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All simulations are performed considering finite regions in R2.
In Ford's view, however, the future is a soundless depth of creativity that endlessly "pluralizes itself into the many finite regions of the present" (Ford 2000, 248).
Due to rapid decay of solutions, it is natural to truncate unbounded domains to finite regions of computational interest.
The external aspect is the fact that AQFT considers only observables connected with finite regions of space-time and not global observables like the total charge or the total energy momentum vector which refer to infinite space-time regions.
In [Electromagnetics 23 (2003) 187], a technique for injecting perfect plane waves into finite regions of space in FDTD was reported.
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Only two rather generic assumptions are essential: i) a spatially infinite universe such as any (island) universe in MWO; the multiverse, while integral to eternal inflation, is not actually required for my argument, ii) the finiteness of the number of macroscopic histories in any finite region of spacetime.
For the infinitesimal neighbourhood of a point on a curved surface there is a local co-ordinate system in which the distance ds between two infinitely near points is given by the equation ds2 = dx2 + dy2 For any arbitrary (Gaussian) co-ordinate-system, however, an expression of the form ds2 = g11dx2 + 2g12dx1dx2 + g22dx22 holds in a finite region of the curved surface.
Usually the shift is confined to a finite region called the hole (for historical reasons).
For a wireless network, the area in which the wireless nodes lie corresponds to a finite region of the plane.
Another example is the creation of a set of bubbles by a propeller in a finite region in space.
Since we need to choose a finite subspace of a countably infinite basis, we restrict ourselves to the finite region −L
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Justyna Jupowicz-Kozak
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