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However, there is not yet direct proof for this.
It is theoretically proved and experimentally observed that this activation characteristic is almost independent of frequency, which provides direct proof for the effectiveness of VI NES in a broad frequency bandwidth.
Recently, Zhou and his collaborators [7] give a direct proof for McKean's theorem [5].
This is a direct proof for less oxygen content for the upper layers of the thicker film.
This is additionally supported by EDAX analysis which provides the direct proof for the adsorption of fluoride ions onto AHAC.
We give a direct proof for the following useful lemma, which can also be deduced from Theorem 2.3.9 in [24].
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These liftings provide direct proofs for the classical theorems of Sarason and of Sz.-Nagy and Foias, as well as a bidimensional version of Sarason′s theorem, and a theorem of Sz.-Nagy-Foias type for two pairs of dilations.
New (direct) proofs for some criteria are provided.
According to Hafner, Bolzano prefers direct proofs for two reasons: 1) indirect proofs proceed by a detour [Umweg] and contain redundant premises, 2) indirect proofs always contain a false premise which cannot be admitted as the ground of other truths.
In contrast with [23], we give a direct proofs for the continuity and compactness of F and G without using a continuity result on superposition operators.
First Saworotnow in [5] proved the strong Schwarz inequality, but the direct proof of that for a semi-inner product -module can be found in [6].
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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