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I not a native English speaker and have real difficulties in the usage of articles in paragraphs, especially the use of article `the'. For instance kindly consider the following paragraph:

In Fig. 11, we have given both analytical and simulated results. The analytical results are plotted using (4). On the other hand, for the simulation results, we have done numerical simulations. Furthermore, for the analytical results, we have approximated T by the discrete parameter t. It can be seen from the figure that the analytical results match well with the simulated ones for most of the illustrated range. However, the tail probabilities of the analytical results do not offer such a nice matching with the simulated results.

Now I am just concerned with the usage of "the" with the words analytical and simulated. Do "the" needs to accompany the words simulated and analytical results every time they are used in the paragraph after the first reference? Or I can omit "the" sometimes? If yes then where and what is the logic of doing so? I have been told that my usage of "the" is quite arbitrary, so need help.

Please also refer to Ram Pillai comment where the aesthetics of the sentence is being referred to. It has been pointed out that in the sentence:

It can be seen from the figure that the analytical results match well with the simulated ones for most of the illustrated range.

'the' is used four times.

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    Yes, you need the definite articles to clarify that you're still talking about all the set you first mentioned. Consider << They received a sum of money from their sponsors. Money was spent on improving facilities. >> vs << They received a sum of money from their sponsors. The money was spent on improving facilities. >> Mar 22, 2020 at 15:46
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    If you remove usages of the later in the paragraph because you think they sound repetitive, this will definitely give the impression to your readers that your usage of "the" is arbitrary. Mar 22, 2020 at 15:50
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    The article is associated with "results", not "analytical" or "simulated".
    – Hot Licks
    Mar 22, 2020 at 17:17
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    If we stick to the rules of using 'the', we will see the scope for using it in many places. That will confuse the writer/reader whether all these 'the's are required or not. E.g., in the OP's example, "It can be seen from the figure that the analytical results match well with the simulated ones for most of the illustrated range" where the is used four times. It affects the aesthetics of sentence making.
    – Ram Pillai
    Mar 22, 2020 at 17:42
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    'The' must be used wherever it is needed; it is exempt from the 'don't keep using the same word' mantra for lexical (as opposed to function) words. But 'wherever it is needed' takes decades to master. Mar 22, 2020 at 17:59

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As long as you are talking about your specific analytical results, you should use the definite article. If you are talking about some other analytical results, or some abstract analytical results in-general, you should not. Here's a contrasting example that refers to some results in-general

We have given both analytical and simulated results. The analytical results are plotted using lines. Analytical results are usually a result of X algorithm, but these analytical results are a result of the new Y analysis algorithm.

Or for a specific other set of analytical results

We have given both analytical and simulated results. The analytical results have a standard deviation of 1.2. Analytical results from Harvard's team generally have a standard deviation of 3.4 - 5.6, because those jerks can't measure as precisely as our team. Those analytical results are less reliable than the analytical results in this paper.

Dropping "the" (or "these") implies a different scope or meaning. Use consistent usage while you are referring to consistent results.

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