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The continuity and curvature terms need to be weighted with values just high enough to maintain a high regularity of the mesh.
The justification for the above assumption is the following: The continuity and curvature terms need to be weighted with values just high enough to maintain a high regularity of the mesh.
More precisely, Holschneider (1995) has shown that a high regularity of the signal is translated via the CWT from a power-law variation: (9)This result confirms that if the stochastic process s(t) is self-affine or, if it has some long-range dependence properties characterised by the local exponent h(t), then the wavelet coefficients, at a fixed scale, form a stationary process.
Since SEM and AFM patterns exhibit a high regularity in the structures across the transition from ripples to surface undulations the role of the amorphization of crystalline silicon during the formation process of ripple structures has to be the subject of further research.
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Furthermore, the width of the peak reduces with time indicating a higher regularity.
In order to obtain a higher regularity of global strong solutions, there are many complicated estimates on higher derivations of the solution involved; this is our difficulty.
The empirical color difference data plotted in the OSA-UCS space show a higher regularity than what has been seen before (Figures 2 and 3), inducing the authors to state a hue-independence hypothesis.
In a regularization method, by decomposing the potential function into two or three components, the singular component can be analytically represented by the Green's function, while other components possess a higher regularity.
Nanoporous AAO characterized by a very high regularity, not registered previously for low purity aluminum, was obtained.
Moreover, due to the strong-coupling property of the k-ε equations, we need a corresponding high regularity of the unknown functions k and ε.
Although crystallography can be used to characterize the disorder in an impure or irregular crystal, crystallography generally requires a pure crystal of high regularity to solve the structure of a complicated arrangement of atoms.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com