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Figure 1 Solution of fractional-in-space diffusion equation ( 3.24 ) showing the trade-off between finite difference and Fourier spectral methods at different instances of α and simulation time t, for (pmb{D=10}).
All three histograms depict the spectrum usage probability of PUs at different instances of time.
Plot (d) is obtained at different instances of time (t= 1, 2, 4, 8)) at fractional value (alpha=1.25).
The evolution of more complex spiral patterns is shown in Figure 4 for kinetics (4.3) at different instances of fractional index α at time (t=1000).
Figure 6 Numerical pattern results in 3D for fractional-in-space reaction-diffusion system ( 2.7 ) using kinetics ( 4.1 ) with both Dirichlet (upper row) and Neumann (lower row) boundary conditions at different instances of (pmb{alpha=0.5, 1.1, 1.5}).
Figure 7 Numerical pattern results in 3D for fractional-in-space reaction-diffusion system ( 2.7 ) using kinetics ( 4.3 ) with both Neumann (upper row) and Dirichlet (lower row) boundary conditions at different instances of (pmb{alpha=0.5, 1.1, 1.5}).
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This allowed for the measurement of the velocities at different instances in the periodic formation cycle with a high temporal resolution (∼5ms).
The total number of assailants involved at different instances ranged from 1 to 9. The management offered is summarized in Table 4.
They come up at different instances through the book.
To apply the signature-based ordering, the session reconstruction tool should be able to identify different instances of the same action at different states.
This platform is able to support different Rule Engines and even different instances of the same Rule Engine at the same time.
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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