and the corresponding boundary

USAGE SUMMARY

The phrase "and the corresponding boundary" is correct and usable in written English.
It can be used when discussing relationships or connections between different elements, particularly in contexts like mathematics, geography, or any field that involves delineating limits or edges. Example: "In this study, we will analyze the data points and the corresponding boundary that defines the area of interest."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

25 human-written examples

The governing equations and the corresponding boundary conditions are derived using the Hamilton's principle.

Composite Structures

The latter are translated into physicochemical properties and the corresponding boundary values for each property are defined.

Comptes Rendus Chimie

The singular solution is derived analytically which satisfies the governing equation and the corresponding boundary conditions containing the singularities.

Journal of Sound and Vibration

The Hamilton's principle is employed to obtain the differential equation of motion and the corresponding boundary conditions.

Composite Structures

Eight dynamic governing equations and the corresponding boundary conditions were derived through the application of Hamilton's principle.

Composite Structures

The geometry of the crack and the corresponding boundary conditions are described by means of a boundary element method with dislocation dipoles as fundamental solution.

Acta Materialia

Human-verified similar examples from authoritative sources

Similar Expressions

35 human-written examples

It is observed from the above figures that, for increasing the values of M, the temperature and nanoparticle concentration distributions increase and also the corresponding boundary layer thickness.

International Journal of Mechanical and Materials Engineering

Finally, points are projected onto the planes they belong to, and the corresponding boundaries are obtained from Voronoi's diagram.

Robotics and Autonomous Systems

At the end of the video, the path identifier held by the token with the minimum alignment cost allows the best event sequence to be traced back and the corresponding boundaries recovered.

EURASIP Journal on Image and Video Processing

Switching to quantile residuals re-scales the residuals and the corresponding boundaries as is shown in Fig. 2.

Computational Statistics and Data Analysis

One can infer from these figures that the temperature and thickness of the corresponding boundary layer of both phases will increase with rising in Ec, γ, and R. Here, Fig. 8a, determines that the effect of radiation is also to enhance the heat transfer.

International Journal of Mechanical and Materials Engineering

Expert writing Tips

Best practice

When using "and the corresponding boundary", ensure that the relationship between the elements and their boundary is clear and well-defined within the context of your writing.

Common error

Avoid using "and the corresponding boundary" if the connection between the elements and the boundary is vague or ambiguous. Clarify the relationship to prevent confusion.

Linguistic Context

The phrase "and the corresponding boundary" functions as a conjunctive phrase that links an element to its associated limit or edge. It clarifies a specific relationship between the primary subject and its defined border. Ludwig AI confirms this usage through numerous examples of similar applications in scientific and technical contexts.

Expression frequency: Common

Frequent in

Science

90%

Formal & Business

5%

News & Media

5%

Less common in

Academia

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "and the corresponding boundary" is a grammatically correct and commonly used expression, especially within scientific and technical contexts. Ludwig AI analysis reveals that it functions as a conjunctive phrase, effectively linking an element to its specific limit. Its primary purpose is to define scope and establish clear relationships. While versatile, ensure clarity when using it, as ambiguity can undermine its effectiveness. Related phrases such as "along with its associated border" or "together with the related perimeter" offer subtle variations in tone and emphasis.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

along with its associated border

Replaces "corresponding" with "associated" and "boundary" with "border" for a slightly less formal tone.

together with the related perimeter

Substitutes "corresponding" with "related" and "boundary" with "perimeter", emphasizing the enclosing nature of the boundary.

and the respective limit

Uses "respective" instead of "corresponding" and "limit" instead of "boundary", focusing on the limiting aspect.

including its matching border

Replaces "corresponding" with "matching" and "boundary" with "border", suggesting a direct correspondence.

with the concomitant margin

Employs more formal vocabulary, using "concomitant" for "corresponding" and "margin" for "boundary".

and the linked frontier

Uses "linked" in place of "corresponding" and "frontier" instead of "boundary", highlighting the connected nature and a more advanced or unexplored context.

coupled with its designated limit

Replaces "corresponding" with "designated" and "boundary" with "limit", emphasizing the defined aspect of the boundary.

alongside the analogous edge

Substitutes "corresponding" with "analogous" and "boundary" with "edge", suggesting a similarity or comparison.

and its parallel demarcation

Uses "parallel" instead of "corresponding" and "demarcation" instead of "boundary", focusing on the separation aspect.

incorporating the pertinent edge

Replaces "corresponding" with "pertinent" and "boundary" with "edge", highlighting the relevance of the edge.

FAQs

How can I use "and the corresponding boundary" in a sentence?

You can use "and the corresponding boundary" to link a data set or physical object to its limiting edge. For example: "Analyze the data points "and the corresponding boundary" to determine the area of interest."

What phrases are similar to "and the corresponding boundary"?

Similar phrases include "along with its associated border", "together with the related perimeter", or "and the respective limit" depending on the context.

Is it correct to say "and its corresponding boundary"?

Yes, "and its corresponding boundary" is grammatically correct. The choice between "and the" versus "and its" depends on the sentence structure and whether you are referring to a specific boundary already mentioned or a general boundary associated with the subject.

What is the difference between "and the boundary" and "and the corresponding boundary"?

While "and the boundary" simply refers to a boundary, "and the corresponding boundary" emphasizes a direct relationship or association between something previously mentioned and its specific boundary. The use of "corresponding" highlights this connection.