under the relation

USAGE SUMMARY

The phrase "under the relation" is correct and usable in written English.
It can be used in contexts involving legal, mathematical, or formal discussions where relationships between entities or concepts are being described. Example: "The findings were analyzed under the relation of economic factors to social behavior."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

13 human-written examples

One very general way to investigate the space of possible mathematical systems is under the relation of interpretability.

SEP

The interpretability hierarchy is the collection of all theories (satisfying our three simplifying assumptions) ordered under the relation ≤.

SEP

If she does so, then she indirectly ascribes the property of being hungry to Bill, under the relation of being a man uniquely seen.

SEP

Note that in the previous theorem (the parts (ii), (iii), (iv)) it is proved that the logical entropy and conditional logical entropy are invariant under the relation ≈.

Advances in Difference Equations

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.

SEP

The equivalence class of all theories mutually interpretable with T is called the interpretability degree of T. The interpretability hierarchy is the collection of all theories ordered under the relation ≤.

SEP

Human-verified similar examples from authoritative sources

Similar Expressions

47 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).

ROBOMECH Journal

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).

ROBOMECH Journal

We recognise that misclassifications of individuals' socioeconomic circumstances can cause under- or overestimates of the relation between socioeconomic circumstances and admission type/procedure use.

British Medical Journal

Under such conditions the relation between cooling rate (q0), and the corresponding frequency can be found from the two independently observed glass transitions.

Polymer

The main results are the behaviour of quantum weak mixing under products, and the relation to weak mixing of the classical limit (geodesic flow).

Journal of Functional Analysis

Expert writing Tips

Best practice

When using "under the relation", ensure the context clearly defines the nature of the relationship being discussed. Clarity is key, especially in technical or academic writing.

Common error

Avoid embedding "under the relation" within already complex sentences. Simplify the sentence structure for better readability and impact.

Linguistic Context

The phrase "under the relation" functions as a prepositional phrase, setting the context or condition for interpreting information or actions. Ludwig examples show its use in defining how things are ordered or classified within a given framework.

Expression frequency: Common

Frequent in

Science

70%

News & Media

18%

Encyclopedias

12%

Less common in

Formal & Business

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, "under the relation" serves as a prepositional phrase used to establish the context or condition for interpreting data or actions, particularly in academic and scientific domains. Ludwig AI confirms its grammatical correctness and appropriateness for formal writing. While alternatives like "in relation to" or "with respect to" exist, the choice depends on the desired level of precision and context. It's advisable to ensure clarity and simplicity in sentence structure when employing this phrase.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

in relation to

This alternative expresses a similar idea of connection or association, but uses a more common phrasing.

with respect to

This phrase suggests a specific aspect or viewpoint being considered, adding a layer of focus compared to the original.

subject to the connection of

This option suggests a dependency or conditional relationship, emphasizing the constraint implied by the relation.

governed by the relationship

This implies a rule or principle dictating the interaction, highlighting a controlling influence.

based on the connection of

Highlights the foundation or premise upon which something else is built, focusing on dependence.

pursuant to the relationship

This option suggests an action taken in accordance with a specified relationship.

dependent upon the relation

Emphasizes the reliance of one element on another through the relation.

conditional on the connection

Highlights the conditional nature of the relationship, where one thing is true only if the other is.

according to the terms of the relation

This suggests adherence to a specific set of rules or conditions defined by the relation.

by virtue of the connection

Indicates that something is a result or consequence of the relationship.

FAQs

How can I use "under the relation" in a sentence?

Use "under the relation" to specify the context or condition in which something is being considered. For example, "The data was analyzed "under the relation" of income and education".

What are some alternatives to "under the relation"?

Alternatives include "in relation to", "with respect to", or "based on" depending on the specific context.

Is it correct to say "under the relation" in formal writing?

Yes, "under the relation" is appropriate for formal writing, especially in academic and scientific contexts, but ensure the relationship is clearly defined for your audience.

What's the difference between "under the relation" and "in light of"?

"Under the relation" specifies a direct connection or condition, while "in light of" implies considering something due to new information or understanding. They are not interchangeable.