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The acceleration command input is mathematically derived.
The proposed DP-based scheme is mathematically derived thus guaranteeing performance.
The model is mathematically derived based on the mechanism of single cutter rock interaction, and calibrated utilizing sets of full scale laboratory data.
The working mechanism of this new damper is first elaborated, and then its dynamic model is mathematically derived based on the first-principle analysis of hydraulic and electric components.
Furthermore, the translating strategy based on the performance measure approach is proposed to shift and update the constraints, and the expression of the translating distance is mathematically derived to accelerate the design procedure.
The controller is mathematically derived and shown to provide asymptotic stability of knee joint angle tracking by electrical stimulation of knee extensor muscle group only, or by electrical stimulation of knee extensor and flexor muscle groups.
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In addition, the equation for the phase velocity was mathematically derived on the complex plane, too, and graphically illustrated.
The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver.
The preconditioned compatibility equations and the corresponding characteristic variables (or the Riemann invariants) based on the characteristic forms of preconditioned Euler equations are mathematically derived for three preconditioners proposed by Eriksson, Choi and Merkle, and Turkel.
General expressions are mathematically derived for the maximum differences between graphical indices and sound insulation in two cases: a maximum allowable sum rule for unfavourable deviations, and a combination for restriction of the maximum single deviation.
The lower bound on outage probability of the inter-relay communication-based protocol was mathematically derived and validated by simulations[7].
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