by the same notation

USAGE SUMMARY

The phrase "by the same notation" is correct and usable in written English.
It can be used when referring to a previously established system of symbols or terms in a mathematical or technical context. Example: "Let us denote the variable x as the length of the side; by the same notation, we can represent the area as A = x²."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

6 human-written examples

The norm on (L X, Y)) shall be denoted by the same notation (Vert cdot Vert ).

Advances in Difference Equations

As is bounded, there exists a subsequence of, still denoted by the same notation, and nonnegative constant such that (3.27).

Boundary Value Problems

For any φ ˜, ψ ˜ ∈ C ˜ sm ( I ), we write φ ˜ ⪯ ψ ˜ by the same notation if φ ⪯ ψ holds.

Journal of Inequalities and Applications

Throughout this article, we simplify the notations (Vert cdot Vert _{2}), (Vert cdot Vert _{H}), and (Vert cdot Vert _{widehat {H}}) by the same notation (Vert cdot Vert ) if there is no confusion.

Boundary Value Problems

From the Aubin-Lions theorem, see Lions [[18], pp.57-58], it follows from (2.21) and (2.22) that there exists a subsequence of { u i }, still represented by the same notation, such that u i ′ → u ′ strongly in  L 2 ( 0, T ; L 2 , which implies u i ′ → u ′ almost everywhere in Ω × ( 0, T ).

Boundary Value Problems

Then there exists a subsequence, still denoted by the same notation, such that (U^{ k)}rightharpoonup U), (U^{ k)+}rightharpoonup U^) in (l^{2}), (U_{n}^{ k)}to U_{n}) for any (nin Z) and begin{aligned} U^{ k)+}to U^quad mbox{in } l_{gamma}^{2}.

Advances in Difference Equations

Human-verified similar examples from authoritative sources

Similar Expressions

54 human-written examples

The new metrics were designed by extending those defined in [9] by using the same notation.

EURASIP Journal on Image and Video Processing

The method will be based on the specification of components in a standardized way, so that both customers and manufacturers can refer to them by using the same notation.

Electronic Notes in Theoretical Computer Science

In [[30], p.537], the authors defined the Kirchhoff matrix over a loopless connected digraph, say D. In fact, by using the same notation as in this reference, we can define it as a matrix K : = M x obtained from the incidence matrix M of D by deleting the row m ( x ).

Journal of Inequalities and Applications

Proof By taking the same notation as that in the proof of Lemma 2.1 of Yang et al. [8], we partition the set { 1, 2, …, n } into 2 k n + 1 subsets with large block of size μ = μ n and small block of size ν = ν n.

Journal of Inequalities and Applications

For briefness, we still denote the inner products and norms of their product spaces l w 2 ( I ) × l w 2 ( I ), l w 2 ( I 1 ) × l w 2 ( I 1 ), and l w 2 ( I 2 ) × l w 2 ( I 2 ) by the same notations as those for l w 2 ( I ), l w 2 ( I 1 ), and l w 2 ( I 2 ), respectively.

Advances in Difference Equations

Expert writing Tips

Best practice

When employing "by the same notation", ensure the notation being referenced is clearly defined and accessible to the reader to avoid ambiguity.

Common error

Avoid using "by the same notation" without explicitly stating or clearly implying which notation is being referenced, as this can confuse readers and undermine clarity.

Linguistic Context

The phrase "by the same notation" functions as an adjunct, modifying a verb or clause to indicate that a previously established system of symbols or terms is being consistently applied. Ludwig AI examples show this phrase commonly appears in scientific and technical contexts.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "by the same notation" is a prepositional phrase used to maintain consistency of previously mentioned symbols, especially in scientific and technical documentation. Ludwig AI confirms that this is commonly employed in formal contexts, particularly within scientific publications. While not frequently used, it's grammatically sound and essential for clarity when dealing with complex symbolic systems. When using this phrase, make sure the referenced notation is clearly defined to avoid any ambiguity.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

using identical symbols

Focuses on the visual aspect of the notation, emphasizing the symbols themselves.

employing the same terminology

Highlights the use of consistent terms rather than specific symbols.

with consistent nomenclature

Emphasizes a system of naming that remains unchanged.

adopting the previous convention

Stresses the acceptance and continuation of a previously established practice.

maintaining uniform designations

Focuses on the consistent use of specific labels or identifiers.

according to established symbolism

Highlights adherence to a recognized system of symbols.

following the defined system

Emphasizes compliance with a set of rules or a framework.

in accordance with prior designations

Highlights agreement with a prior assignation or denomination.

using consistent representation

Focuses on the uniformity in how something is depicted or presented.

as per the defined convention

Indicates that something is being done as instructed or agreed.

FAQs

How can I use "by the same notation" in a sentence?

You can use "by the same notation" to indicate that you are maintaining a consistent symbolic representation throughout your work. For example, "Let x represent the length; by the same notation, y represents the width."

What's a good alternative to "by the same notation"?

Alternatives include "using identical symbols", "employing the same terminology", or "with consistent nomenclature", depending on the specific context.

When is it appropriate to use "by the same notation"?

It's appropriate when you want to emphasize the consistent application of a defined system of symbols or terms, particularly in technical or mathematical contexts where clarity and uniformity are crucial.

Is "by the same notation" formal or informal?

"By the same notation" leans towards formal usage, typically found in academic, scientific, or technical writing where precision and consistency are valued.