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A capacity region is then defined as the set of all dimensional rate vectors that are achievable in the channel.
In what follows we discuss an example built on the global NPC space (of all dimensional positive definite matrices with real coefficients), when endowed with the trace metric, (4.1).
Unpaired t-test was employed to determine the difference of all dimensional and angular parameters between genders and the left and right pedicles at the same vertebral level.
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Such mixtures are located at the centroid of the (q − 1 -dimensional simplex and the centroids of all the lower dimensional simplexes within the (q − 1 -dimensional simplex.
Catalyst design requires consideration of all the different dimensional scales involved in heterogeneous catalysis.
In fact, of all the possible four dimensional state combinations (position and velocity of the first and second pendulum) the trajectories of the two synchronized pendula visit only the subpart where the two speeds and two positions are equal to each other, which is a two-dimensional subset of the whole four-dimensional state-space.
In fact, of all the possible four-dimensional state combinations (positions and velocities of the two pendula), the trajectories of the two synchronized pendula visit only the subpart where the two speeds and two positions are equal to each other, which is a two-dimensional subset of the whole four-dimensional state-space.
It took me five years to understand the multi-dimensional matrix of all the possibilities.
The three-dimensional structures of all these channels have been determined.
Lastly, a three-dimensional plot of all the data points included in the "optimal" cut-off determination was generated and the appropriate cutoffs illustrated as orthogonal planes.
Throughout this study, (mathbb{R}^{n}) and (mathbb{R}^{ntimes n}) represent the set of all n dimensional real column vectors and the set of all (ntimes n) dimensional real matrices.
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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