Sentence examples for the order of differentiation from inspiring English sources

With U regarded as a function U S, V), its differential dU is      (40) A comparison with the preceding equation shows immediately that the partial derivatives are     (41) Furthermore, the cross partial derivatives,     (42) must be equal because the order of differentiation in calculating the second derivatives of U does not matter.

where is the order of differentiation and with being the Chebyshev spectral differentiation matrix (see e.g., [23, 25]).

where is the order of differentiation and is the Chebyshev spectral differentiation matrix (see, e.g., [20, 21]).

where s is the order of differentiation and, with being the Chebyshev spectral differentiation matrix (see, for example [29, 31]) whose entries are defined as (2.22).

We compare both ranges in Figure 3. Figure 3 Comparison between ranges depending on the order of differentiation α and the angle ϕ ( (pmb{v_{0}=2}) ).

Figure 1 Range (Caputo) depending on the order of differentiation α, (pmb{1

with ℓ denoting the order of the differentiation of y ( t ).

It is found that the flux increases when one of the parameters defining the diffusion model, the pseudo-diffusivity, is increasing or when the other parameter defining the diffusion, the order of fractional differentiation, is decreasing.

In agreement with Figure 2A and B, the tubular-like colon adenocarcinomas, which are on the higher order of differentiation than the sieve-like ones, expressed higher level of HOXB9 (Tables 2, P=0.0068).

An analytical expression relating the fractional order of differentiation n with the characteristics of the modal interferometer was also derived, with the purpose to simplify the design procedure.

In both cases, the maximum order of differentiation of each output appearing in the model inversion constitutes relevant information since it characterizes the regularity of the trajectory to be followed.