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For the robust computation of quantities of engineering interest, such as the shear force, the proposed method yields very satisfactory results without the need for any additional post-processing.
X-Tracker is able to support quantitation data coming from many different approaches, both at the MS or MS/MS level and its analysis workflow can be divided in four main steps: (i) loading of raw data and protein identifications; (ii) peak selection; (iii) computation of quantities; and (iv) reporting of the results.
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Worst case scenario analysis (corresponding to the load envelope) of the structure require computation of local quantities of interest.
We consider the computation of these quantities by the perturbation approach.
In the framework of the design of laminated and sandwich structures, the computation of local quantities needs a layer-wise approach.
Computation of Lyapunov quantities is a hot topic with large number of articles per year, but it is very difficult to obtain general results.
The methods of computation of Lyapunov quantities when the critical points are non-degenerate have been greatly developed by many mathematicians.
Another approach to numerical computation of Lyapunov quantities which uses the passage to the polar coordinates and the procedure of sequential construction of solution approximations is related with the obtaining of approximations of system solution, see [2], they also could be seen in [6, 7].
In the computation of physical quantities such as electron and hole densities as well as the corresponding current densities, the summation over all conduction or valence bands needs to be performed, e.g., for the electron density: Table 1 Band parameters used in simulations (from [3, 26]) Si SiO x 0.3 0.3 0.98 0.4 0.19 0.4 0.16 0.4 0.49 0.4 E g, Γ v - Γ c (eV) 3.5 5.5 E g, Γ v - X (eV) 1.1 3.1.1
A major advantage of the use of splines is that they greatly facilitate the computation of derived quantities from the primary data.
Table 1 lists the definitions and formulas for the computation of these quantities (note that in our notation a tilde on top of a symbol indicates "partial").
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