formulated below

USAGE SUMMARY

The phrase "formulated below" is correct and usable in written English.
It can be used when referring to information, ideas, or concepts that will be presented in the following text. Example: "The hypothesis for this study is formulated below for clarity and reference."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

16 human-written examples

The objective function is formulated below.

Journal of Modern Power Systems and Clean Energy

The optimization problem is formulated below.

EURASIP Journal on Wireless Communications and Networking

Similar reduction is demonstrated for IGP formulated below.

Boundary Value Problems

The corresponding decision list coloring problem is formulated below.

EURASIP Journal on Wireless Communications and Networking

On the basis of the above consideration, Model-2 is formulated below.

EURASIP Journal on Wireless Communications and Networking

The total reception power consumption of node i is the sum of all power consumed to receive data from other nodes, as formulated below, where λ is a constant coefficient: {P}_{ri=}{displaystyle sum lambda cdot {r}_{ki}.} (7).

Human-centric Computing and Information Sciences

Human-verified similar examples from authoritative sources

Similar Expressions

44 human-written examples

The definitions and theorems we formulate below carry over to continuous transformations without further ado, and where this is not the case we explicitly say so and treat the two cases separately.

SEP

Specifically, logistic regression can be formulated as below: 1 in which x i represents a certain type of histone modification, y represents the CE inclusion level and β i is the regression coefficient.

BMC Genomics

In addition, from the extracted exhaustive set of node behaviours, a Markov-based transition probability matrix can be formulated as below in (10).

EURASIP Journal on Wireless Communications and Networking

The aggregation is formulated as below: D i j = ( 1 / m ) ⊗ ( D i j 1 ⊕ D i j 2 ⊕ … ⊕ D i j m ), t = 1, 2, …, k (1 where, ⊗ is the multiplication of fuzzy numbers, ⊕ is the add operation of fuzzy numbers, and D ij is the overall average weighting valuation of alternative i under criterion j over m assessors.

Journal of Industrial Engineering International

We used Shannon's entropy equation [55] which can be formulated as below: <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0009186.e001.PNG" class= inline-graphic"/> where pi is the frequency of amino acid i (of 20) at the alignment position.

Plosone

Expert writing Tips

Best practice

Use "formulated below" when introducing a specific equation, model, or complex concept that you will define or explain in detail immediately after.

Common error

Don't use "formulated below" too frequently in your writing. Overusing it can make your writing sound repetitive. Vary your language by using synonyms like "described below" or "explained below".

Linguistic Context

The primary grammatical function of "formulated below" is that of an adverbial phrase acting as a discourse marker. It signals to the reader that a formulation (such as a definition, equation, or model) will be introduced in the subsequent text. Ludwig AI confirms its correct usage.

Expression frequency: Common

Frequent in

Science

80%

Formal & Business

10%

Encyclopedias

5%

Less common in

News & Media

2%

Wiki

2%

Academia

1%

Ludwig's WRAP-UP

In summary, the phrase "formulated below" is a common and grammatically sound expression used to introduce a definition, equation, or model. As Ludwig AI confirms, it's particularly prevalent in academic and scientific writing. While acceptable in professional contexts, it may be less suited to informal settings. Remember to use it judiciously, and consider alternative phrasing such as "explained below" or "described below" to avoid repetition. The examples show its use in diverse scientific contexts. It’s a useful tool for clear, structured writing in formal settings.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

defined below

Focuses more specifically on a definition rather than a broader formulation.

explained below

Highlights the explanatory aspect of the subsequent content.

described below

Emphasizes a descriptive approach in the following text.

presented below

Suggests a formal presentation of information.

outlined below

Indicates that the key points will be summarized.

detailed below

Implies a comprehensive explanation will follow.

shown below

Suitable when visual representation is being referred to.

given below

A more general alternative applicable in various contexts.

stated below

Focuses on the assertion of information.

elucidated below

Indicates that complex information will be made clear.

FAQs

How can I use "formulated below" in a sentence?

You can use "formulated below" to introduce a detailed explanation, equation, or model that you will present immediately afterward. For instance, "The mathematical model is formulated below for clarity."

What's a simple alternative to "formulated below"?

Alternatives include "explained below", "described below", or "outlined below". Choose the option that best reflects the content that follows.

Is it more appropriate to use "formulated below" or "stated below"?

The best choice depends on the context. "Formulated below" is suitable when referring to a model, plan, or set of rules. "Stated below" is generally used when referring to facts or opinions.

What is the difference between "formulated below" and "presented below"?

"Formulated below" suggests that something is being structured or created, while "presented below" simply indicates that something will be shown or displayed. They can sometimes be used interchangeably, but not always.