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

Both phrases are correct, but they are used in different contexts. 'With the well-known results' is used when referring to specific, previously mentioned results that are well-known. 'With well-known results' is used when talking about results in general that are widely recognized.

Last updated: March 19, 2024 • 1082 views

with the well-known results

This phrase is correct and commonly used when referring to specific, previously mentioned results that are well-known.

This phrase is used when you want to emphasize that the results being mentioned are already familiar or famous.

Examples:

The study confirmed our suspicions, with the well-known results clearly supporting our hypothesis.
She presented the project with the well-known results from previous research.

Show examples from the web [+]

Dec 24, 2015 ... The expression received for the sound velocity matches with the well-known results in both low and high temperature limits. The results of this ...
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-known results.
... light scattering spectrum from a fluid undergoing a plane Couette flow. Our corrected results are in complete agreement with the well-known results.
more, compatibility with the well-known results for this problem provides a test of the efficacy of the first-principles-based simula- tion methodology employed ...

Alternatives:

with those well-known results
with these well-known results
with some well-known results
with certain well-known results
with familiar results

with well-known results

This phrase is correct and commonly used when talking about results in general that are widely recognized.

This phrase is used when you want to refer to results that are well-known in a general sense, without specifying particular results.

Examples:

The company has a reputation for producing products with well-known results.
The research team is known for their work with well-known results in the field.

Show examples from the web [+]

Nov 9, 2015 ... Combining this insight with well-known results of Mémin and Słominski ( Séminaire de Probabilités de Strasbourg XXV, pp. 162–177, 1991) ...
... 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 ...
The integration of the ideas in this paper with well-known results in contractual theory allows us to understand the form of optimal wage contracts in different ...
contrasts with well-known results for bounded noise. In low-noise regimes, we find that the la- bel complexity is well-characterized by a simple combinatorial ...

Alternatives:

with widely recognized results
with famous results
with renowned results
with established results
with acknowledged results

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