The proposed susceptibility mapping method utilized two complementary equations: (1) the Fourier relationship of phase and magnetic susceptibility; and (2) the first-order partial derivative of the first equation in the spatial frequency domain.
The proposed estimation structure is based on process model, complementary equations, and the combination of classic estimators in order to obtain the N f based on the information of other directly mesaured variables.
If we adopt traditional methods to build the force and moment equilibrium equations of all movable bodies and complementary equations, the rank of the coefficient matrix of those equations will be very large.
In view that the constraint forces and moments are in direct proportion to the stiffness of the corresponding limbs, the complementary equations can be given as left{ begin{aligned} f_{p,gamma + 1} = eta_{gamma } f_{p,gamma } left( {gamma = 1,2, cdots,p - 1} right), hfill f_{q,lambda + 1} = eta_{lambda } f_{q,lambda } left( {lambda = 1,2, cdots,q - 1} right), hfill end{aligned} right.
A complementary differential equation is then employed to compute the inverse which can be used to compensate for hysteresis and nonlinear dynamics in control design.
The complementary mild-slope equation (CMSE) is a depth-integrated equation, which models refraction and diffraction of linear time-harmonic water waves.
The complementary solution of Equation (35) is obtained in terms of confluent hypergeometric function in the following form: θ c = C 0 ξ α M [ α − 4, α + 1, − ξ 1 + 4 3 K ], (37).
It was based on the assumption that P aw and P mus were complementary according to the equation of motion and therefore that the ventilator accurately delivered PAV.
Equation (12), complementary to Eq. (2), ensures that a portion of the part demand can be produced at the given period if its operations are assigned in the constraint given in Eq. (2).
We observe that differential equations in complementary Lidstone problems as well as derivatives in boundary conditions are odd orders, in contrast to the Lidstone problem (1.6).
