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In order to exclude this possibility, we consider and define next non-redundant patterns.
When all points have zero measure the measure is called nonatomic as we formally define next.
We define next the vector with components, for all possible values of sorted in natural order, that is, according to.
We define next the geodesic X-ray transform for any compact Riemannian manifold ( M, g ) with boundary of any dimension.
To kick this effort off, the city is planning an event for February 24 and 25 "to help the City redefine taxi access and help us define next steps".
We define next the singular surface S, which is filled by singular extremals of ((mathcal {P}_{S})), by begin{aligned} S &= left{{vphantom{= frac{-p^{0} costhetacospsi}{a+g_{x}sin theta cos psi-g_{y}sin psi+g_{z}cos theta cos psi}, quad p_{v_{y}}}} x,p) mid omega_{x}=omega_{y}=0, quad p_{theta}=p_{psi}=p_{phi}=p_{omega_{x}}right.
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The architecture here put forward can be used to define next-generation 400 Gb/s Ethernet standard.
We've got the hardware, but half a year after the PlayStation 4 and Xbox One went on sale, gamers are still waiting for a new type of experience to truly define next-generation console gaming.
The turtle's "ask" method will be defined next.
This concept of solution is formally defined next.
Each element of this distribution is defined next in turn.
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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