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respectively, where N l is the number of Fourier modes contained in Z l and * indicates the conjugate transpose.
The optical modes contained in the memories of one user (e.g. Alice's) are propagated to the other user (Bob, in this case).
Multivariate imaging, using principal component analysis (PCA), was used to evaluate all of the vibrational modes contained in the spectral data to hone in on the specific differences between the native and modified sugarcane.
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From (8) and (12), the frequency f i and damping ς i of the i th oscillation mode contained in x t) are left{ begin{array}{l} f_{i} = frac{{omega_{ni} }}{2pi } hfill varsigma_{i} = - frac{{frac{{{text{d}}left( {ln left| {Wleft( {tau_{i},t} right)} right|} right)}}{{{text{d}}t}}}}{{omega_{ni} }} hfill end{array} right.
"The ideas of singular things, or of modes, that do not exist must be comprehended God's infinite idea in the same way as the formal essences of singular things, or modes, are contained in God's attributes" (IIp8).
In the multiplayer matchmaking, ODST includes Halo 3s multiplayer game modes contained on a separate disc.
Since the maximum power of the fundamental MCF mode will lead to the desired laser beam profile, higher the fraction of the fundamental MCF mode power contained in the total output power contributes to higher beam quality.
We can find the tensor-based subspace estimate only based on the r-mode subspaces contained in Û r s.
A thought stands for the state of affairs that contains those particulars and properties that are represented by the modes of presentation contained in the thought and that are combined in a way that is analogous to the way the modes of presentations are combined in the thought.
These modes contain the largest fraction of fluctuation energy in the spectra.
One of the performance issues addressed by the waffle-iron filter is that in many waveguide filters the attenuation is dependent on the transmission modes of the incident signal and some filters can be quite bad at suppressing spurious modes which may be contained in this signal.
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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