Sentence examples for harmonic case from inspiring English sources

With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for general anisotropic media, we investigate the accuracy aspects of local ABCs designed for the scalar anisotropic wave equation in the frequency domain (time harmonic case).

Finally the effectiveness of the solution and the adequacy of the expressions derived from the harmonic case are proven under railway traffic excitation taking into account the three-dimensional deformation of the deck.

In the harmonic case, Armitage [6] showed that universal harmonic functions can also have slow growth.

This is certainly the case for polynomial growth since polynomial growth (either in the entire or in the harmonic case) implies that the function is a polynomial and, obviously, the translation of a polynomial is another polynomial of the same degree.

While (0leeta_{{ mathrm{B}} }[{V}]le1), the upper bound being reached if and only if the external potential (hat{V}(hat{x})) gives rise to a GS orthogonal to that of the corresponding harmonic case, (eta_{mathrm{NG}}) is unbound from above, which complicates the quantitative comparison between the two figures of merit.

We remark that the classes (mathcal{H}^{0}(A,B)) and (mathcal {G}^{0}(A,B)) for the analytic case, i.e. (gequiv0), were introduced by Janowski [9] and the classes (mathcal{S}_{mathcal{H}}^{ast} alpha)=mathcal {H}^{0}(2andha-1,1)) and (mathcal{S}_{mathcal{H}}^{c} alpha)=mathcal {H}^{1}(2alpha-1,1)) for the harmonic case were investigated by Jahangiri [10, 11] and Silverman [12].

With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for heterogeneous anisotropic elastic media, we investigate the accuracy aspects of local ABCs designed for tilted elliptic anisotropy in the frequency domain (time-harmonic case).

The general methodology is presented for both the time-harmonic case (Helmholtz equation) and the time-dependent case (the wave equation) and is demonstrated numerically in the former case.

For the external, harmonic forcing case an interesting resonance condition will be derived.

In this paper, the new concept of nonlinear output frequency response functions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the generalized frequency response functions (GFRFs).

Two critical driving frequencies associated with each mn are then obtained for a stationary harmonic load case, where m is the axial half-wave number and n is the circumferential wavenumber.