by applying the trace

USAGE SUMMARY

The phrase "by applying the trace" is correct and usable in written English.
It can be used in contexts where you are discussing the process of utilizing a trace, such as in mathematics, computer science, or data analysis. Example: "The results can be improved by applying the trace to the dataset, allowing for better insights."

✓ Grammatically correct

Science

Formal & Business

News & Media

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

By applying the trace inequality we have (4.26).

Journal of Inequalities and Applications

Then, by applying the trace theorem [27, Section 1.8.2] to the space, we obtain the assertion.

Boundary Value Problems

By applying the trace theorem [27, Section 1.8.2], we have the following.

Boundary Value Problems

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

Via applying the trace identity proposed by Tu [6], we could deduce the Hamiltonian structure of the ((1+1))-dimensional discrete integrable hierarchy (6).

Advances in Difference Equations

See Tables  5, 6 and 7.>>> -wrap-foot> These results can be understood by applying the path diagram tracing rules to Fig.  3 (bearing in mind αk = 0).

Behavior Genetics

Another result of interest is that, in 2014, Hansen [3], among other things, gave new and simplified proofs of the Carlen-Lieb theorem concerning concavity of certain trace functions by applying the theory of operator monotone functions.

Journal of Inequalities and Applications

Duplicates were marked, indels were realigned, base quality scores recalibrated, and variants identified and simultaneously genotyped for our trace data by applying the GATK MarkDuplicates, IndelRealigner, BaseRecalibrator, and HaplotypeCaller algorithms respectively.

F1000Research

Moreover, bias was further reduced by applying the algorithm to exactly the same ROIs traced during manual analysis.

Biomedical Optics Express

In the default setting, the user can choose from all the possible instances of the reduction rules by reducing the input, and proceed by applying the rules incrementally to observe a possible computation trace of the DNA soup.

Bioinformatics

In this study, the geometrical distortions such as the pen curvature, uneven paper speed and skew on seismic traces have been corrected by applying the formula of Grabrovec and Allegretti (1994) and Samardjieva et al. (1998).

Earth, Planets and Space

The figure also shows the delay lower-bound obtained by applying the BSDBR benchmark algorithm (presented in Section 6) on the topology traces collected from on-body experiments.

EURASIP Journal on Wireless Communications and Networking

Expert writing Tips

Best practice

When using "by applying the trace", ensure the context clearly defines what the 'trace' refers to, be it a mathematical function, a data analysis technique, or a forensic process.

Common error

Avoid using "by applying the trace" without clearly specifying what kind of trace is being applied. Ambiguity can confuse the reader and weaken your statement.

Linguistic Context

The phrase "by applying the trace" functions as an adverbial phrase, modifying a verb by specifying the method or means by which an action is performed. As Ludwig AI points out, it often appears in contexts where specific techniques are discussed.

Expression frequency: Rare

Frequent in

Science

60%

Formal & Business

20%

News & Media

20%

Less common in

Wiki

0%

Encyclopedias

0%

Reference

0%

Ludwig's WRAP-UP

In summary, "by applying the trace" is a grammatically correct phrase used to indicate a specific method or technique. As Ludwig AI explains, it is most commonly found in scientific and formal contexts. While not very frequent, its proper usage contributes to clarity and precision in technical writing. Remember to clearly define what 'trace' means within your specific domain to avoid ambiguity. Consider alternatives like "through the application of the trace" or "using the trace" for stylistic variation.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

through the application of the trace

Replaces "by applying" with a more formal phrasing using "through the application of".

utilizing the trace

Replaces "applying" with the more concise verb "utilizing".

employing the trace

Similar to "utilizing", but potentially in a more technical context.

using the trace as a method

Highlights the trace as a tool or technique being utilized.

making use of the trace

Emphasizes that the trace is being actively used as a resource.

via the trace's implementation

Focuses on the practical implementation of the trace.

with the trace being applied

Changes the structure to passive voice, emphasizing the trace.

by means of the trace

Uses a more formal and concise construction to indicate the method.

through trace analysis

Shortens the phrase by directly referring to the method of trace analysis.

in applying the trace

Inverts the phrase's structure, placing emphasis on applying the trace.

FAQs

How can I rephrase "by applying the trace"?

You can use alternatives like "through the application of the trace", "using the trace as a method", or "utilizing the trace" depending on the specific context.

In what contexts is it appropriate to use "by applying the trace"?

This phrase is suitable in technical fields such as mathematics, computer science, and data analysis where the term "trace" has a specific meaning. It can also be used in formal settings such as science and business.

Is "by applying the trace" grammatically correct?

Yes, "by applying the trace" is grammatically sound. The phrase uses a preposition followed by a gerund and a noun phrase.

What is the difference between "by applying the trace" and "through "trace application""?

"By applying the trace" emphasizes the action of applying, while ""trace application"" focuses on the method or process itself.