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A) First order contiguity.
For this purpose, a second order model has been identified by adopting the sensitivity theory involving the Lyapunov function giving rise to stable solutions in the on-line environment, renewing model parameters at every changes occurring on the physical system.
For this purpose, a second-order perturbation method is extended and employed in the current study.
For this purpose, a fourth-order finite-difference numerical method is employed to calculate the diffusion-broadened transfer function of two widely used DMA units: the "long" DMA (TSI Model 3081) and the "nano -DMA (TSI Model 3085).
For introductory purpose, a first-order Sugeno-type FIS (see [19]) in Figure 2 and equivalent ANFIS architecture in Figure 3 has been shown next.
For this purpose we use a first-order Markov model with annual transitions between states.
A first order optimization method is adopted for that purpose while the gradients required are efficiently derived analytically.
Additionally, a first order sliding mode controller (SMC) is designed for the purpose of comparative analysis.
For this purpose, the full, time dependent equations of viscous flow, diffusion and chemical reaction for a first order, isothermal reaction in a porous catalyst are solved numerically.
Subsequently, the signal was filtered using a third order two-pass elliptic low-pass filter at 500 Hz for the purpose of down-sampling at 1 kHz.
For this purpose, Sanders first order shear deformation shell theory is combined with nonlocal elasticity and equations of motion are found.
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