We deduce the signal reconstruction error bound, proving that appropriate selection of the stretching factor and smoothness order guarantees low reconstruction error.
The smoothness is guaranteed under an extra condition, frac{partial U^{partial x}(c,y,varepsilon)=frac{partial U^{partial x}(c,y, varepsilon).
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It also guarantees smoothness of the acceleration profile of the entire path by controlling the curvature values of the curves that composes it.
end{aligned} Since the uniform smoothness of X guarantees the uniform continuity of j on every nonempty bounded subset of X, we deduce from (32), (lambda_{k}to0) and the boundedness of ({y_{k}}) that lim_{ktoinfty} biglVert j(x_{k}-z -jbigl( Pi_{C}(I-lambda_{k}F)GV_{k}x_{k}-z -jbiglbigrVert =0.
According to Lemma 1.2, the 2-uniform smoothness of X guarantees the nonexpansivity of the mapping I − μ i B i for an α i -inverse-strongly accretive mapping B i : C → X with 0 ≤ μ i ≤ α i κ 2 for i = 1, 2, and hence the composite mapping G : C → C is nonexpansive where G = Π C ( I − μ 1 B 1 ) Π C ( I − μ 2 B 2 ).
It is from [15] that the smoothness properties of guarantee the global existence and uniqueness of solutions to the system (1.3).
Here, a regularity criterion in terms of the vorticity and oxygen concentration is established to guarantee smoothness up to time T. It will help people to gain understanding of the model.
In addition, boundary nodes of neighboring areas were scaled according to the two adjacent eigenforms, and the nodal coordinates obtained were mediated to avoid singularities and guarantee smoothness of the surface.
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