When you look down on the slums from above, as you do from the elevated highways — the elite corridors that ferry the middle classes commuting between the city center and the suburbs — the alleys and blocks look just the same as the ancient clusters of housing that existed in Cairo before the Khedive's grand plan.
Meanwhile, the service class commutes in from the surrounding periphery to tidy up and run restaurants, while high housing costs and an overall lack of opportunities for other kinds of workers drive away much of the middle class, particularly families.
But adults, who need education almost as badly as the kids do, can't always spend the whole day in class or commute to night classes.
As an application, necessary and sufficient conditions for the existence of selfadjoint and normal extensions for some classes of commuting tuples of unbounded linear operators are obtained.
After setting up the necessary general background, we start with two classes of commuting squares and compute the principal graphs of the resulting subfactors, one of them being related to the group dual of a suitable (closed) subgroup ofU N), and the other to the Cayley graph of a (non-closed) group, modulo scalars, generated byNelements ofU N).
A student would have to put in all the hours of classes, studying, commuting; find child care; commit personal and family money, Pell grants, GI bill; and take out the high-interest private loans often needed to attend expensive schools.
But working-class Brazilians commuting from far-flung, lower-income areas to work in Barra say the Olympics brought them few tangible benefits.
Let H0 (respectively H∞) denote the class of commuting pairs of subnormal operators on Hilbert space (respectively subnormal pairs), and for an integer k⩾1 let Hk denote the class of k-hyponormal pairs in H0.
We study LPCS within the class of commuting 2-variable weighted shifts T≡(T1,T2) with subnormal components T1 and T2, acting on the Hilbert space ℓ2(Z2+) with canonical orthonormal basis {e k1,k2)}k1,k2⩾0.
Let G be a finite group and denote by CG the commuting square associated to G. The defect of the group G, given by the formula orderd(G)="∑g∈G|G|(g), was introduced in [9] as an upper bound for the number of linearly independent directions in which CG can be continuously deformed in the class of commuting squares.
