In the sequel, here, we aim at presenting a general explicit formula for the determinants of the Laplacians on S k ( k = 2 n + 1 ; n ∈ N ) by mainly using a summation formula of the series involving zeta function.
In the deterministic analysis, the effect of mutual impedance by water loading on the velocity of the plate is illustrated analytically by using a modal summation method.
The average radiation efficiency of point-excited rectangular plates, including those with a very large aspect ratio ('strips'), is investigated by using a modal summation method based on the farfield sound intensity.
Using a summation by parts argument as done in [26, Theorem 71, p. 128], Theorem 5.1 (used with (S) in place of (kappa )) leads immediately to the following corollary.
The total amount of lipids in each plasma sample was obtained by using an established summation formula based on serum cholesterol and serum triglyceride concentrations [ 37].
Synthetic seismograms (P-SV and SH waves) have been calculated along six profiles in Santiago de Cuba basin, with a cutoff frequency of 5 Hz, by using a hybrid approach (modal summation for a regional 1D structure plus finite differences for a local 2D structure embedded in the first).
Therefore, the mechanism achieving differential privacy must include a way to protect the summation operation by using a secure aggregation scheme, e.g., as described in section Multi-resolution secure aggregation.
After Shirley background subtraction, the deconvolution of the XPS curves was conducted by using a fitting procedure based on the summation of Gaussian functions.
The linear systems are solved iteratively and accelerated by using a newly developed kernel-independent wideband fast directional algorithm (FDA) for fast summation of oscillatory kernels.
Each (homogeneous) sub domain is discretized using narrow-diagonal summation by parts operators and, then, patched to its neighbors by using a penalty method, leading to fully explicit time integration.
