1) the close-loop transfer function is(s+4)/(s^2+s+3)and the characteristic equation is s^2+s+3=0.the real part of the roots of the equation is negtive,so the system is stable.2)……3)……closed-loop transfer functions+4/s(square)+s+3characteristic equationD（s）=s(square)+s+3by Routh Stability Criterionthe ...
polynomial of G (s), then the pole of the transfer function G (s) is defined as the root of the characteristic equation D (s) =0, and the zero point of the transfer function G (s) is defined as the root of the equation M (s) =0. The values of poles (zeros) can be ...
The characteristic equation of radiative transfer theory. In: Kokhanovsky A.A., editor. Light Scattering Reviews, 4, 47-429, Chichester, UK; Springer-Praxis Publishing.Rogovtsov, N.N. and Borovik, F.N., The Characteristic Equation of Radiative Transfer Theory, in Light Scattering Reviews, Ko...
Equation [6.13] can also be examined by looking for the poles of the transfer function. If, at the denominator, there is a positive real root, then the system oscillates. This is indeed the case in equation [6.14], and the root can be positioned on the axis of positive real numbers. ...
1. Here, x(t) is the external force, as the summation of wave and wind loads, and y(t) is the ship response function as the output that is transferred to the Laplacian domain, and H(s) denotes the Laplacian of the TF. As such, the mass-spring-damper state equation can be ...
This then leads to non-positive values of a phase–space quasi-probability distribution such as the Glauber–Sudarshan P(α)-function47. where χ(ξ) is the characteristic function of the bosonic quantum state. However, highly singular behaviour of P(α) can make its characterization challenging...
and the fluid mass function c ( x ) as: $$ \begin{array}{l} \pi_{i}(x) ={\lim}_{t \rightarrow \infty}{\lim}_{\delta \rightarrow 0} \frac{\pr\left\{ n(t) = j, x \leq x(t) <x+\delta \right\}}{\delta}, \\ c_{i}(x) ={\lim}_{t \rightarrow \infty} \...
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The dimensionless inclination parameter Y* (Eq. 2), calculated as a function of the Eötvös number Eo (Eq. 3), the thermodynamic vapor quality x, the liquid and the vapor densities ρL and ρG, allows to predict a gravity dependent region during condensation:...
In contrast to the Butterworth filter, the magnitude function of a type 1 Chebyshev filter has ripple in the passband and is monotone decreasing in the stopband (a type 2 Chebyshev filter has the opposite characteristic). By allowing ripple in the passband or stopband, we are able to ...