Your English writing platform
Discover LudwigExact(1)
We prove that the transformation introducing such coordinates maps analytically a complex ball of radius R/Nα (in discrete Sobolev-analytic norms) into a ball of radius R′/Nα (with R,R′>0 independent of N) if and only if α≥2.
Similar(59)
The transformation introduced is proved to be bijective.
The techniques we use build on a time transformation introduced in previous work.
For all alloys, the α↔γ phase transformation introduces a volume change of 1.0%.
Moreover, the physical iterative transformation between crystalline and amorphous phase transformation introduces a swelling and deswelling effect.
The transformation introduces an elliptic boundary value problem which is solved by a preconditioned conjugate gradient method.
Although this transformation introduces many benefits, it arouses new challenges of data security due to the outsourcing storage on untrusted cloud servers.
Most importantly, in the presence of uncertainties and disturbances, the transformation introduced in Teel (1992) would considerably shrink the region where the controller is unsaturated and, severely limit the level of uncertainties and disturbances which can be tolerated.
This transformation introduces odd powers of x and y to this polynomial.
Rancho Valencia's transformation introduced chef Eric Bauer's Veladora, which serves coastal cuisine in a rustic-chic space anchored by a Damien Hirst kaleidoscope of butterfly wings.
With all the consequences concerning the possibility of introducing new governance instruments, more sensitive to urban transformation and to the needs of security that this transformation introduces into the public debate and public agenda.
Write better and faster with AI suggestions while staying true to your unique style.
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
CEO of Professional Science Editing for Scientists @ prosciediting.com