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It provides an approach to build a new theory by the limit of some sequence of formal theories and also has potential applications to scientific and engineering problems.
The following example will show that there exists some sequence of a partial cone metric, which is convergent but not strongly convergent if P is non-normal.
For some sequence of observations, each expert calculates the posterior probability of each phonetic class given the observation and its model.
So, t designates some sequence of relations and functions that satisfies TC, in the context of an antecedently given interpretation of V-o.
If, on input \(w\), some sequence of these choices leads to acceptance, then we say that \(\mathbf{N}\) accepts \(w\), and we say the nondeterministic time taken by \(\mathbf{N}\) on input \(w\), is just the number of steps taken in the sequence that leads to acceptance.
It is well known that the strict contractive condition d ( A ( x ), A ( y ) ) < d ( S ( x ), S ( y ) ) does not ensure the existence of common fixed points unless the space taken to be compact or some sequence of iterates is assumed to be a Cauchy sequence.
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This means that some sequences of 14 letters may not constitute a valid first block of InChIKey.
The proposed method to solve the inverse problem is based on the solution of some sequences of the direct problem by applying the Levenberg-Marquardt iteration method.
These results suggest that the copolymers exhibited some sequences of acetoacetate units with a microphase-separated morphology in agreement with the value of reactivity ratio previously determined.
In this paper, we present some sequences of polynomial operators for one-sided L p -approximation which realize the rate of convergence given in (2).
A PRVSM system is motivated by the observation that some sequences of phones that exist in one language rarely exist in another.
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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