Sentence examples for irreducible group from inspiring English sources

In other words, this is supposed to show that there is no need to think in terms of irreducible group level interactors.

Taken together, these data indicate that each cell type defined by our criteria likely represents an irreducible group of equivalent cells, and that the split-GAL4 screen and PA-GFP tracing identified perhaps all of the neurons in the MB lobes.

Whereas there are many subdirectly irreducible groups, the only subdirectly irreducible Boolean algebra is the initial or two-element one, while the subdirectly irreducible rings satisfying xn = x for some n > 1 are exactly the finite fields.

By twisting, it is enough to show that for an irreducible loop reductive group H the canonical map H t o r a l 1 ( R n, H ) → H 1 ( F n, H ) has trivial kernel.

So taking into consideration Theorem 11.1 (applied to the irreducible loop reductive group scheme D L and chasing the above diagram we see that L ( R n ) / f R n ( ( D L ) ( R n ) × C ( R n ) ) ⟶ ∼ L ( F n ) / f F n ( ( D L ) ( F n ) × C ( F n ) ).

The resulting modes at the BZ centre were classified according to the irreducible species of point group D 2 h ; this was done using standard group theory techniques with the help of the program SAM (Kroumova et al., 2003 ▸), available at the Bilbao crystallographic server (Aroyo et al., 2006 ▸).

For manifolds of odd dimension, we study the asymptotic behavior of the analytic torsion with respect to certain sequences of representations obtained by restriction of irreducible representations of the group of isometries of the hyperbolic space to the fundamental group.

The resulting modes at the BZ centre were classified according to the irreducible species of point group C 2 h ; this was done using standard group-theory techniques with the help of the program SAM (Kroumova et al., 2003 ▶), available at the Bilbao Crystallographic server (Aroyo et al., 2006 ▶).

It has been proved by K. C. Hannabuss and by Roger Howe that if G is locally compact and nilpotent and σ is a type I multiplier on G, then (G, σ) is a monomial group: every irreducible σ-representation of G is induced by a one-dimensional σ-representation of a closed subgroup.

This type of singularity is actually due to the divergencelessness condition needed to associate this field with a specific unitary irreducible representation of dS group.

The transformation properties of the various irreducible representations of point group D 3h can be found in the character table available in the literature [23].