associated to a linear

USAGE SUMMARY

The phrase "associated to a linear" is not correct in standard written English.
The correct expression would be "associated with a linear." Example: "The results are associated with a linear relationship between the variables."

⚠ May contain grammatical issues

Science

Human-verified examples from authoritative sources

Exact Expressions

6 human-written examples

Abel functional equations are associated to a linear homogeneous functional equation with constant coefficients.

Advances in Difference Equations

The solution of a generalized Sylvester equation associated to a linear descriptor system and subject to some rank and regional pole-placement constraints, is studied in this paper.

Systems & Control Letters

They are associated to a linear array of VLIW processors which are interconnected using a simple tree network that ensures an O log(n)) data propagation time.

Real-Time Imaging

Indeed, performing this characterisation in the unit sphere (S^{N-1}) one sees that the eigenvalues are the critical points of the functional associated to a linear operator L in the unit ball partialSigma:=bigl{ v : Vert vVert =1bigr}.

Boundary Value Problems

The criterion is given in terms of a certain algebraic hypersurface S π in the maximal ideal of A associated to a linear projection π on with range Soc A), where we assume that dimk A>1.

Complex Analysis and its Synergies

A coordinate change is associated to a linear basis, (e_1,ldots,e_N) of ({mathbb {R}}^{N}) via begin{aligned} varvec{rho }_j varvec{x}_1,ldots,varvec{x}_N)= sum _{r=1}^{N} e_{jr}varvec{x}_r end{aligned} (11.26)(the (e_{jr} in {mathbb {R}}) and (varvec{x}_r in {mathbb {R}}^nu ).) To be a trifle pedantic, we note that X and (X^*) depend on N and (nu ).

Bulletin of Mathematical Sciences

Human-verified similar examples from authoritative sources

Similar Expressions

54 human-written examples

To this end we embed a non-skewselfadjoint representation of g into a more complicated structure, that we call a g-operator vessel and that is associated to an overdetermined linear conservative input/state/output system on the corresponding simply connected Lie group G.

Journal of Functional Analysis

The statistical framework we have used to address this hypothesis (described in detail in the methods section) relies on a regression model explaining the activity of a given pathway (which we remind is the first or second principal component computed from the gene expression matrix associated to a given pathway) as a linear combination of three chemical features.

Plosone

Pop [11] studied the GBS operators associated to a certain class of linear and positive operators defined by an infinite sum and discussed the approximation of B-continuous and B-differentiable functions by these operators.

Journal of Inequalities and Applications

Based on the finite element method a starting point corresponding to a non-linear solution associated to a given frequency and amplitude of excitation is computed.

Journal of Sound and Vibration

We need to understand the scale of fractional powers spaces associated to the linear operator A, especially the embeddings into known spaces like (L^{p}) spaces, and the ϵ-regularity properties (see Definition 2.4) of the nonlinearity f in this scale of spaces.

Advances in Difference Equations

Expert writing Tips

Best practice

Always double-check your grammar when using "associated"; the correct preposition is almost always "with" rather than "to". For example, use "associated with a linear model".

Common error

A common mistake is using "to" instead of "with" after "associated". To avoid this, remember that "associated" typically describes a relationship with something, not a direction to something. Use "associated with a linear function" instead of "associated to a linear function".

Linguistic Context

The phrase "associated to a linear" functions as a prepositional phrase attempting to link a subject with a linear element. However, Ludwig AI indicates this phrasing is not standard English, and the correct form is "associated with a linear".

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Ludwig's WRAP-UP

In summary, the phrase "associated to a linear" is generally considered grammatically incorrect. Ludwig AI highlights that the correct phrasing is "associated with a linear". While the phrase appears primarily in scientific contexts, it's essential to use the grammatically correct alternative, "associated with", to ensure clarity and credibility in writing. Remember to use "associated with" to maintain proper English usage.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

related to a linear

This alternative simply replaces "associated" with "related", maintaining the core meaning.

connected to a linear

This alternative replaces "associated" with "connected", suggesting a link or relationship.

linked to a linear

This alternative uses "linked" instead of "associated", implying a direct connection.

in relation to a linear

This alternative rephrases the connection using "in relation to", indicating a proportional or comparative link.

corresponding to a linear

This phrase suggests a direct correspondence or mapping to a linear element.

relevant to a linear

This alternative emphasizes the relevance or importance of the connection to the linear concept.

attributable to a linear

This phrasing suggests that something can be caused or explained by a linear factor.

tied to a linear

Implies a strong and inseparable connection with something linear.

correlated with a linear

Indicates a statistical relationship or correlation.

dependent on a linear

Highlights that something relies or is contingent upon a linear element.

FAQs

What is the correct preposition to use with "associated"?

The correct preposition to use with "associated" is almost always "with". For example, it's correct to say something is "associated with" a particular outcome, not "associated to" it.

What can I say instead of "associated to a linear"?

Instead of "associated to a linear", you can use phrases like "related to a linear", "linked to a linear", or "connected to a linear" depending on the context.

Is it ever correct to say "associated to"?

While rare, "associated to" might be acceptable in specific technical contexts, especially if referring to a direct assignment or mapping. However, "associated with" is generally preferred and more widely accepted.

How can I ensure I'm using "associated" correctly?

To ensure correct usage, always consider the nature of the relationship. If you're describing a general connection or relationship, "associated with" is almost always the right choice. If you’re thinking of a more direct mapping or assignment, review if "related to" would be even more appropriate.