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Generally use a comma to separate introductory phrases from the main clause (in this case, we needed one after the title).
In this paper, for convenience, we use a comma to denote partial differentiation, for example, (u_{,i}=frac{partial u}{partial x_{i}}), (u_{,ij}=frac{partial^{2}u}{partial x_{i}, partial x_{j}}).
In this section, we will use a comma to denote partial differentiation and adopt the summation convection, i.e., if an index is repeated, summation from 1 to N is understood, for example, u_{,i}u_{,k}u_{,ik}=sum _{i,k=1}^{N}frac{partial u}{partial x_{i}}frac {partial u}{partial x_{k}} frac{partial^{2} u}{partial x_{i},partial x_{k}}.
Use a comma to separate an absolute phrase.
Use a comma to separate an adverb clause.
Use a comma to separate dates and addresses.
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Provide a maximum of 5 Categories for each of your businesses using a comma to separate them.
A comma splice run-on sentence uses a comma to separate two independent clauses, as in "I played chess, the boy watched".
For example, if you're writing to your supervisor, Mr. Brown, write "Dear Mr. Brown," and remember to use a comma at the end of the sentence.
By Ryan Bloom May 28 , 2012From the first time we step into an English class, we're told that the rules matter, that they must be followed, that we must know when it's appropriate to use a comma and what it means to employ the subjunctive mood.
There are several formats that could be used, but we're going to use a Comma Separated Value (.csv) spreadsheet like Excel to organize our data.
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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