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The Ulam stability problem asks whether or not there exists a true solution of near.
In the following theorem we find that for some conditions there exists a true quadratic mapping near an approximately quadratic mapping.
In other words, we are looking for situations when the homomorphisms are stable, i.e., if a mapping is almost a homomorphism, then there exists a true homomorphism near it.
In other words, we are looking for situations when the homomorphisms are stable; that is, if a mapping is almost a homomorphism, then there exists a true homomorphism near it.
While it is mostly used to obtain an approximate model of a signal or image, for compression or coding purposes, it can also be applied for identification, estimation or even detection purposes, when there exists a true exact sparse representation, which is then the object of interest.
In his analysis of the Liar paradox, Russell assumed that there exists a true entity the proposition that is presupposed by a genuine statement (e.g., when I say that Socrates is mortal, there is a fact corresponding to my assertion and it is this fact that is called 'proposition').
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The assertion of a false or misleading financial report implies some belief that there could exist a true or not-misleading report.
The gingival margin-papillae measurement, however, found no difference where no difference in the position of the gingival margin existed, a true negative finding (Table 7).
Where copy number losses relative to chicken were detected, two possible explanations exist: a true copy number loss, or sequence divergence leading to lack of hybridization on the microarray.
Optimally, there exists a 'true' set of parameters, i.e., a set of parameters that reflects the biological reality.
Furthermore, it means that there exists a 'true' value θ* for the parameters θ such that (1) represents reality.
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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