3.1 Intensity binary coding of monogenic local imaginary part
[[epsilon].sub.i] is the imaginary part
and provides a measure of the dissipative rate of the wave in the medium.
Appell's O-functions are defined as follows; Let r [greater than or equal to] 1 and let [omega] = ([[omega].sub.1], ..., [[omega].sub.r]) be a r-tuple consisting of complex numbers with positive imaginary part
. We put
The second part illustrates the results received in simulation by using a set-point first-order filter for different values of its time constant, and in the third section, there is a confirmation of the boundary condition for the selection of the imaginary part
of the desired poles has been presented by using a simulation.
At resonance frequency, the real part of [Z.sub.i] will match closely with the free space impedance and the imaginary part
will tend to infinity.
In Sections 2.1 and 2.2 we study the real and imaginary part
of the potential in the isotropic medium and effective fugacity quasi-particle model (EQPM) in Section 2.3.
The impedance magnitude, phase angle, real part, and imaginary part
varied markedly with the alteration of the ripening state.
Here, we chose to compare the properties of the studied composites by looking at the imaginary part
of the permittivity, shown in a wide range of frequency and temperature in Figure 4.
The strategy to get a good silencer design is to create a system where the imaginary part
is small or close to zero.
In the phenomenological spin-glass model prescribing a wide distribution of relaxation times, it has been reported that the imaginary part
of the AC susceptibility is related to the density of relaxation times [6-8].
The onsets in the imaginary parts
reflect the similar bandgaps already seen in the electronic band structures, and the heights and widths of the different peaks reflect the similarity in regions of nearly parallel bands in the band structures where large transition matrix elements give rise to stronger features in the imaginary part
of the dielectric functions.