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by the results of applying vs by the results of applying the

by the results of applying vs by the results of applying the which is much better to use in a sentence. Which is more popular in English form?

Looking on the internet deeply has found these results:

by the results of applying is the most popular phrase on the web.

by the results of applying the

1968 results on the web

by the results of applying

11,760 results on the web

More popular!

Some examples and use cases from the internet:

Some examples and use cases from the internet:

  • This is demonstrated by the results of applying the construction heuristic to the test instances provided by Dr. Frank Meisel, as shown in Table 3. Table 3.
  • Oct 8, 2013 ... The study is then supported by the results of applying the methodology on 40 test images from the RIDER breast MRI dataset. The results of the ...
  • This article presents a method for applying root cause analysis to problems of this class, followed by the results of applying the method to the sustainability ...
  • Apr 21, 2015 ... by the results of applying the method to the sustainability problem. The method is the System. Improvement Process. Process application led to ...
  • This representation begins with “ < ”, followed by the results of applying elemToStr to each element of in ascending index order interleaved with “ , ”, and ends ...
  • informed by the results of applying particular analytical research methods. (for example, textual or statistical). Whilst you should justify in the text which research  ...
  • This article presents a method for applying root cause analysis to problems of this class, followed by the results of applying the method to the sustainability ...
  • ... that are more accurate than that made by either the background knowledge alone, or by the results of applying an induction algorithm on the training data.

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