(49) and (54) are the starting equations for analyzing the dynamics and statics of the piezoelectric laminated membrane mirror.
The optimal online policy ((phi ^{ast }_{n})_{n=1,2,dots,N}) consists of maximizers of the right hand sides of Equations 23 and 24 and can be found with backward induction, starting from Equation 23 and going backwards using Equation 24.
For example, let's say that our starting cubic equation is 3x3 + -2x2 + 14x = 0. Factoring a single x out of this equation, we get x(3x2 + -2x + 14) = 0. Use the quadratic formula to solve the portion in parentheses.
The search for Lyapunov-type inequalities in which the starting differential equation is constructed via fractional differential operators has begun very recently.
The proposition can be proven using Lemma 1 starting from Equation 27 given by the following: η 2 = χ + η 1 e χ (31).
Starting from equation (8), if we assume that the concentration of the signal sx t) is constant or time-invariant (for example, being at saturation), then we can assume F1 t) is also a constant value, F1.
In particular, starting with Equation (1), we need to show how the computation of each sum is done when the state space is in a factored form.
