at the coefficient of

USAGE SUMMARY

The phrase "at the coefficient of" is correct and usable in written English.
It can be used in mathematical or scientific contexts when discussing the value or factor associated with a particular variable in an equation or expression. Example: "In the equation, the term at the coefficient of x determines the slope of the line."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

In summary, so as to specify the relative importance of each factor on the model response, the implementation of a sensitivity analysis is mandatory, while in the RSM model, the relative importance of each input parameter can be determined simply by looking at the coefficient of each factor in the model equation.

Journal of Petroleum Exploration and Production Technology

However, looking at the coefficient of variation (CV) both nuclear phospho-p38 and cytosolic phospho-Hsp27 show a decrease of variation with increasing stimulation due to increasing steady state particle numbers.

BMC Systems Biology

In light of these studies ([ 17, 27, 28]) we chose to focus on the established logarithmic and linear (not segmented) models and have only included the power model at the coefficient of determination analysis, with subsequent analyses focusing on individual target digits which were likely to have been positioned with the aid of an external factor or strategy.

Behavioral and Brain Functions

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

Deviations for COPr, ECOPr and F at a generator temperature of ∼90 °C (cut off temperature) at which the coefficient of performance of the system is maximum are 0.9%, 1.8%, and 0.1%, respectively, for other working temperatures.

Energy Conversion and Management

The optimum generator temperature is found to be in the range of 65 70 °C at which the coefficient of performance is 0.36.

Applied Thermal Engineering

A project was carried out aimed at reducing the coefficient of thermal expansion (CTE) of photosensitive polyimide formulations (photoresists) through the incorporation of small amounts of an organoclay.

Polymer

At 25 °C, the coefficient of friction (COF) is ~ 0.2 for low V-contents and above 0.5 for high V-contents, respectively.

Surface and Coatings Technology

For the evaluation of HRV at rest, the coefficient of variation was used [ 18].

European Journal of Nuclear Medicine and Molecular Imaging

After controlling for traffic and other local sources at stops, the coefficient of distance from the main road was nonsignificant in most models.

Environmental Health Perspectives

We therefore reduced the threshold from 0.200 µg/L to 0.050 µg/L, the lowest concentration at which the coefficient of variation was ≤10%, for the clinical diagnosis of myocardial infarction.

British Medical Journal

The lowest limit of detection for the assay was defined by Myriad RBM as the lowest concentration of an analyte in a sample at which the coefficient of variation of replicate standard samples was 30%.

Arthritis Research and Therapy

Expert writing Tips

Best practice

When using "at the coefficient of", ensure the context clearly defines what 'at' refers to, such as a specific condition, temperature, or stage in a process.

Common error

Avoid using "at the coefficient of" without specifying the condition or parameter. For example, instead of "performance at the coefficient of 0.5", clarify with "performance at a coefficient of 0.5 under these conditions".

Linguistic Context

The phrase "at the coefficient of" functions as a prepositional phrase specifying the condition, level, or point at which a coefficient is being considered. Ludwig examples show its usage in scientific contexts.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "at the coefficient of" is a grammatically correct prepositional phrase primarily used in scientific and technical contexts to specify a condition or state under which a coefficient is being considered. As Ludwig highlights, the phrase's correctness hinges on a clear context. While grammatically sound, its relatively uncommon usage suggests a need for precision when employing it. For alternatives, consider "regarding the coefficient of" or "concerning the coefficient of" for similar expressions that focus on the coefficient as the subject.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

regarding the coefficient of

Replaces "at" with "regarding", focusing on the coefficient as the subject of discussion.

concerning the coefficient of

Similar to "regarding", this alternative emphasizes the coefficient as the topic under consideration.

in relation to the coefficient of

This alternative highlights the connection or association with the coefficient.

with respect to the coefficient of

Indicates a specific aspect or parameter being considered in relation to the coefficient.

pertaining to the coefficient of

Suggests that the topic is directly related to the coefficient.

in terms of the coefficient of

Focuses on expressing something using the coefficient as a measure or basis.

based on the coefficient of

Highlights that something is determined or calculated using the coefficient.

depending on the coefficient of

Emphasizes that a result or outcome changes based on the coefficient's value.

given the coefficient of

States that something is considered in light of a known coefficient value.

utilizing the coefficient of

Emphasizes the active use of the coefficient in a process or calculation.

FAQs

How is "at the coefficient of" used in scientific writing?

In scientific writing, "at the coefficient of" typically specifies a particular condition or level where a coefficient value is observed or applied. For example, "The reaction rate increased at the coefficient of friction of 0.8".

What are some alternatives to "at the coefficient of"?

Alternatives include "regarding the coefficient of", "concerning the coefficient of", or "with respect to the coefficient of", depending on the specific context.

Is it grammatically correct to say "at the coefficient of"?

Yes, "at the coefficient of" is grammatically correct when used to indicate a specific point, level, or condition related to a coefficient value. Its correctness relies on the context providing a clear referent for "at".

What does "at the coefficient of variation" mean?

"At the coefficient of variation" typically refers to a specific threshold or point on the coefficient of variation, which is a statistical measure of the dispersion of data points in a data series around the mean. For example, a threshold used to define acceptable data quality.