The approximation in the second line of eq 6.27 neglects second-order terms in λD – λH.
We therefore start by describing the visualization techniques in the first part, and then move on to storage size reduction by sparse approximation in the second part of the results.
The cross-correlation of f and g at a shift (or distance) of d is (1) The approximation in the second line results from the summation in the first line not being taken over exactly the same values of b as the summations in the formulae for and.
A modified midpoint method (MMP, Algorithm 3) is used to generate the initial approximations in the first column of the table.
Next, we will show how to find (u_{2,1}), which is the approximation of (u_{3}) in the third level.
In the first best approximation theorem, we establish a sequence { x n } which converges strongly to the unique best approximation point; while in the second best approximation theorem, we obtain the existence of a minimum best approximation point and a maximum best approximation point in order intervals.
For the realistic choice of qubit and transmission line parameters, the figures of merit (beta= sqrt{E_{EM}/ Delta} sim30) and (nu= hbarmax(Gamma_{qb},Gamma_{TL})/Delta sim10^{-3}) (Ref. [18]) ensure that the continuum approximation is justified, and that in the first approximation the effects of decoherence can be neglected.
In Figure 4 and Figure 5(a - d), we compa - dhe simulation for the full model and for the approximation obtained from the limiting model in the third scaling.
The use of small perturbation around steady-state leads to important simplification to the evolution equation, which can be highly non-linear (Eq. 1), resulting in the approximation of the first-order term.
In the same manner, we can obtain further approximations (v_{3} x,t), ldots) Setting (beta=1) in the first approximation (24) and the second approximation (25) and after some simplifications, we obtain the same approximations as (15) and (16) on returning to the original variable.
