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The asymptotic theory of the first order nonlinear approximation allows for simultaneous evaluation of the effect of imperfections and interactions of various modes of buckling on the behaviour of thin-walled structures.
This approximation allows for the application of a known solution for the a scattering efficiency factor, Q, as detailed in the Supporting Information Methods.
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The value of using the approximations is twofold: first, the use of polynomials is computationally efficient; second, the relative simplicity of the polynomial approximations allows for field engineering computations by hand calculators in the determination of the theoretical values of diffraction coefficients and phase relationships.
This approximation allows us to reuse the implementation for computing linkages in Section 2.4.1.
Such an approximation allows us to employ the steady-state solutions for the channel conductivities as a function of membrane potential and Ca2+ concentration.
An analytical approximation is used for the reliability estimation that allows for computationally efficient, gradient-based design optimization.
This approximation allowed Newton to estimate the rate of precession for arbitrary central forces.
Therefore, efforts have been focused on developing a numerical approximation scheme, allowing for a pricing of the American option that is more accurate as well as a faster one than the lattice- or simulation- based methods that are time consuming and computationally more demanding.
It is then clear that we need to go beyond this treatment in order to understand heating in a Mott Insulator state with finite U. To study thermalization of spontaneous emission we have to go to the next order in the approximation and allow for states with 0, 1, and 2 particles per site.
Therefore, we use an approximation to allow for real-time calculation within the solution framework.
Moreover, we modified this peakedness approximation to allow for time-dependent arrivals, which is exploited in the step of admission scheduling.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com