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Therefore, it is better to establish the corresponding timescale theory on some classical problems directly through Δ-calculus theory on time scales.
The four lowest spin-degenerate energy levels are E 1 = 3.938 meV, E 2 = 4.030 meV, E3 = 9.782 meV, E 4 = 11.590 meV counted from the bottom of a single quantum dot with the tunneling splitting ΔE g = E 2 - E 1 = 0.092meV, and the corresponding timescale 2π ħ/ΔE g = 45ps.
In this case, the corresponding timescale is spread across the entire network.
Our theory gives the dependence of the eigenvector width on network parameters and on the corresponding timescale.
For v λ to be localized, the real part of α must be positive when evaluated at the corresponding timescale.
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We decompose the field and its SV according to the well separated temporal windows already seen in geomagnetic data at inter-decadal (20 30 years), sub-centennial (60 90 years), and inter-centennial (≥ 400 years) timescales, probably caused by core flow evolutions with different intensities and geographical patterns at the corresponding timescales.
The two corresponding timescales in our model are d/ Dlip, for the lateral diffusion motion of lipids, and d/ Dprot, for the diffusion of adsorbing macromolecule, where d is the lattice constant, Dlip is the lipid diffusion coefficient, and Dprot is the diffusion coefficient of the macromolecule on a homogeneous membrane.
Conventionally, cross-layer designs with same timescale updates can work well; however, there is a difference in layers' timescales and each layer normally operates at its corresponding timescale when implemented in real systems.
In our model framework, this is inevitable, unfortunately, due to the fact that a phylogenetic independent dataset, i.e. a dataset of instantaneous rate estimates and their corresponding timescale, is extremely difficult, if not impossible, to obtain for FVs.
All model states, input and output variables, and corresponding timescales are given in Table 1.
During deswelling (shrinking), the hydrogel loses 95 wt% water in 1 min, compared to a timescale for the corresponding cross-linked copolymers prepared by conventional methods of about 5 h for 50 wt% water loss.
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