It discusses how to characterize, extract, and preserve regularities at different abstraction levels.
Whereas the modulation at the rim of the ablated area is characterized by very deep trenches between the ripples, further out the ripples appear as slight crests above the unperturbed surface, but preserving the regularity.
When Does Partial Commutative Closure Preserve Regularity?
To preserve the regularity of the level set function ϕ, a level set regularization term P = ∫Ω x (|∇ ϕ(x)|−1)/2 dx is introduced, which is necessary for accurate computation and the stable evolution.
Several pairs of moons are in stable dynamic resonances i.e., the members of each pair pass one another in their orbits in a periodic fashion, interacting gravitationally in a way that preserves the regularity of these encounters.
In the spatially homogeneous case, we first prove that the analytical solution preserves the regularity of the initial data in the random space, and then use it to establish the spectral accuracy of the proposed stochastic Galerkin method.
To preserve the regularity of the level set function, we add an extra internal energy [31]: P ϕ = ∫ Ω 1 2 ∇ ϕ x, y − 1 2 dx dy (18).
Trying to preserve the regularity and parallelism typical of the full-complexity LORD, we restrict our attention to square subsets of the QAM constellation, centered in the received (equalized) signal ỹ N t ( t ) / r N t, N t ( t ), at the root layer (red cross in Figure 2a).
Properties including regularity preserving, L ∞ contraction are discussed.
Ordered carbon material that preserves the structural regularity of the parent zeolite template was synthesized by using ethylene as carbon source and HY-zeolite in a batch reactor.
As we can observe in Figure 4a,b,c,d, our method preserves the spatiotemporal regularity of the input, and the borderlines between blocks are practically invisible.
