It is important to note at the outset that in general, if F is a subgraph of E, then L K ( F ) need not correspond to a subalgebra of L K ( E ), because the (CK2) relation imposed at a vertex v in L K ( F ) need not be the same as the relation imposed at v in L K ( E ).
Then in a purely ring-theoretic context, the symbol ∑ e ∈ s - 1 ( v ) e e ∗, which would be the natural generalization of the (CK2) relation imposed at v, is not defined.
The expected middle-ground construction may be formalized: if X is any subset of the regular vertices Reg ( E ) of E, then the Cohn path K -algebra relative to X, denoted C K X ( E ), is the algebra C K ( E ), modulo the (CK2) relation imposed only at the vertices v ∈ X.
The novel portrayed the decline of an aristocratic family, taken aback by the transformations in power relations imposed by the newly unified state of Italy.
The local, national and international relations impose into these social systems different force fields determining the space of possibilities in which they evolve.
In most representations, the behavior of the crack and the fracture process zone is idealized within the geometric relations imposed by geometry and loading (Hillerborg et al. 1976; ACI 544.8R 2016).
This method is fit to the particular algebraic structure of the power flow problem resulting from the combination of a globally linear set of equations and nonlinear local relations imposed by power conversion devices, such as loads and generators.
Moreover, partition of passenger sources is found having marked impact in departure, while social relation structure imposes a great influence in arrival.
Russia recently introduced a law that bans "propaganda of nontraditional sexual relations" and imposes fines on those holding gay pride rallies.
1960: US breaks off diplomatic relations and imposes trade embargo.
