a dual relation

USAGE SUMMARY

The phrase "a dual relation" is correct and usable in written English.
It can be used in contexts where two entities or concepts are interconnected or have a reciprocal relationship. Example: "In mathematics, a dual relation can often provide insights into the properties of the original relation."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

An answer is given in terms of a dual relation which involves positive measures in the disk with bounded Poisson balayage.

Journal of Functional Analysis

Based on the theory of first-order ordinary differential equations, a dual relation between two solutions in the dual local coordinates for a single layer in the laminate is derived, which is further arranged in a manner that can avoid the numerical instability usually encountered in the state space method.

Journal of Sound and Vibration

The extant commentary on the Categories mentions only a dual relation, that between words and things, whereas other sources attribute to Porphyry a triadic relation between words, concepts and things.

SEP

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

His philosophy has also presented to his Buddhist and Christian readers serious challenges, such as a notion of a non-dual relation between God and man, and an emphasis, unusual in Buddhism, on the embodied self in the historical world.

SEP

By further conducting a dual variant relation analysis, p-mTOR was positively correlated with VEGF-C and VEGF-D (p < 0.05).

BMC Cancer

By further conducting a dual variant relation analysis, p-Akt was positively correlated with p-mTOR/VEGF-C/VEGF-D (p < 0.05) and p-mTOR was also positively related to VEGF-C/VEGF-D (p < 0.05).

BMC Cancer

Solving from primal dual relation for different values of weights, we get the optimal values of the decision variables which are given in Table 1.

Journal of Industrial Engineering International

While the existing algorithm is based on the equivalence of G(D) and G P DD), the proposed algorithm uses the dual relation between H(D) and G P DD).

EURASIP Journal on Wireless Communications and Networking

In future, the dual relation between ideal space and kernel space can be further used to switch the computation of kernel space into that of ideal space, thereby realizing the application of commutative algebra to efficiently solve the machine learning problem.

EURASIP Journal on Wireless Communications and Networking

By the dual relation, it is easy to obtain the similar upper estimate of the Kolmogorov's N-widths d N ( T ) of operators from ℓ 2 m into ℓ ∞ m, i.e., d N ( T ) ≤ C ( log ( m N + 1 ) N ) 1 / 2 ∥ T ∥.

Journal of Inequalities and Applications

We showed that the linear system derived from the dual relation G P D T H D =[=[0] can be easily solved by doing at most n matrix inversions and at most n 2+2n matrix multiplications of the K×K coefficient matrices (S_{r}^{(j)}(Z))'s having a nice structural property, so that the computational complexity of the proposed algorithm is only O(K 4) compared to that of the existing algorithm O(K 6).

EURASIP Journal on Wireless Communications and Networking

Expert writing Tips

Best practice

When using "a dual relation", ensure the context clearly establishes the two elements involved and the nature of their relationship. Avoid ambiguity by specifying what is being related and how.

Common error

Avoid using "a dual relation" when the relationship is multifaceted or involves more than two elements. Choose a more descriptive phrase if the connection is not strictly binary.

Linguistic Context

The phrase "a dual relation" functions as a noun phrase, typically used to describe a connection or association characterized by two distinct aspects or components. Ludwig AI confirms its grammatical correctness.

Expression frequency: Rare

Frequent in

Science

60%

News & Media

20%

Academia

20%

Less common in

Formal & Business

0%

Wiki

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "a dual relation" is a grammatically sound phrase used to describe a connection characterized by two distinct elements. Ludwig AI confirms this, and its presence in academic and scientific sources suggests a formal register. However, its relatively low frequency indicates it's not a commonly used expression. When employing this phrase, ensure clarity regarding the interconnected elements and the nature of their relationship. Alternatives like "a reciprocal connection" or "a two-way relationship" might offer more specific or common ways to convey a similar meaning.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a reciprocal connection

Emphasizes the mutual or give-and-take nature of the relationship.

a two-way relationship

Highlights the interaction and influence flowing in both directions.

a binary association

Focuses on the presence of two distinct elements linked together.

a paired correlation

Suggests a statistical or causal link between two variables or entities.

a linked interdependence

Stresses the reliance of two elements on each other for survival or function.

a mirrored correspondence

Implies a similarity or reflection between two elements, like a mirror image.

a coupled interaction

Emphasizes the joint action or effect of two elements.

a dyadic bond

Refers to a close, personal connection between two individuals.

a twofold linkage

Highlights the existence of two distinct connections or links.

a mutual dependency

Stresses the need of both parties on each other.

FAQs

How can I use "a dual relation" in a sentence?

Use "a dual relation" to describe a connection or link between two things where both influence each other. For example, "The spines of Chilean columnar cacti have "a dual functional value" in relation to parasitism."

What's the difference between "a dual relation" and "a reciprocal relationship"?

"A dual relation" highlights the existence of two interconnected elements, while "a reciprocal relationship" emphasizes that the interaction is mutual or give-and-take. They can be similar, but "a reciprocal relationship" /s/a+reciprocal+relationship specifies the nature of the interaction more clearly.

What are some alternatives to using "a dual relation" in writing?

Depending on the context, you could use phrases like "a two-way relationship", "a paired correlation", or "a reciprocal connection".

Is "a dual relation" commonly used in academic writing?

While grammatically correct, "a dual relation" is not particularly common, suggesting there might be more precise or widely accepted ways to express the same idea in academic writing.