Sentence examples for sum of the representations from inspiring English sources
Huemer and Landerer identify the inhibition sum correctly, but then say that \(\sigma\) is "[the inhibition sum's] already sunken part", whereas as we saw above, Herbart says \(\sigma\) is the sum of the representations' already dimmed portions (Huemer and Landerer 2010: 76).
Further this chapter defines what an embedded system's architecture is in terms of the sum of the various representations of a system.
end{aligned}The adjoint representation of (mathfrak {g}) on (mathfrak {q}(W)) restricts to the Lie algebra representation of (mathfrak {g}_0 = mathfrak {o}(W_1) oplus mathfrak {sp}(W_0)) on (W = W_1oplus whichwhish is just the direct sum of the fundamental representations of (mathfrak {o}(W_1)) and (mathfrak {sp}(W_0)).
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.
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.
If the defining representation of G is the direct sum of finite dimensional representations with determinant one the fixed point subalgebra OG of O∞ is a simple C∗-algebra.
In a second stage the controller's gains are adjusted through a sum of squares representation of the LF.
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 )}.
Since vertex corresponds to the AND gate we can write B i in the form This is a so-called sum-of-product representation of B i.
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.
We also show that a semialgebraic set solves the truncated moment problem in terms of natural "degree-bounded" positivity conditions if and only if each polynomial strictly positive on that set admits a degree-bounded weighted sum-of-squares representation.
