Sentence examples for using the analytic form from inspiring English sources

A detailed description of the transformation method as well as the resulting SHG tensors obtained in Néel and Bloch-type DWs is provided as Supplementary Note 2. Knowing the susceptibility tensors, the SHG intensity can be calculated for any wall type as a function of the polarizer angles (α and ϕ) using the analytic form given in the Methods section (equations (1) and (2)).

A semi-analytic method for matching the boundary conditions is proposed by using the analytic form of the extremal solutions and a closed form solution for the exponential map.

Using the analytic form of the solution, it is shown that the observed discrepancy is related to interaction between the damped hydrodynamic mode and a downstream propagating higher order acoustic mode.

Proof Using the analytic form of the modified generalized Laguerre polynomials L i ( x ) of degree i (6) and (2), then J ν L i ( x ) = ∑ k = 0 i ( − 1 ) k β k Γ ( i + α + 1 ) ( i − k ) ! k !

For the UV LF, we adopt the Schechter function (Schechter, 1976): (16)For the IR, we use the analytic form for the LF proposed by Saunders et al. (1990): (17)We use the re-normalized version of Eqs.

We develop an explicit closed-form solution to the boundary-value problem using the analytic element method.

Our algorithm uses the simplest analytic form of beam steering, that is, the linear phase ϕ(x)=kxx.

Therefore the analytic form of the tan β enhanced corrections depend on the chosen renormalization scheme.

Deriving Insights using the correct analytics methodologies.

Graphical overview was obtained using the CGH analytics software (v3.4.27).

In Choi et al. [9], the martingale method is used to provide an analytic form for the value function and optimal strategies.