Sentence examples for it follows again from inspiring English sources

Exact(7)

It follows again from (3.35) or (3.36) that or.

It follows again by Lemma 6 that (finoperatorname{KAA}(mathbb{R},X)).

It follows again by Lemma 6 that (tmapsto y t-sigma(t))inoperatorname{KAA}(mathbb {R},mathbb{R})).

It follows again from the proof of Theorem 2.8 that z is a unique fixed point of T as desired.

Thus ∂ F ( x, y ) ∂ x ≥ 0. Similarly, it is easy to prove that ∂ G ( x, y ) ∂ x ≥ 0. Then it follows again by Theorem A that the equilibrium point ( x ¯, y ¯ ) = ( x ¯, x ¯ ) of System (9) is a global attractor of all positive solutions of System (9).

where J : E → 2 E ∗ is the normalized duality map on E. It follows, again from inequality (1.3), that A is accretive if and only if ( I + s A ) is expansive and, consequently, its inverse ( I + s A ) − 1 exists and is nonexpansive as a mapping from R ( I + s A ) into D ( A ), where R ( I + s A ) denotes the range of ( I + s A ).

Show more...

Similar(53)

Its existence follows again from Tarski's fixed-point theorem.

The conclusion follows again by Theorem 3.4.

The uniqueness follows again from Lemmas 2.5 and 3.8.

The optimal importance sampling distribution for the present case follows again from (22) as follows: (35).

It was followed again after the 1990s when Germany's reunification boom and devaluations by some trading partners pushed up its relative wage costs.The wage discipline was remarkable.

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: