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In this section, we present some propositions that will be used in Sections 4-11.
In this section, we give some definitions and present some propositions of solutions for the problem (1.1 - 1.2 1.1 - 1.2
Based on similarities between bacterial respiration and electrodic processes, we here present some propositions about microbial activities in electrochemical systems, which justify why microorganisms could interact with polarized surfaces and how these interactions could potentially be utilized for bioengineering as well as life science issues.
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Before formulating the results on a relative controllability of (1.6), we present some auxiliary propositions.
Next, we present some important definitions, propositions and theorems from [36].
Now, we present some definitions and propositions in a partial b-metric space.
Now we present some definitions and propositions in a G b -metric space.
In this section, we present some basic definitions, propositions and relevant relation-theoretic variants of some metrical notions namely: completeness and continuity.
However, G ( x, y, z ) = max { d ( x, y ), d ( y, z ), d ( z, x ) } is a G b -metric on ℝ with s = 2. Now we present some definitions and propositions in a G b -metric space.
Before stating and proving our results, we present some definition and proposition in b-metric space.
First, we present some known definitions and propositions.
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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