is defined upon

USAGE SUMMARY

The phrase "is defined upon" is not commonly used in written English and may be considered awkward or incorrect in some contexts.
It can be used when discussing mathematical functions or concepts that are established based on certain criteria or conditions. Example: "The function f(x) is defined upon the interval [0, 1], where x represents the input values."

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

6 human-written examples

The detector is defined upon three different stages.

EURASIP Journal on Advances in Signal Processing

where F(A) is defined upon matrix A = [a ij ] such that (16).

EURASIP Journal on Wireless Communications and Networking

Finally, Markov random field is defined upon this graph to extract road network in satellite images.

EURASIP Journal on Image and Video Processing

The generalized fractional derivative is defined upon a weight function and a scale function, which contains many fractional derivatives in the literature as special cases.

Advances in Difference Equations

Davies-Bouldin (DB) makes use of similarity measure (R_{ij}) between the clusters (C_i) and (C_j), which is defined upon a measure of dispersion ((s_i)) of a cluster (C_i) and a dissimilarity measure between two clusters ((d_{ij})).

Human-centric Computing and Information Sciences

The following defines a shorthand for comparing two sets of atoms an interpretation is defined upon with respect to the subset-relation.

Artificial Intelligence

Human-verified similar examples from authoritative sources

Similar Expressions

54 human-written examples

It was based on growth of the deposit mass accumulated in individual filter layers, which was defined upon the scanning electron microscope images, the clearance of layer samples, and the overall increase of the filter mass.

Chemical Engineering Research and Design

Especially in the field of medical imaging, we are often dealing with a situation when the topology of the object of interest is known from anatomical knowledge and can be defined upon algorithm execution.

EURASIP Journal on Advances in Signal Processing

Host gene clusters were defined upon a correlation-based adjacency matrix.

BMC Genomics

Bacteremia was defined upon isolation of S. aureus from at least one blood culture set.

European Journal of Clinical Microbiology and Infectious Diseases

The issue of whether MetS should be defined upon exclusion of diabetes is relevant to both clinical practice and epidemiology.

Cardiovascular Diabetology

Expert writing Tips

Best practice

While grammatically acceptable, consider using more common and clearer alternatives like "is based on" or "is determined by" to enhance clarity and readability.

Common error

Avoid using "is defined upon" repeatedly in formal writing. Vary your phrasing by using alternatives such as "is based on" or "is determined by" to maintain reader engagement and demonstrate a broader vocabulary.

Linguistic Context

The phrase "is defined upon" primarily functions as a linking verb phrase indicating a relationship of dependence or foundation. As Ludwig AI notes, its usage might be seen as less common, with alternatives often preferred for enhanced clarity.

Expression frequency: Uncommon

Frequent in

Science

71%

News & Media

29%

Formal & Business

0%

Less common in

Encyclopedias

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, while grammatically permissible, the phrase "is defined upon" is not the most common or preferred choice in contemporary English. As demonstrated by Ludwig, alternatives like "is based on" or "is determined by" often offer greater clarity and are more frequently used. Predominantly found in scientific and formal contexts, its purpose is to establish the conditions or basis for a definition. Given Ludwig AI's assessment and the available alternatives, it's advisable to consider more conventional phrasing for enhanced readability and impact.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

is based on

Focuses on the foundation or basis rather than the specific act of defining.

is determined by

Emphasizes the causal relationship and the factors that influence the definition.

is contingent upon

Highlights the dependency of the definition on certain conditions.

is dependent on

Similar to "is contingent upon", but with a slightly broader scope of dependency.

relies on

Focuses on the reliance or dependence on something for its definition.

is predicated on

Implies a fundamental assertion or basis upon which the definition rests.

is grounded in

Suggests a solid foundation or basis in something.

is established on

Emphasizes the creation or establishment of the definition on a particular basis.

is formulated upon

Emphasizes the formulation of a definition, adding precision and methodology to the way the definition is presented or constructed.

is built upon

Focuses on gradual addition, which may involve multiple elements to compose something.

FAQs

What does "is defined upon" mean?

"Is defined upon" means that the definition of something depends or is based on specific criteria or conditions. However, it is often clearer to use alternatives like "is based on" or "is determined by".

Is "is defined upon" grammatically correct?

While grammatically acceptable, "is defined upon" is not as common as other alternatives and can sound awkward. It's generally better to use clearer and more common phrases such as "is based on" or "is determined by".

What are some alternatives to "is defined upon"?

Some alternatives to "is defined upon" include "is based on", "is determined by", "is contingent upon", and "is dependent on". The best choice depends on the specific context.

How can I use "is defined upon" in a sentence?

You can use "is defined upon" to indicate that something's definition is reliant on specific factors. For example, "Success is defined upon hard work and dedication." However, consider using clearer alternatives such as "Success is based on hard work and dedication".