are not uniquely characterized.
As discussed in Section 6.1, quasifree states are uniquely characterized by the expectation values of the m x m y operators.
Similar(1)
For example, whether a given connective is uniquely characterized in the sense of being governed by rules which when reduplicated to govern a new connective render compounds formed from the same component sentences using the original and the new connective completely interchangeable is relative not just to a logic but to a particular proof system (set of rules systematizing the logic).
More suggestions(15)
only characterized
uniquely realized
uniquely appreciated
uniquely characterised
exclusively characterized
typically characterized
uniquely attributed
particularly characterized
uniquely recognized
unambiguously characterized
unequivocally characterized
uniquely ascertained
uniquely indicated
unusually characterized
uniquely articulated
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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