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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
under the relation of
Grammar usage guide and real-world examplesUSAGE SUMMARY
The phrase "under the relation of" is correct and usable in written English.
It can be used in contexts where you are describing a specific relationship or connection between two entities or concepts. Example: "The findings were analyzed under the relation of economic factors influencing consumer behavior."
✓ Grammatically correct
Science
Academia
News & Media
Alternative expressions(20)
in relation to
with respect to
regarding
concerning
in terms of
relative to
in connection with
pursuant to
by virtue of
on the basis of
under the direction of
under the scope of
under the backdrop of
under the ambit of
under the light of
under the control of
under the supervision of
under the guidance of
considering
through the lens of
Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Human-verified examples from authoritative sources
Exact Expressions
5 human-written examples
One very general way to investigate the space of possible mathematical systems is under the relation of interpretability.
Science
If she does so, then she indirectly ascribes the property of being hungry to Bill, under the relation of being a man uniquely seen.
Science
Let us define a world as a maximal fact under the relation of fact-containment: x is a world iff for every fact y, if x ≤ y, then x = y.
Science
1. Probably the best all-purpose understanding of what logics are would take them as equivalence classes of proof systems under the relation of having mutually interderivable rules, though even this ignores issues about translational equivalence across differing languages.
Science
In other words, [ j] is the equivalence class of vertex j under the relation of strong connectivity, as defined above.
Science
Human-verified similar examples from authoritative sources
Similar Expressions
55 human-written examples
The region (pi _g (L_i,L_j,L_k)) is classified into eight geometrical patterns (Fig. 3a) under the relations of variables (h_{mathrm{ref}}^i, h_{mathrm{ref}}^j) and (h_{mathrm{ref}}^k) (see Table 2).
Science
end{aligned} (10)The region (pi _{{mathrm{grp}},g} (L_i,L_j,L_{mathrm{grp}})), which is represented by Eqs. 9 and 10, is classified into four geometrical patterns (Fig. 3b) under the relations of the variables (h_{mathrm{ref}}^i, h_{mathrm{ref}}^j) and (h_{mathrm{ref}}^{mathrm{grp}}) (see Table 2).
Science
Under lossless situation, the relation of voltage and current at the head and end is: {mathrm{V}}_s= cosh beta lkern1em {V}_R+{Z}_c sinh beta l{I}_R (3) {I}_S=frac{1}{Z_c} sinh beta lkern0.5em {V}_R+ cosh beta lkern0.5em {I}_R (4).
Especially the attainment of a well-defined and rather homogeneous polarization of the LSF electrode (despite being a poor electronic conductor under reducing conditions) allows the relation of changes in the electrochemical surface activity to the observed changes in surface chemistry.
In Under Blue Cup, Rosalind Krauss explores the relation of aesthetic mediums to memory—her own memory having been severely tested by a ruptured aneurysm that temporarily washed away much of her short-term memory.
We have already considered relation, and under different views; but it was the relation of parts to parts, of the parts of an animal to other parts of the same animal, or of another individual of the same species.
Expert writing Tips
Best practice
When using "under the relation of", ensure the context clearly establishes a well-defined relationship between the elements being discussed. Overuse can make writing sound convoluted; consider more direct alternatives like "in relation to" or "regarding" for improved clarity.
Common error
A common mistake is using "under the relation of" when a simpler prepositional phrase would suffice. This can lead to unnecessarily complex sentences that obscure your intended meaning. Choose clarity over complexity to improve readability.
Source & Trust
84%
Authority and reliability
4.2/5
Expert rating
Real-world application tested
Linguistic Context
The phrase "under the relation of" functions as a prepositional phrase, establishing a specific connection or dependency between elements. As confirmed by Ludwig, it indicates the conditions or perspective from which something is being considered or analyzed. It provides a framework for understanding the link between concepts.
Frequent in
Science
60%
Academia
20%
News & Media
20%
Less common in
Formal & Business
0%
Encyclopedias
0%
Wiki
0%
Ludwig's WRAP-UP
In summary, "under the relation of" is a grammatically sound prepositional phrase that signifies a specific connection or dependency between elements. While Ludwig confirms its correctness, it is more formal and less common than alternatives like "in relation to" or "with respect to". Predominantly used in scientific and academic contexts, this phrase serves to set a framework for analysis and interpretation. When writing, prioritize clarity and consider whether a simpler alternative might better suit your intended meaning. The key is to maintain sentence structure and readability.
More alternative expressions(6)
Phrases that express similar concepts, ordered by semantic similarity:
in relation to
Changes the preposition from 'under' to 'in', offering a more common and direct expression of connection.
with respect to
Replaces the entire phrase with a more formal term, emphasizing consideration of a specific aspect.
in terms of
Indicates that the following information is being presented from a specific point of view or measurement.
regarding
A concise alternative that introduces a subject of discussion or connection.
concerning
Similar to 'regarding', but can imply a greater degree of importance or relevance.
relative to
Highlights the comparative aspect of the relationship, suggesting a scale or baseline.
in connection with
Emphasizes the link or association between two or more things.
pursuant to
Indicates that an action is taken or a decision is made according to a specific rule or guideline.
by virtue of
Suggests that something is true or happens because of a specific quality or characteristic.
on the basis of
Highlights the foundation or reason for a particular judgment or decision.
FAQs
How can I use "under the relation of" in a sentence?
Use "under the relation of" to describe how one thing is connected to or influenced by another. For example, "The data was analyzed under the relation of supply and demand."
What are some alternatives to "under the relation of"?
Alternatives include "in relation to", "with respect to", "regarding", or "concerning". The best choice depends on the specific context.
Is "under the relation of" formal or informal?
"Under the relation of" tends to be more formal and is often found in academic or scientific writing. For informal contexts, consider simpler alternatives.
When is it best to use "under the relation of" instead of simpler phrases?
Use "under the relation of" when you want to emphasize a specific, defined relationship or connection between two elements, particularly in technical or academic contexts. However, ensure it adds clarity rather than unnecessary complexity.
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Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Source & Trust
84%
Authority and reliability
4.2/5
Expert rating
Real-world application tested