Sentence examples for exclusive cycle from inspiring English sources

Neither Mob crime nor financial depredation occurs in a vacuum or, for that matter, in an exclusive cycle.

It shows that having a maximal exclusive cycle is not enough to guarantee the (right) amenability of path algebras (compare with Theorem 5.10).

A cycle c is called an exclusive cycle if it is disjoint with every other cycle; equivalently, no vertex v on c is the base of a different cycle other than the cyclic permutation of c based at v. The following lemma was shown in the row-finite case in [13, Lemma 7.3].

Moreover, by [5, Theorem 5 (1)], (L_{mathbb {K}}(E)) has polynomially bounded growth if and only if every cycle of E is an exclusive cycle, and in this case a precise formula for the Gelfand Kirillov dimension of (L_{mathbb {K}}(E)) is obtained ([5, Theorem 5 (2)]).

Note that the exclusive cycles are precisely those cycles c such that ([c]= { c }), and that (C/{sim } ) is a finite set if E has a finite number of vertices.

If (vin E^0) belongs to a non-exclusive cycle, then v is a properly infinite idempotent in (L_mathbb {K}(E)).

E is acyclic; (E^0) is infinite; (E^0 {{setminus }} H) contains at least one infinite emitter; E has an exclusive maximal cycle.

Finally, we assume (B3d) holds but both (B3b) and (B3c) fail, i.e., (E^0) is finite, (E^0{setminus }H) consists of regular vertices, and there is an exclusive maximal cycle, which we denote by c.

The condition (A3) (L_mathbb {K}(E)) is properly algebraically amenable   holds if and only if one or more of the following conditions hold: (B3a) E is acyclic;   (B3b) (E^0) is infinite;   (B3c) (E^0 {{setminus }} H) contains at least one infinite emitter;   (B3d) E has an exclusive maximal cycle.  .

Let E be the following graph: Open image in new window Here we also have that the path algebra (mathcal A : = mathbb {K}E) is left properly algebraically amenable but not right algebraically amenable, despite the existence of an exclusive maximal cycle.

To determine whether there is a difference in pregnancy outcomes between women undergoing a shared versus exclusive donor oocyte cycle.