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It is seen that these singular terms depend only on four-velocity and four-acceleration and nothing else such as curvature or derivative of acceleration.

Investigating many well-known chaotic systems, we found that the nonlinear terms depend only on one variable or have a single common variable such as Hènon [35], Rossler system [36], Lorenz system [37], Lu system [38], etc.

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Also, only the ratio k sp / kT was defined as a model parameter (determined from experiment, 1/ σ = k sp / kT) since all force terms depends only on this combination of k sp and kT.

In this paper, we identify an unknown source term depending only on one variable in two-dimensional Poisson equation.

Consequently, we can consider that the intrinsic interference term depends only on this restricted set (denoted by (phantom {dot {i}!}Omega _{k',n'})).

In this paper, the Fourier method is used to identify the unknown source term depending only on the spatial variable for a Riesz-Feller space-fractional diffusion equation.

The SV in the second term on the RHS of Eq. (32) can be replaced by its expression (4), leading to: (33) Obviously, this second term depends only on the field and the flow.

The third term in the right-hand side corresponds to the multiple-scattering P wave having an order higher than or equal to 2. This term depends only on k.

Most importantly, this term depends only on the signals that are available within the AEC application, i.e., the microphone signal, d(n), and the output of the adaptive filter, (widehat {y}(n)).

The nonresonant scattering term depends only on the total electron density within a material and is related to the overall elementary composition and the bulk density, whereas the resonant scattering term depends on E. Thus, the total amplitude deviates significantly from the atomic number Z by varying the energy around an elemental absorption edge.

Then, the rate of substitution between s and s' is: (13) where is the mutation term depending only on the two sequences s nuc and. is the energy difference between s aa and, and β ≥ 0 can be considered as the strength of the structure-sequence constraint enforced by the model.

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