Sentence examples for the article denoted from inspiring English sources

Exact(2)

Throughout the article denoted by ℝ is the set of all real numbers, by (mathbb{R}_) is the set of all positive real numbers and by ℕ is the set of all natural numbers.

Throughout the article denoted by ℝ is the set of all real numbers, by ℝ+ is the set of all positive real numbers and by ℕ is the set of all natural numbers.

Similar(58)

Almost sure events are Palmost sure in this article denoted by "a.s".. Suppose f t, 0, y) = 0, g t, 0, y) = 0 and I i (t, 0) = 0 for t > t0, then x t) ≡ 0 is the solution of (1), which is called zero solution of (1).

Test coverage in the context of this article denotes the percentage of equivalence classes rather than the percentage of possible signals that is reached by the test.

The mechanism of the process-based route within this article denotes that the reaction process between the oxidant and the redox-sensitive cysteine associated with its relevant residue(s) perturbs the protein binding interaction with its counterpart.

In the case of steganalysis as performed in this article, denotes the feature vector corresponding to image, while is the corresponding class of the image (i.e., stego or cover).

To validate our opinion different annotators reach high agreement on noun phrases, we randomly select 20 articles and annotate keyphrases that may contain adjectives for each article, denoted by S. Then we compare our manually labeled keyphrases with the benchmark that is used in the work [31], denoted by T. We find that the proportion of common general phrases is (|S cap T|/|S cup T|) = 44%.

Throughout the article, ℝ denotes the set of real numbers, x = ( x 1, x 2, …, x n ) denotes n-tuple (n-dimensional real vectors), the set of vectors can be written as R n = { x = ( x 1, …, x n ) : x i ∈ R, i = 1, …, n }, R + n = { x = ( x 1, …, x n ) : x i > 0, i = 1, …, n }.

Throughout the article, ℕ denotes the set of positive integers.

Throughout the article, ⊤ denotes the matrix transpose, H the Hermitian transpose, ¯ the entry-wise complex conjugate of a matrix, and by Gl(m) the set of all m×m invertible complex matrices.

Throughout the article,,, and denote, respectively, the spaces of all, bounded, and -absolutely summable sequences with the elements in, where is a seminormed space.

Show more...

Ludwig, your English writing platform

Write better and faster with AI suggestions while staying true to your unique style.

Student

Used by millions of students, scientific researchers, professional translators and editors from all over the world!

MitStanfordHarvardAustralian Nationa UniversityNanyangOxford

Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak quote

Justyna Jupowicz-Kozak

CEO of Professional Science Editing for Scientists @ prosciediting.com

Get started for free

Unlock your writing potential with Ludwig

Letters

Most frequent sentences: