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with the well-known results vs with well-known results

with the well-known results vs with well-known results 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:

with the well-known results is the most popular phrase on the web.

with well-known results

11,040 results on the web

with the well-known results

11,470 results on the web

More popular!

Some examples and use cases from the internet:

Some examples and use cases from the internet:

  • The integration of the ideas in this paper with well
  • known results for bounded noise. In low
  • known results in contractual theory allows us to understand the form of optimal wage contracts in different ...
  • contrasts with well
  • ... topology which has been introduced by C. Stricker [32]. Combining this insight with well known results from J. M´emin and L. S lominski [26]... Working Papers ...
  • Nov 9, 2015 ... Combining this insight with well
  • known results of MĂ©min and SĹ‚ominski ( SĂ©minaire de ProbabilitĂ©s de Strasbourg XXV, pp. 162–177, 1991) ...
  • noise regimes, we find that the la
  • Dec 24, 2015 ... The expression received for the sound velocity matches with the well
  • known results.
  • known results in both low and high temperature limits. The results of this ...
  • more, compatibility with the well
  • known results for this problem provides a test of the efficacy of the first
  • Jul 30, 2015 ... ... of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well
  • ... light scattering spectrum from a fluid undergoing a plane Couette flow. Our corrected results are in complete agreement with the well
  • known results.

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