A visualization of the integrands of the Ffowcs Williams and Hawkings integral shows that sound sources are located on both sides of the lip of the inlet, at the position of impact of the vortices, and along the vortex wakes.
The far-field spectra obtained from the source models for two different flow conditions are in good agreement with the spectra obtained with a Ffowcs Williams-Hawkings integral, showing the accuracy of the source model from the observer's standpoint.
The continuity of the integral shows that there exists (eta > 0) such that, for all measurable set (B subset[0, tau]) with (lambda(B) < eta), we have int_{B} h(theta) gbigl( mathbb{E} bigl(bigl|Vbigl(f(theta) bigr) - G_{l}bigl(f(theta bigr bigr|^{2}bigr bigr),dtheta< frac {epsilon}{kappa}.
Similarly, ({Gamma _{2}^{q}}(psi,m,t)) and (Gamma _{3}^{q,q'}(psi,m,t)) are, respectively, the primitives of integrals shown in the third and fourth terms of Eq. (13).
Bottom: mean size of calcium events ('ΔF/F-integral') shown for each dendrite (black dots).
In addition, the analysis on validity of J-integral showed that KIe converted from JIC was able to evaluate the fracture toughness of ultra-high strength steel.
This was confirmed by comparison of the relative intensities from metabolite integrals, showing a significant increase in lactate levels in response to treatment in non-survivors (p = 0.004) but not in survivors (Table 3).
For L∞-functions on a (closed) compact Riemannian manifold, the noncommutative residue and the Dixmier trace formulation of the noncommutative integral are shown to equate to a multiple of the Lebesgue integral.
By letting (Delta _{1}=left (frac {1+K}{bar gamma _{x}}right)) and (Delta _{2}=left (frac {1+K}{bar gamma _{y}}right)), and after some algebraic manipulations, this integral is shown in (68).
The barometric variations observed at SN-3 and STG200 with respect to a time integral are shown with a red and a green line, respectively, in the lower portion of Fig. 5.
