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We modified the advection dispersion equation by replacing the time derivative with the new fractional derivative.
This can be calculated by replacing the time average with the ensemble average.
Many applications of fractional calculus amount to replacing the time derivative in a given evolution equation by a derivative of fractional-order.
By replacing the time consuming "Remeshing" process, which is necessary by the finite element method (FEM) approach at large deformations with FVM, the ability of material flow simulation is increased.
Rashidinia and Mohammadi [33] developed an approximation for finding the numerical solution of differential equation (3) by replacing the time derivative by a finite difference approximation and the space derivative by sextic spline functions using off-step points to obtain three-level implicit methods of accuracies (O k^{2}+h^{4})) and (O k^{4}+h^{4})).
Therefore, the concept of holographic lithography was brought as a breakthrough to generate the periodic structure over large area, replacing the time consuming serial writing process; but, there is still a matter to be solved concerning the creation of functional defects within it.
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Social media activity, he lamented, seemed to be replacing the time-honored tradition of the street protest.
There were "no compromises" made in replacing the time-honoured desktop with Windows 8's colourful tile-based interface, Ballmer insisted.
Theorem 3.2 is now extended by replacing the time-invariant controllers by time-varying ones.
Replacing the time-consuming FEA by neural network approximations may be a computationally efficient alternative, but the error in such approximation may misguide the optimization procedure.
Hence, we adapted the Oozie triggering semantics, by replacing the time-based and data detection triggering mechanisms, with a notification scheme that is interfaced with the F l u χ framework process through Java RMI.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com