Sentence examples for a unitary group from inspiring English sources

By studying the dissipation towards high modes of a unitary group valued SDE it is proved that the loop group does not have any infinitesimally invariant measure.

From now on, we assume that X has a unit e and a unitary group U X X ) : = { u ∈ X : u ∗ u = u u ∗ = e }.

10), (e^{-itA}) with A given by (8.7) is a unitary group which leaves ({mathcal {D}}= C_0^infty ({mathbb {R}}^nu )oplus C_0^infty ({mathbb {R}}^nu )) invariant and with ({mathcal {D}}subset D^infty (A)).

On (L^2({mathbb {R}}^nu,d^nu x)), let (U theta ),thetaa in {mathbb {R}}) be the set of real scalings: begin{aligned} (U theta )f)(varvec{r}) = e^{nu theta /2}f(e^theta varvec{r}) end{aligned} (4.7 which defines a unitary group.

We analysed these single mothers as a unitary group, irrespective of pregnancies following consensual sex or rape.

We analysed these men's perspectives as a unitary group, however it would be valuable to study variations between different groups of men based on socio-economic background, age and marital status, in future research, as this would provide a more nuanced and differentiated picture.

For any such counterexample A, the unitary group U A) acts transitively on the pure states, which are the extreme points of the state space S(A).

Furthermore, when these excluded participants were included in analyses as a third unitary group or as two separate groups, their average scores consistently sat between the High-Mechanistic and Low-Mechanistic groups' scores for all outcome measures (except for the number of wheels included in memory drawings, which was not significantly different from either group).

Let Q be a symmetric operator and Ux a one parameter unitary group in a Hilbert space such that Ux dom Q ⊂ dom Q and UxQUx∗ ϑ = Qϑ + xϑ for ϑ ϵ dom Q.

We consider a Hamiltonian systems which is invariant under a one-parameter unitary group and give a criterion for the stability and instability of bound states for the degenerate case.

This entails the existence of a selfadjoint extension of Q to a larger space satisfying the analogus commutation relation with a suitable extended unitary group.