If we define a scalar
field [sigma] in the form of [phi] = [[sigma].sup.2][xi], where [xi] = 1/4, by rewriting (6), the effective action is obtained as follows:
At this point, it should be mentioned that there is an important difference--first noted in --with respect to the previously studied scalar
field case, which we will now address.
In this study, the size of the vector IMs is limited to two parameters containing all possible dual combinations of the adopted scalar
are bounded scalar
type spectral operators on X defined in the same manner as for a normal operator (see, e.g., [9, 10]).
In the beginning of this section, we present the theoretical results for two variants of the scalar
companding system based on G.711, non-adaptive and adaptive, described in Section II, which are used as baselines.
dissipation rate can be interpreted as the inverse of a characteristic diffusion time.
[??] is a source term for passive scalar
is the dyadic Green function and [mathematical expression not reproducible] is the scalar
We showed that, through observation of the diminished scalar
signal, estimation of the scalar
position and scalar
translocation is possible.
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In section V, we briefly review the results for the scalar
and the vector field separately and then, in section VI, we consider the coupled scalar-vector system.
The aim of the work is determination of the connection between the IP and integral powers and obtaining the complex form of the scalar
and vectorial IP for nonsinusoidal modes classification in the 3-phase 4-wire electric power supply circuit in the terms of the spectral approach.