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The conservation of areal density is given by mathop int limits_{0}^{zeta } frac{pi }{3}dzeta big/frac{2pi }{3} = mathop int limits_{0}^{b} 2left( {1 - left| b right|} right)db big/2 Leftrightarrow zeta = bleft( {2 - left| b right|} right) (55 and the horizontal coordinate is modified proportionally a = frac{6}{pi }gamma left( {1 - left| b right|} right).
In this approach, the relative differences in pollutant concentrations between different spatial locations remain the same but absolute concentrations at all locations rise and fall together as city-wide pollutant concentrations are proportionally modified by temporal variation in city-wide weather conditions.
To simulate the ratcheting behaviour of the high strength rail steels, an existing cyclic plasticity model was modified by coupling a non-proportionally multi-axial parameter into isotropic softening and kinematic hardening rules.
We propose a modified version of RDBC by replacing (widehat{varvec{beta}}) by a proportionally allocated, stratified m-out-of-n bootstrap estimate of β.
Temperatures are often modified by sea winds.
Basically we were genetically modified by aliens.
(modified) by James W. Heisig.
[Image Credit: Getty/ZoneCreative, modified by TechCrunch].
Image: Shutterstock/Nikita Chisnikov (modified by Bryce Durbin).
It has been modified by the VICE US staff.
Photo modified from original by Flickr user Edward Corpuz.
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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