This is achieved by making suitable design choices of the various parameters in the Gaussian Sum representation.
We propose a new power index based on the minimum sum representation (MSR) of a weighted voting game.
As opposed to that, in the presence even of a small delay, the spectrum is infinite and a finite sum representation is not possible.
Assuming that and take integer values, we are able to replace the lower incomplete gamma function, appearing in (12), with its finite sum representation [10, equation (8.352.1)].
Therefore, two different sum rate representations, a lower bound and a first order approximation, are used to estimate and compare the sum rates.
Therefore, a sum rate representation that can be used to estimate the ergodic sum rates in all parameter ranges is needed.
As an application of this result to the reductive groups viewed as symmetric spaces, we are able to realize any Harish-Chandra module as a subquotient of a direct sum of induced representations from parabolic subgroups, the inducing representations being trivial on the unipotent radical.
We introduce a filtration of a (g,K -module of some space of functions on a reductive symmetric space g,K -modulempute the assofiated grading asomedirect spacef induced representatiofs.
Now, since we work over ({mathbb {C}}), the vector space V splits uniquely, up to permutation of the summands, as a direct sum of irreducible representations begin{aligned} V_m = bigoplus _{rho in Irr (G)} W_{rho }^{n(rho )}.
Suppose that a group Γ acts on a vector space V with an irreducible subspace W. Then an isotypic component of that action is the sum of all representations of Γ in V that are isomorphic to W. The theory of equivariant Hopf bifurcations states that such bifurcations occur generically with a center subspace in one of the isotypic components of the symmetry group acting on phase space.
