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The ergodic capacity of the ZF beamformer and the basic IEEE802.11s access scheme is derived to analytically measure the gain of employing beamforming techniques in IEEE802.11s networks.
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Tuning rules were analytically derived to cope with both set-point tracking and disturbance rejection problems.
The effects of such errors induced by faults are analytically derived to verify the probability of intrinsic masking in the final neural outputs.
An effective relationship was analytically derived to determine the mechanical skin, the geometrical skin and the bi-phase skin in the case of injection tests.
The workspace of the mechanism is analyzed in detail and its boundary is analytically derived to provide a closed-form solution for the reachable workspace.
Combining this conclusion with the overlapping effect of multiple engaged cutting edges, optimal helix angle corresponding to the minimum of peak cutting forces is analytically derived to be the function of axial depth of cut, number of flutes and cutter diameter.
A matrix transformation is analytically derived to induce the desired structure on H, while avoiding computationally complex operations such as pseudo-inversion.
Maximum likelihood function (MLF) is formulated and the mathematical relationships of gradient and Hessian matrix are analytically derived to carry out the estimation process.
It can also be analytically derived to compute the MFI and NV of large cell populations at steady state.
However, unlike other iterative methods, it is semi-analytical in the sense that flight time functions are derived analytically to second order vs. first order finite differences.
An approximation of the proposed model allows to derive delays analytically, and can be used to schedule control parameters.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com