is defined as shown below

USAGE SUMMARY

The phrase "is defined as shown below" is correct and usable in written English.
It can be used when introducing a definition or explanation that will follow in the text. Example: "The term 'sustainability' is defined as shown below: the ability to be maintained at a certain rate or level."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

where G(x t ) denotes the NNs mapping of x t and is defined as shown below: G(x_{t})=(G^{1}circ G^{2}cdotcdotcirct cdotcirc G^{L}) = bigodot_{l=1}^{ L}G^{ l}(x_{t}) (10).

EURASIP Journal on Audio, Speech, and Music Processing

Leverage centrality is a measure of the relationship between the degree of a given node (ki) and the degree of each of its neighbors (kj), averaged over all neighbors (Ni), and is defined as shown below.

Plosone

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

The general state system was defined as shown below, including the input λ, white noise d, and the state variable X.

ROBOMECH Journal

(For more details, please see [17].) The other parameters for model (1.2) are defined as shown below: (r(t)) is the growth rate of the predator population.

Advances in Difference Equations

In this paper, different models are compared using two error measuring parameters, Mean Absolute Percentage Error (MAPE) and Symmetric Mean Absolute Percentage Error (SMAPE) which can be defined as shown below.

Renewables: Wind, Water, and Solar

Average system goodput per cell (GDPUT) is defined as below.

EURASIP Journal on Wireless Communications and Networking

MCC is defined as below.

BioData Mining

These two groups were defined as below.

BMC Psychiatry

Domains of potential confounders were defined as below.

British Journal of Psychiatry

Saturation Index (SI) is defined as log of saturation ratio as shown below begin{aligned} {text{SI}};;{text{Log((CaCO}}_{ 3} ) /K_{text{sp}} )hfill hfill end{aligned} (55).

Applied Water Science

Recovery here is defined as being below the clinical cut-off for each scale, and showing reliable improvement during treatment.

Behaviour Research and Therapy

Expert writing Tips

Best practice

Use "is defined as shown below" to clearly signal that a formal definition or explanation will immediately follow. This helps readers anticipate and understand the upcoming information.

Common error

Avoid using "is defined as shown below" in casual or informal writing. This phrase is best suited for academic, scientific, or technical documents where precision and clarity are essential. In less formal contexts, simpler alternatives like "is" or "means" are more appropriate.

Linguistic Context

The phrase "is defined as shown below" serves as an introductory phrase. It functions to explicitly signal the forthcoming presentation of a definition or explanation, creating anticipation and structuring the subsequent content. As Ludwig AI confirms, this is correct.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Ludwig's WRAP-UP

The phrase "is defined as shown below" is a formal introductory phrase used to signal the forthcoming presentation of a definition or explanation. As Ludwig AI indicates, it is grammatically correct and most appropriate in scientific and technical contexts where clarity and precision are paramount. While alternatives like "is defined as follows" exist, this specific phrasing should be reserved for situations where a visual or textual presentation directly follows. While grammatically sound, its limited frequency suggests that other alternatives might be more commonly employed in general writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

is defined as follows

This alternative offers a slightly more concise way to introduce a definition.

is characterized as follows

This phrase is suitable when describing key characteristics or attributes.

is formally defined as

This option emphasizes the formal or official nature of the definition.

is understood to mean

This alternative focuses on the common understanding or interpretation.

can be defined as

This phrase introduces the possibility of defining something in a particular way.

is explained in detail below

This option is more descriptive, indicating a comprehensive explanation will follow.

is illustrated below

This phrase indicates that an illustration or example will be provided.

is specified below

This option is suitable when outlining precise specifications or requirements.

is detailed in the subsequent section

This phrase indicates a more extended discussion in a later part of the text.

is elaborated upon below

This suggests that the definition will be expanded and clarified further.

FAQs

What does "is defined as shown below" mean?

The phrase "is defined as shown below" indicates that a formal definition or explanation will follow directly after the phrase. It's commonly used in academic or technical writing to introduce precise meanings or concepts.

When should I use "is defined as shown below"?

Use "is defined as shown below" in formal contexts, such as scientific papers, technical manuals, or academic essays, when you need to provide a clear and specific definition. Simpler alternatives like "is" or "means" are more suitable for informal writing.

What are some alternatives to "is defined as shown below"?

Alternatives include "is defined as follows", "is characterized as follows", or "can be defined as". The best choice depends on the specific context and the level of formality required.

Is "is defined as shown below" grammatically correct?

Yes, "is defined as shown below" is grammatically correct and commonly used in formal writing. It clearly signals that a definition or explanation will be presented immediately following the phrase.