be defined over

USAGE SUMMARY

The phrase 'be defined over' is grammatically correct and can be used in written English.
It is generally used to refer to the scope of an idea, law, or other concept. For example: "We must ensure that our rights and responsibilities are clearly defined over a wide scope of situations."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

28 human-written examples

While linear autoencoders can be defined over any field, only real-valued linear autoencoders have been studied so far.

Neural Networks

Arbitrary force regimens may be defined over a wide range of frequency (DC to 10 Hz) and force (100 pN to 10 nN).

Acta Biomaterialia

Net benefits should be defined over an individual's life cycle, comparing all taxes paid with all benefits received, an approach sometimes referred to as generational accounting.

The New York Times

* To capture the flexibility and productivity of human cognition, generative models can be defined over richly structured symbolic systems such as graphs, grammars, predicate logics, and most generally probabilistic programs.

Massachusetts Institute of Technology

Instead, Kenny's premiership will be defined over the next few weeks when he goes to Europe to renegotiate the IMF/European Central Bank €80bn-plus rescue package for Ireland.

The Guardian

"I see here an environment where there's a lot happening within a short amount of time, and that's why that layer, the foundation, will still be defined over the next 12 to 14 months," he said, adding: "It's fun.

The New York Times - Sports

Human-verified similar examples from authoritative sources

Similar Expressions

32 human-written examples

Three levels of neuromuscular blockade were defined: "over-paralyzed" (TOF = 0), "well-paralyzed" (TOF = 1 2), and "under-paralyzed" (TOF = 3 4).

Annals of Intensive Care

Value functions are defined over a fixed set of outcomes.

Artificial Intelligence

Finally, manifold splines are defined over this affine atlas.

Computer-Aided Design

EtherNert/IP is defined over IP so that it runs on a whole family of links.

University of California, Berkeley

The constraints are defined over the underlying structural geometry represented by the filtered and physical fields.

Computer Methods in Applied Mechanics and Engineering

Expert writing Tips

Best practice

When using "be defined over", ensure clarity regarding what is being defined and the specific range or domain it applies to. Providing concrete examples can enhance understanding.

Common error

Avoid using "be defined over" without clearly specifying the boundaries or parameters. Ambiguity can lead to misinterpretation. Be precise about what the definition encompasses.

Linguistic Context

The phrase "be defined over" functions as a verbal phrase specifying the domain, range, or context to which a definition, function, or concept applies. Ludwig AI provides examples of its use in various scientific and mathematical contexts, highlighting its role in setting boundaries and parameters.

Expression frequency: Uncommon

Frequent in

Science

66%

Academia

16%

News & Media

16%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "be defined over" is a verbal phrase used to specify the scope or domain to which a definition, function, or concept applies. Ludwig AI indicates it is grammatically correct and commonly used in scientific, academic, and news contexts. It is crucial to ensure clarity and precision by specifying the boundaries or parameters when using this phrase. Related phrases include "be applicable to" and "fall within the scope of". A common error is using the phrase without clearly defining these boundaries, which can lead to vagueness. In conclusion, while not the most frequent expression, "be defined over" serves an important function in technical and formal writing contexts.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

be delineated by

Focuses on clearly marking the boundaries or limits of the definition.

be characterized by

Emphasizes the distinctive features that constitute the definition.

be circumscribed by

Focuses on the limitations and constraints that shape the definition.

be determined by

Focuses on the factors that influence or establish the definition, rather than the domain it applies to.

fall within the scope of

Indicates inclusion within a defined boundary or area.

be applicable to

Highlights the range of situations or entities to which the definition is relevant.

be restricted to

Indicates limitations or constraints on the definition's application.

be governed by

Specifies the rules or principles that dictate the definition.

be predicated on

Emphasizes the foundational assumptions underlying the definition.

be contingent upon

Highlights the dependence of the definition on specific conditions.

FAQs

How is the phrase "be defined over" typically used in academic writing?

In academic writing, "be defined over" often specifies the domain or set upon which a function, concept, or property is valid. For example, "the function is defined over the set of real numbers" indicates where the function operates.

What's the difference between "be defined over" and "be defined by"?

"Be defined over" specifies the scope or domain, whereas "be defined by" indicates the characteristics or attributes that constitute the definition. The first addresses 'where', the second addresses 'what'.

Can "be defined over" be used in contexts other than mathematics or science?

Yes, although common in technical fields, "be defined over" can apply to any situation where specifying the scope or range of a concept is necessary. For example, "the project's success will be defined over a three-year period".

What are some alternatives to "be defined over" that I can use in my writing?

Depending on the context, you could use phrases like "be applicable to", "fall within the scope of", or "be restricted to" to convey a similar meaning of scope or domain.